--- _id: '2812' abstract: - lang: eng text: 'We consider the problem of deciding whether the persistent homology group of a simplicial pair (K, L) can be realized as the homology H* (X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in ℝ3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard.' acknowledgement: Some of the authors were partially supported by the GIGA ANR grant (contract ANR-09-BLAN-0331-01) and the European project CG-Learning (contract 255827). author: - first_name: Dominique full_name: Attali, Dominique last_name: Attali - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Olivier full_name: Devillers, Olivier last_name: Devillers - first_name: Marc full_name: Glisse, Marc last_name: Glisse - first_name: André full_name: Lieutier, André last_name: Lieutier citation: ama: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. In: Proceedings of the 29th Annual Symposium on Computational Geometry. ACM; 2013:117-125. doi:10.1145/2462356.2462373' apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2013). Homological reconstruction and simplification in R3. In Proceedings of the 29th annual symposium on Computational Geometry (pp. 117–125). Rio de Janeiro, Brazil: ACM. https://doi.org/10.1145/2462356.2462373' chicago: Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” In Proceedings of the 29th Annual Symposium on Computational Geometry, 117–25. ACM, 2013. https://doi.org/10.1145/2462356.2462373. ieee: D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” in Proceedings of the 29th annual symposium on Computational Geometry, Rio de Janeiro, Brazil, 2013, pp. 117–125. ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2013. Homological reconstruction and simplification in R3. Proceedings of the 29th annual symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 117–125.' mla: Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” Proceedings of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–25, doi:10.1145/2462356.2462373. short: D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, in:, Proceedings of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–125. conference: end_date: 2013-06-20 location: Rio de Janeiro, Brazil name: 'SoCG: Symposium on Computational Geometry' start_date: 2013-06-17 date_created: 2018-12-11T11:59:44Z date_published: 2013-06-01T00:00:00Z date_updated: 2023-02-23T10:15:15Z day: '01' department: - _id: HeEd doi: 10.1145/2462356.2462373 language: - iso: eng main_file_link: - open_access: '1' url: http://hal.archives-ouvertes.fr/hal-00833791/ month: '06' oa: 1 oa_version: Submitted Version page: 117 - 125 publication: Proceedings of the 29th annual symposium on Computational Geometry publication_status: published publisher: ACM publist_id: '4072' quality_controlled: '1' related_material: record: - id: '1805' relation: later_version status: public scopus_import: 1 status: public title: Homological reconstruction and simplification in R3 type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2013' ... --- _id: '2822' abstract: - lang: eng text: Identification of genes that control root system architecture in crop plants requires innovations that enable high-throughput and accurate measurements of root system architecture through time. We demonstrate the ability of a semiautomated 3D in vivo imaging and digital phenotyping pipeline to interrogate the quantitative genetic basis of root system growth in a rice biparental mapping population, Bala x Azucena. We phenotyped >1,400 3D root models and >57,000 2D images for a suite of 25 traits that quantified the distribution, shape, extent of exploration, and the intrinsic size of root networks at days 12, 14, and 16 of growth in a gellan gum medium. From these data we identified 89 quantitative trait loci, some of which correspond to those found previously in soil-grown plants, and provide evidence for genetic tradeoffs in root growth allocations, such as between the extent and thoroughness of exploration. We also developed a multivariate method for generating and mapping central root architecture phenotypes and used it to identify five major quantitative trait loci (r2 = 24-37%), two of which were not identified by our univariate analysis. Our imaging and analytical platform provides a means to identify genes with high potential for improving root traits and agronomic qualities of crops. author: - first_name: Christopher full_name: Topp, Christopher last_name: Topp - first_name: Anjali full_name: Iyer Pascuzzi, Anjali last_name: Iyer Pascuzzi - first_name: Jill full_name: Anderson, Jill last_name: Anderson - first_name: Cheng full_name: Lee, Cheng last_name: Lee - first_name: Paul full_name: Zurek, Paul last_name: Zurek - first_name: Olga full_name: Symonova, Olga id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87 last_name: Symonova - first_name: Ying full_name: Zheng, Ying last_name: Zheng - first_name: Alexander full_name: Bucksch, Alexander last_name: Bucksch - first_name: Yuriy full_name: Mileyko, Yuriy last_name: Mileyko - first_name: Taras full_name: Galkovskyi, Taras last_name: Galkovskyi - first_name: Brad full_name: Moore, Brad last_name: Moore - first_name: John full_name: Harer, John last_name: Harer - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Thomas full_name: Mitchell Olds, Thomas last_name: Mitchell Olds - first_name: Joshua full_name: Weitz, Joshua last_name: Weitz - first_name: Philip full_name: Benfey, Philip last_name: Benfey citation: ama: Topp C, Iyer Pascuzzi A, Anderson J, et al. 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. 2013;110(18):E1695-E1704. doi:10.1073/pnas.1304354110 apa: Topp, C., Iyer Pascuzzi, A., Anderson, J., Lee, C., Zurek, P., Symonova, O., … Benfey, P. (2013). 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1304354110 chicago: Topp, Christopher, Anjali Iyer Pascuzzi, Jill Anderson, Cheng Lee, Paul Zurek, Olga Symonova, Ying Zheng, et al. “3D Phenotyping and Quantitative Trait Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1304354110. ieee: C. Topp et al., “3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture,” PNAS, vol. 110, no. 18. National Academy of Sciences, pp. E1695–E1704, 2013. ista: Topp C, Iyer Pascuzzi A, Anderson J, Lee C, Zurek P, Symonova O, Zheng Y, Bucksch A, Mileyko Y, Galkovskyi T, Moore B, Harer J, Edelsbrunner H, Mitchell Olds T, Weitz J, Benfey P. 2013. 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. 110(18), E1695–E1704. mla: Topp, Christopher, et al. “3D Phenotyping and Quantitative Trait Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS, vol. 110, no. 18, National Academy of Sciences, 2013, pp. E1695–704, doi:10.1073/pnas.1304354110. short: C. Topp, A. Iyer Pascuzzi, J. Anderson, C. Lee, P. Zurek, O. Symonova, Y. Zheng, A. Bucksch, Y. Mileyko, T. Galkovskyi, B. Moore, J. Harer, H. Edelsbrunner, T. Mitchell Olds, J. Weitz, P. Benfey, PNAS 110 (2013) E1695–E1704. date_created: 2018-12-11T11:59:47Z date_published: 2013-04-30T00:00:00Z date_updated: 2021-01-12T06:59:58Z day: '30' department: - _id: MaJö - _id: HeEd doi: 10.1073/pnas.1304354110 external_id: pmid: - '25673779' intvolume: ' 110' issue: '18' language: - iso: eng main_file_link: - open_access: '1' url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4378147/ month: '04' oa: 1 oa_version: Submitted Version page: E1695 - E1704 pmid: 1 publication: PNAS publication_status: published publisher: National Academy of Sciences publist_id: '3979' quality_controlled: '1' scopus_import: 1 status: public title: 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 110 year: '2013' ... --- _id: '2843' abstract: - lang: eng text: 'Mathematical objects can be measured unambiguously, but not so objects from our physical world. Even the total length of tubelike shapes has its difficulties. We introduce a combination of geometric, probabilistic, and topological methods to design a stable length estimate for tube-like shapes; that is: one that is insensitive to small shape changes.' alternative_title: - LNCS author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: 'Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. In: 17th IAPR International Conference on Discrete Geometry for Computer Imagery. Vol 7749. Springer; 2013:XV-XIX. doi:10.1007/978-3-642-37067-0' apa: 'Edelsbrunner, H., & Pausinger, F. (2013). Stable length estimates of tube-like shapes. In 17th IAPR International Conference on Discrete Geometry for Computer Imagery (Vol. 7749, pp. XV–XIX). Seville, Spain: Springer. https://doi.org/10.1007/978-3-642-37067-0' chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” In 17th IAPR International Conference on Discrete Geometry for Computer Imagery, 7749:XV–XIX. Springer, 2013. https://doi.org/10.1007/978-3-642-37067-0. ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” in 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Seville, Spain, 2013, vol. 7749, pp. XV–XIX. ista: 'Edelsbrunner H, Pausinger F. 2013. Stable length estimates of tube-like shapes. 17th IAPR International Conference on Discrete Geometry for Computer Imagery. DGCI: Discrete Geometry for Computer Imagery, LNCS, vol. 7749, XV–XIX.' mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” 17th IAPR International Conference on Discrete Geometry for Computer Imagery, vol. 7749, Springer, 2013, pp. XV–XIX, doi:10.1007/978-3-642-37067-0. short: H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX. conference: end_date: 2013-03-22 location: Seville, Spain name: 'DGCI: Discrete Geometry for Computer Imagery' start_date: 2013-03-20 date_created: 2018-12-11T11:59:53Z date_published: 2013-02-21T00:00:00Z date_updated: 2023-02-23T10:35:00Z day: '21' department: - _id: HeEd doi: 10.1007/978-3-642-37067-0 intvolume: ' 7749' language: - iso: eng month: '02' oa_version: None page: XV - XIX publication: 17th IAPR International Conference on Discrete Geometry for Computer Imagery publication_status: published publisher: Springer publist_id: '3952' quality_controlled: '1' related_material: record: - id: '2255' relation: later_version status: public scopus_import: 1 status: public title: Stable length estimates of tube-like shapes type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 7749 year: '2013' ... --- _id: '2859' abstract: - lang: eng text: Given a continuous function f:X-R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case X=R3 has ramifications in the fields of medical imaging and scientific visualization. author: - first_name: Paul full_name: Bendich, Paul id: 43F6EC54-F248-11E8-B48F-1D18A9856A87 last_name: Bendich - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Dmitriy full_name: Morozov, Dmitriy last_name: Morozov - first_name: Amit full_name: Patel, Amit id: 34A254A0-F248-11E8-B48F-1D18A9856A87 last_name: Patel citation: ama: Bendich P, Edelsbrunner H, Morozov D, Patel A. Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. 2013;15(1):51-72. doi:10.4310/HHA.2013.v15.n1.a3 apa: Bendich, P., Edelsbrunner, H., Morozov, D., & Patel, A. (2013). Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2013.v15.n1.a3 chicago: Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “Homology and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications. International Press, 2013. https://doi.org/10.4310/HHA.2013.v15.n1.a3. ieee: P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “Homology and robustness of level and interlevel sets,” Homology, Homotopy and Applications, vol. 15, no. 1. International Press, pp. 51–72, 2013. ista: Bendich P, Edelsbrunner H, Morozov D, Patel A. 2013. Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. 15(1), 51–72. mla: Bendich, Paul, et al. “Homology and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications, vol. 15, no. 1, International Press, 2013, pp. 51–72, doi:10.4310/HHA.2013.v15.n1.a3. short: P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, Homology, Homotopy and Applications 15 (2013) 51–72. date_created: 2018-12-11T11:59:58Z date_published: 2013-05-01T00:00:00Z date_updated: 2021-01-12T07:00:18Z day: '01' department: - _id: HeEd doi: 10.4310/HHA.2013.v15.n1.a3 external_id: arxiv: - '1102.3389' intvolume: ' 15' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1102.3389v1 month: '05' oa: 1 oa_version: Preprint page: 51 - 72 publication: Homology, Homotopy and Applications publication_status: published publisher: International Press publist_id: '3930' quality_controlled: '1' scopus_import: 1 status: public title: Homology and robustness of level and interlevel sets type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2013' ... --- _id: '2887' abstract: - lang: eng text: 'Root system growth and development is highly plastic and is influenced by the surrounding environment. Roots frequently grow in heterogeneous environments that include interactions from neighboring plants and physical impediments in the rhizosphere. To investigate how planting density and physical objects affect root system growth, we grew rice in a transparent gel system in close proximity with another plant or a physical object. Root systems were imaged and reconstructed in three dimensions. Root-root interaction strength was calculated using quantitative metrics that characterize the extent towhich the reconstructed root systems overlap each other. Surprisingly, we found the overlap of root systems of the same genotype was significantly higher than that of root systems of different genotypes. Root systems of the same genotype tended to grow toward each other but those of different genotypes appeared to avoid each other. Shoot separation experiments excluded the possibility of aerial interactions, suggesting root communication. Staggered plantings indicated that interactions likely occur at root tips in close proximity. Recognition of obstacles also occurred through root tips, but through physical contact in a size-dependent manner. These results indicate that root systems use two different forms of communication to recognize objects and alter root architecture: root-root recognition, possibly mediated through root exudates, and root-object recognition mediated by physical contact at the root tips. This finding suggests that root tips act as local sensors that integrate rhizosphere information into global root architectural changes.' article_processing_charge: No article_type: original author: - first_name: Suqin full_name: Fang, Suqin last_name: Fang - first_name: Randy full_name: Clark, Randy last_name: Clark - first_name: Ying full_name: Zheng, Ying last_name: Zheng - first_name: Anjali full_name: Iyer Pascuzzi, Anjali last_name: Iyer Pascuzzi - first_name: Joshua full_name: Weitz, Joshua last_name: Weitz - first_name: Leon full_name: Kochian, Leon last_name: Kochian - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Hong full_name: Liao, Hong last_name: Liao - first_name: Philip full_name: Benfey, Philip last_name: Benfey citation: ama: Fang S, Clark R, Zheng Y, et al. Genotypic recognition and spatial responses by rice roots. PNAS. 2013;110(7):2670-2675. doi:10.1073/pnas.1222821110 apa: Fang, S., Clark, R., Zheng, Y., Iyer Pascuzzi, A., Weitz, J., Kochian, L., … Benfey, P. (2013). Genotypic recognition and spatial responses by rice roots. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1222821110 chicago: Fang, Suqin, Randy Clark, Ying Zheng, Anjali Iyer Pascuzzi, Joshua Weitz, Leon Kochian, Herbert Edelsbrunner, Hong Liao, and Philip Benfey. “Genotypic Recognition and Spatial Responses by Rice Roots.” PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1222821110. ieee: S. Fang et al., “Genotypic recognition and spatial responses by rice roots,” PNAS, vol. 110, no. 7. National Academy of Sciences, pp. 2670–2675, 2013. ista: Fang S, Clark R, Zheng Y, Iyer Pascuzzi A, Weitz J, Kochian L, Edelsbrunner H, Liao H, Benfey P. 2013. Genotypic recognition and spatial responses by rice roots. PNAS. 110(7), 2670–2675. mla: Fang, Suqin, et al. “Genotypic Recognition and Spatial Responses by Rice Roots.” PNAS, vol. 110, no. 7, National Academy of Sciences, 2013, pp. 2670–75, doi:10.1073/pnas.1222821110. short: S. Fang, R. Clark, Y. Zheng, A. Iyer Pascuzzi, J. Weitz, L. Kochian, H. Edelsbrunner, H. Liao, P. Benfey, PNAS 110 (2013) 2670–2675. date_created: 2018-12-11T12:00:09Z date_published: 2013-02-12T00:00:00Z date_updated: 2021-01-12T07:00:29Z day: '12' department: - _id: HeEd doi: 10.1073/pnas.1222821110 external_id: pmid: - '23362379' intvolume: ' 110' issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574932/ month: '02' oa: 1 oa_version: Published Version page: 2670 - 2675 pmid: 1 publication: PNAS publication_status: published publisher: National Academy of Sciences publist_id: '3872' quality_controlled: '1' scopus_import: 1 status: public title: Genotypic recognition and spatial responses by rice roots type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 110 year: '2013' ... --- _id: '2901' abstract: - lang: eng text: ' We introduce the M-modes problem for graphical models: predicting the M label configurations of highest probability that are at the same time local maxima of the probability landscape. M-modes have multiple possible applications: because they are intrinsically diverse, they provide a principled alternative to non-maximum suppression techniques for structured prediction, they can act as codebook vectors for quantizing the configuration space, or they can form component centers for mixture model approximation. We present two algorithms for solving the M-modes problem. The first algorithm solves the problem in polynomial time when the underlying graphical model is a simple chain. The second algorithm solves the problem for junction chains. In synthetic and real dataset, we demonstrate how M-modes can improve the performance of prediction. We also use the generated modes as a tool to understand the topography of the probability distribution of configurations, for example with relation to the training set size and amount of noise in the data. ' alternative_title: - ' JMLR: W&CP' author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov - first_name: Zhu full_name: Yan, Zhu last_name: Yan - first_name: Dimitris full_name: Metaxas, Dimitris last_name: Metaxas - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: 'Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. Computing the M most probable modes of a graphical model. In: Vol 31. JMLR; 2013:161-169.' apa: 'Chen, C., Kolmogorov, V., Yan, Z., Metaxas, D., & Lampert, C. (2013). Computing the M most probable modes of a graphical model (Vol. 31, pp. 161–169). Presented at the AISTATS: Conference on Uncertainty in Artificial Intelligence, Scottsdale, AZ, United States: JMLR.' chicago: Chen, Chao, Vladimir Kolmogorov, Zhu Yan, Dimitris Metaxas, and Christoph Lampert. “Computing the M Most Probable Modes of a Graphical Model,” 31:161–69. JMLR, 2013. ieee: 'C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, and C. Lampert, “Computing the M most probable modes of a graphical model,” presented at the AISTATS: Conference on Uncertainty in Artificial Intelligence, Scottsdale, AZ, United States, 2013, vol. 31, pp. 161–169.' ista: 'Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. 2013. Computing the M most probable modes of a graphical model. AISTATS: Conference on Uncertainty in Artificial Intelligence, JMLR: W&CP, vol. 31, 161–169.' mla: Chen, Chao, et al. Computing the M Most Probable Modes of a Graphical Model. Vol. 31, JMLR, 2013, pp. 161–69. short: C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, C. Lampert, in:, JMLR, 2013, pp. 161–169. conference: end_date: 2013-05-01 location: Scottsdale, AZ, United States name: ' AISTATS: Conference on Uncertainty in Artificial Intelligence' start_date: 2013-04-29 date_created: 2018-12-11T12:00:14Z date_published: 2013-01-01T00:00:00Z date_updated: 2021-01-12T07:00:35Z day: '01' department: - _id: HeEd - _id: VlKo - _id: ChLa intvolume: ' 31' language: - iso: eng main_file_link: - open_access: '1' url: http://jmlr.org/proceedings/papers/v31/chen13a.html month: '01' oa: 1 oa_version: None page: 161 - 169 publication_status: published publisher: JMLR publist_id: '3846' quality_controlled: '1' scopus_import: 1 status: public title: Computing the M most probable modes of a graphical model type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 31 year: '2013' ... --- _id: '2906' abstract: - lang: eng text: "Motivated by an application in cell biology, we describe an extension of the kinetic data structures framework from Delaunay triangulations to fixed-radius alpha complexes. Our algorithm is implemented\r\nusing CGAL, following the exact geometric computation paradigm. We report on several\r\ntechniques to accelerate the computation that turn our implementation applicable to the underlying biological\r\nproblem." alternative_title: - ALENEX author: - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Kerber M, Edelsbrunner H. 3D kinetic alpha complexes and their implementation. In: 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments. Society of Industrial and Applied Mathematics; 2013:70-77. doi:10.1137/1.9781611972931.6' apa: 'Kerber, M., & Edelsbrunner, H. (2013). 3D kinetic alpha complexes and their implementation. In 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments (pp. 70–77). New Orleans, LA, United States: Society of Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611972931.6' chicago: Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes and Their Implementation.” In 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, 70–77. Society of Industrial and Applied Mathematics, 2013. https://doi.org/10.1137/1.9781611972931.6. ieee: M. Kerber and H. Edelsbrunner, “3D kinetic alpha complexes and their implementation,” in 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, New Orleans, LA, United States, 2013, pp. 70–77. ista: 'Kerber M, Edelsbrunner H. 2013. 3D kinetic alpha complexes and their implementation. 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments. ALENEX: Algorithm Engineering and Experiments, ALENEX, , 70–77.' mla: Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes and Their Implementation.” 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2013, pp. 70–77, doi:10.1137/1.9781611972931.6. short: M. Kerber, H. Edelsbrunner, in:, 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2013, pp. 70–77. conference: end_date: 2013-01-07 location: New Orleans, LA, United States name: 'ALENEX: Algorithm Engineering and Experiments' start_date: 2013-01-07 date_created: 2018-12-11T12:00:16Z date_published: 2013-01-01T00:00:00Z date_updated: 2021-01-12T07:00:36Z day: '01' ddc: - '500' department: - _id: HeEd doi: 10.1137/1.9781611972931.6 file: - access_level: open_access checksum: a15a3ba22df9445731507f3e06c9fcee content_type: application/pdf creator: system date_created: 2018-12-12T10:08:57Z date_updated: 2020-07-14T12:45:52Z file_id: '4720' file_name: IST-2016-547-v1+1_2013-P-08-MedusaII.pdf file_size: 403013 relation: main_file file_date_updated: 2020-07-14T12:45:52Z has_accepted_license: '1' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 70 - 77 publication: 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments publication_status: published publisher: Society of Industrial and Applied Mathematics publist_id: '3841' pubrep_id: '547' quality_controlled: '1' scopus_import: 1 status: public title: 3D kinetic alpha complexes and their implementation type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2013' ... --- _id: '2815' abstract: - lang: eng text: The fact that a sum of isotropic Gaussian kernels can have more modes than kernels is surprising. Extra (ghost) modes do not exist in ℝ1 and are generally not well studied in higher dimensions. We study a configuration of n+1 Gaussian kernels for which there are exactly n+2 modes. We show that all modes lie on a finite set of lines, which we call axes, and study the restriction of the Gaussian mixture to these axes in order to discover that there are an exponential number of critical points in this configuration. Although the existence of ghost modes remained unknown due to the difficulty of finding examples in ℝ2, we show that the resilience of ghost modes grows like the square root of the dimension. In addition, we exhibit finite configurations of isotropic Gaussian kernels with superlinearly many modes. acknowledgement: This research is partially supported by the National Science Foundation (NSF) under Grant DBI-0820624, by the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053. article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Brittany Terese full_name: Fasy, Brittany Terese id: F65D502E-E68D-11E9-9252-C644099818F6 last_name: Fasy - first_name: Günter full_name: Rote, Günter last_name: Rote citation: ama: 'Edelsbrunner H, Fasy BT, Rote G. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Discrete & Computational Geometry. 2013;49(4):797-822. doi:10.1007/s00454-013-9517-x' apa: 'Edelsbrunner, H., Fasy, B. T., & Rote, G. (2013). Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-013-9517-x' chicago: 'Edelsbrunner, Herbert, Brittany Terese Fasy, and Günter Rote. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” Discrete & Computational Geometry. Springer, 2013. https://doi.org/10.1007/s00454-013-9517-x.' ieee: 'H. Edelsbrunner, B. T. Fasy, and G. Rote, “Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions,” Discrete & Computational Geometry, vol. 49, no. 4. Springer, pp. 797–822, 2013.' ista: 'Edelsbrunner H, Fasy BT, Rote G. 2013. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Discrete & Computational Geometry. 49(4), 797–822.' mla: 'Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” Discrete & Computational Geometry, vol. 49, no. 4, Springer, 2013, pp. 797–822, doi:10.1007/s00454-013-9517-x.' short: H. Edelsbrunner, B.T. Fasy, G. Rote, Discrete & Computational Geometry 49 (2013) 797–822. date_created: 2018-12-11T11:59:44Z date_published: 2013-06-01T00:00:00Z date_updated: 2023-02-23T11:13:49Z day: '01' department: - _id: HeEd doi: 10.1007/s00454-013-9517-x intvolume: ' 49' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00454-013-9517-x month: '06' oa: 1 oa_version: Published Version page: 797 - 822 publication: Discrete & Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer publist_id: '3991' quality_controlled: '1' related_material: record: - id: '3134' relation: earlier_version status: public scopus_import: '1' status: public title: 'Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 49 year: '2013' ... --- _id: '2939' abstract: - lang: eng text: In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ > 0, it returns only those homology classes with persistence at least Γ. Instead of the classical reduction via column operations, our algorithm performs rank computations on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0, 1), the running time is O (C (1 - δ) Γ R d (n) log n), where C (1 - δ) Γ is the number of homology classes with persistence at least (1 - δ) Γ, n is the total number of simplices in the complex, d its dimension, and R d (n) is the complexity of computing the rank of an n × n matrix with O (d n) nonzero entries. Depending on the choice of the rank algorithm, this yields a deterministic O (C (1 - δ) Γ n 2.376) algorithm, an O (C (1 - δ) Γ n 2.28) Las-Vegas algorithm, or an O (C (1 - δ) Γ n 2 + ε{lunate}) Monte-Carlo algorithm for an arbitrary ε{lunate} > 0. The space complexity of the Monte-Carlo version is bounded by O (d n) = O (n log n). acknowledgement: The authors thank Herbert Edelsbrunner for many helpful discussions and suggestions. Moreover, they are grateful for the careful reviews that helped to improve the quality of the paper. author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Chen C, Kerber M. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 2013;46(4):435-447. doi:10.1016/j.comgeo.2012.02.010' apa: 'Chen, C., & Kerber, M. (2013). An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2012.02.010' chicago: 'Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology.” Computational Geometry: Theory and Applications. Elsevier, 2013. https://doi.org/10.1016/j.comgeo.2012.02.010.' ieee: 'C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,” Computational Geometry: Theory and Applications, vol. 46, no. 4. Elsevier, pp. 435–447, 2013.' ista: 'Chen C, Kerber M. 2013. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 46(4), 435–447.' mla: 'Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology.” Computational Geometry: Theory and Applications, vol. 46, no. 4, Elsevier, 2013, pp. 435–47, doi:10.1016/j.comgeo.2012.02.010.' short: 'C. Chen, M. Kerber, Computational Geometry: Theory and Applications 46 (2013) 435–447.' date_created: 2018-12-11T12:00:27Z date_published: 2013-05-01T00:00:00Z date_updated: 2023-02-23T11:24:10Z day: '01' department: - _id: HeEd doi: 10.1016/j.comgeo.2012.02.010 intvolume: ' 46' issue: '4' language: - iso: eng month: '05' oa_version: None page: 435 - 447 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '3796' quality_controlled: '1' related_material: record: - id: '3367' relation: earlier_version status: public scopus_import: 1 status: public title: An output sensitive algorithm for persistent homology type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 46 year: '2013' ... --- _id: '10897' abstract: - lang: eng text: Taking images is an efficient way to collect data about the physical world. It can be done fast and in exquisite detail. By definition, image processing is the field that concerns itself with the computation aimed at harnessing the information contained in images [10]. This talk is concerned with topological information. Our main thesis is that persistent homology [5] is a useful method to quantify and summarize topological information, building a bridge that connects algebraic topology with applications. We provide supporting evidence for this thesis by touching upon four technical developments in the overlap between persistent homology and image processing. acknowledgement: This research is partially supported by the European Science Foundation (ESF) under the Research Network Programme, the European Union under the Toposys Project FP7-ICT-318493-STREP, the Russian Government under the Mega Project 11.G34.31.0053. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Edelsbrunner H. Persistent homology in image processing. In: Graph-Based Representations in Pattern Recognition. Vol 7877. LNCS. Berlin, Heidelberg: Springer Nature; 2013:182-183. doi:10.1007/978-3-642-38221-5_19' apa: 'Edelsbrunner, H. (2013). Persistent homology in image processing. In Graph-Based Representations in Pattern Recognition (Vol. 7877, pp. 182–183). Berlin, Heidelberg: Springer Nature. https://doi.org/10.1007/978-3-642-38221-5_19' chicago: 'Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” In Graph-Based Representations in Pattern Recognition, 7877:182–83. LNCS. Berlin, Heidelberg: Springer Nature, 2013. https://doi.org/10.1007/978-3-642-38221-5_19.' ieee: H. Edelsbrunner, “Persistent homology in image processing,” in Graph-Based Representations in Pattern Recognition, Vienna, Austria, 2013, vol. 7877, pp. 182–183. ista: 'Edelsbrunner H. 2013. Persistent homology in image processing. Graph-Based Representations in Pattern Recognition. GbRPR: Graph-based Representations in Pattern RecognitionLNCS vol. 7877, 182–183.' mla: Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” Graph-Based Representations in Pattern Recognition, vol. 7877, Springer Nature, 2013, pp. 182–83, doi:10.1007/978-3-642-38221-5_19. short: H. Edelsbrunner, in:, Graph-Based Representations in Pattern Recognition, Springer Nature, Berlin, Heidelberg, 2013, pp. 182–183. conference: end_date: 2013-05-17 location: Vienna, Austria name: 'GbRPR: Graph-based Representations in Pattern Recognition' start_date: 2013-05-15 date_created: 2022-03-21T07:30:33Z date_published: 2013-06-01T00:00:00Z date_updated: 2023-09-05T15:10:20Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-642-38221-5_19 ec_funded: 1 intvolume: ' 7877' language: - iso: eng month: '06' oa_version: None page: 182-183 place: Berlin, Heidelberg project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Graph-Based Representations in Pattern Recognition publication_identifier: eisbn: - '9783642382215' eissn: - 1611-3349 isbn: - '9783642382208' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' series_title: LNCS status: public title: Persistent homology in image processing type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 7877 year: '2013' ... --- _id: '2849' author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Nataliya full_name: Strelkova, Nataliya last_name: Strelkova citation: ama: Edelsbrunner H, Strelkova N. On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. 2012;67(6):1167-1168. doi:10.1070/RM2012v067n06ABEH004820 apa: Edelsbrunner, H., & Strelkova, N. (2012). On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. IOP Publishing Ltd. https://doi.org/10.1070/RM2012v067n06ABEH004820 chicago: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space of Steiner Minimal Trees.” Russian Mathematical Surveys. IOP Publishing Ltd., 2012. https://doi.org/10.1070/RM2012v067n06ABEH004820. ieee: H. Edelsbrunner and N. Strelkova, “On the configuration space of Steiner minimal trees,” Russian Mathematical Surveys, vol. 67, no. 6. IOP Publishing Ltd., pp. 1167–1168, 2012. ista: Edelsbrunner H, Strelkova N. 2012. On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. 67(6), 1167–1168. mla: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space of Steiner Minimal Trees.” Russian Mathematical Surveys, vol. 67, no. 6, IOP Publishing Ltd., 2012, pp. 1167–68, doi:10.1070/RM2012v067n06ABEH004820. short: H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168. date_created: 2018-12-11T11:59:55Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T07:00:13Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1070/RM2012v067n06ABEH004820 file: - access_level: open_access checksum: 44ee8d173487e8ed41a51136816bbeb4 content_type: application/pdf creator: system date_created: 2018-12-12T10:14:26Z date_updated: 2020-07-14T12:45:51Z file_id: '5078' file_name: IST-2016-546-v1+1_2014-J-05-SteinerMinTrees.pdf file_size: 392021 relation: main_file file_date_updated: 2020-07-14T12:45:51Z has_accepted_license: '1' intvolume: ' 67' issue: '6' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 1167 - 1168 publication: Russian Mathematical Surveys publication_status: published publisher: IOP Publishing Ltd. publist_id: '3943' pubrep_id: '546' quality_controlled: '1' scopus_import: 1 status: public title: On the configuration space of Steiner minimal trees type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 67 year: '2012' ... --- _id: '2903' abstract: - lang: eng text: In order to enjoy a digital version of the Jordan Curve Theorem, it is common to use the closed topology for the foreground and the open topology for the background of a 2-dimensional binary image. In this paper, we introduce a single topology that enjoys this theorem for all thresholds decomposing a real-valued image into foreground and background. This topology is easy to construct and it generalizes to n-dimensional images. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Olga full_name: Symonova, Olga id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87 last_name: Symonova citation: ama: 'Edelsbrunner H, Symonova O. The adaptive topology of a digital image. In: IEEE; 2012:41-48. doi:10.1109/ISVD.2012.11' apa: 'Edelsbrunner, H., & Symonova, O. (2012). The adaptive topology of a digital image (pp. 41–48). Presented at the ISVD: International Symposium on Voronoi Diagrams in Science and Engineering, New Brunswick, NJ, USA : IEEE. https://doi.org/10.1109/ISVD.2012.11' chicago: Edelsbrunner, Herbert, and Olga Symonova. “The Adaptive Topology of a Digital Image,” 41–48. IEEE, 2012. https://doi.org/10.1109/ISVD.2012.11. ieee: 'H. Edelsbrunner and O. Symonova, “The adaptive topology of a digital image,” presented at the ISVD: International Symposium on Voronoi Diagrams in Science and Engineering, New Brunswick, NJ, USA , 2012, pp. 41–48.' ista: 'Edelsbrunner H, Symonova O. 2012. The adaptive topology of a digital image. ISVD: International Symposium on Voronoi Diagrams in Science and Engineering, 41–48.' mla: Edelsbrunner, Herbert, and Olga Symonova. The Adaptive Topology of a Digital Image. IEEE, 2012, pp. 41–48, doi:10.1109/ISVD.2012.11. short: H. Edelsbrunner, O. Symonova, in:, IEEE, 2012, pp. 41–48. conference: end_date: 2012-06-29 location: 'New Brunswick, NJ, USA ' name: 'ISVD: International Symposium on Voronoi Diagrams in Science and Engineering' start_date: 2012-06-27 date_created: 2018-12-11T12:00:15Z date_published: 2012-08-06T00:00:00Z date_updated: 2021-01-12T07:00:35Z day: '06' ddc: - '000' department: - _id: HeEd - _id: MaJö doi: 10.1109/ISVD.2012.11 file: - access_level: open_access checksum: 444869a4e8abf07834f88b6e5cb5e9c3 content_type: application/pdf creator: system date_created: 2018-12-12T10:09:41Z date_updated: 2020-07-14T12:45:52Z file_id: '4765' file_name: IST-2016-545-v1+1_2012-P-10-AdaptiveTopology.pdf file_size: 760548 relation: main_file file_date_updated: 2020-07-14T12:45:52Z has_accepted_license: '1' language: - iso: eng month: '08' oa: 1 oa_version: Submitted Version page: 41 - 48 publication_status: published publisher: IEEE publist_id: '3844' pubrep_id: '545' quality_controlled: '1' scopus_import: 1 status: public title: The adaptive topology of a digital image type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '2941' author: - first_name: Nikolai full_name: Dolbilin, Nikolai last_name: Dolbilin - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Oleg full_name: Musin, Oleg last_name: Musin citation: ama: Dolbilin N, Edelsbrunner H, Musin O. On the optimality of functionals over triangulations of Delaunay sets. Russian Mathematical Surveys. 2012;67(4):781-783. doi:10.1070/RM2012v067n04ABEH004807 apa: Dolbilin, N., Edelsbrunner, H., & Musin, O. (2012). On the optimality of functionals over triangulations of Delaunay sets. Russian Mathematical Surveys. IOP Publishing. https://doi.org/10.1070/RM2012v067n04ABEH004807 chicago: Dolbilin, Nikolai, Herbert Edelsbrunner, and Oleg Musin. “On the Optimality of Functionals over Triangulations of Delaunay Sets.” Russian Mathematical Surveys. IOP Publishing, 2012. https://doi.org/10.1070/RM2012v067n04ABEH004807. ieee: N. Dolbilin, H. Edelsbrunner, and O. Musin, “On the optimality of functionals over triangulations of Delaunay sets,” Russian Mathematical Surveys, vol. 67, no. 4. IOP Publishing, pp. 781–783, 2012. ista: Dolbilin N, Edelsbrunner H, Musin O. 2012. On the optimality of functionals over triangulations of Delaunay sets. Russian Mathematical Surveys. 67(4), 781–783. mla: Dolbilin, Nikolai, et al. “On the Optimality of Functionals over Triangulations of Delaunay Sets.” Russian Mathematical Surveys, vol. 67, no. 4, IOP Publishing, 2012, pp. 781–83, doi:10.1070/RM2012v067n04ABEH004807. short: N. Dolbilin, H. Edelsbrunner, O. Musin, Russian Mathematical Surveys 67 (2012) 781–783. date_created: 2018-12-11T12:00:28Z date_published: 2012-11-01T00:00:00Z date_updated: 2021-01-12T07:39:55Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1070/RM2012v067n04ABEH004807 file: - access_level: open_access checksum: 389a5ae53d6347de36c3468034f2821d content_type: application/pdf creator: system date_created: 2018-12-12T10:16:49Z date_updated: 2020-07-14T12:45:55Z file_id: '5239' file_name: IST-2013-132-v1+1_2012-J-04-Functional-E.pdf file_size: 253816 relation: main_file file_date_updated: 2020-07-14T12:45:55Z has_accepted_license: '1' intvolume: ' 67' issue: '4' language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version page: 781 - 783 publication: Russian Mathematical Surveys publication_status: published publisher: IOP Publishing publist_id: '3792' pubrep_id: '132' quality_controlled: '1' scopus_import: 1 status: public title: On the optimality of functionals over triangulations of Delaunay sets type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 67 year: '2012' ... --- _id: '2971' abstract: - lang: eng text: 'We study the task of interactive semantic labeling of a segmentation hierarchy. To this end we propose a framework interleaving two components: an automatic labeling step, based on a Conditional Random Field whose dependencies are defined by the inclusion tree of the segmentation hierarchy, and an interaction step that integrates incremental input from a human user. Evaluated on two distinct datasets, the proposed interactive approach efficiently integrates human interventions and illustrates the advantages of structured prediction in an interactive framework. ' author: - first_name: Georg full_name: Zankl, Georg last_name: Zankl - first_name: Yll full_name: Haxhimusa, Yll last_name: Haxhimusa - first_name: Adrian full_name: Ion, Adrian id: 29F89302-F248-11E8-B48F-1D18A9856A87 last_name: Ion citation: ama: 'Zankl G, Haxhimusa Y, Ion A. Interactive labeling of image segmentation hierarchies. In: Vol 7476. Springer; 2012:11-20. doi:10.1007/978-3-642-32717-9_2' apa: 'Zankl, G., Haxhimusa, Y., & Ion, A. (2012). Interactive labeling of image segmentation hierarchies (Vol. 7476, pp. 11–20). Presented at the Pattern Recognition, Graz, Austria: Springer. https://doi.org/10.1007/978-3-642-32717-9_2' chicago: Zankl, Georg, Yll Haxhimusa, and Adrian Ion. “Interactive Labeling of Image Segmentation Hierarchies,” 7476:11–20. Springer, 2012. https://doi.org/10.1007/978-3-642-32717-9_2. ieee: G. Zankl, Y. Haxhimusa, and A. Ion, “Interactive labeling of image segmentation hierarchies,” presented at the Pattern Recognition, Graz, Austria, 2012, vol. 7476, pp. 11–20. ista: Zankl G, Haxhimusa Y, Ion A. 2012. Interactive labeling of image segmentation hierarchies. Pattern Recognition vol. 7476, 11–20. mla: Zankl, Georg, et al. Interactive Labeling of Image Segmentation Hierarchies. Vol. 7476, Springer, 2012, pp. 11–20, doi:10.1007/978-3-642-32717-9_2. short: G. Zankl, Y. Haxhimusa, A. Ion, in:, Springer, 2012, pp. 11–20. conference: end_date: 2012-08-31 location: Graz, Austria name: Pattern Recognition start_date: 2012-08-28 date_created: 2018-12-11T12:00:37Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T07:40:10Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-642-32717-9_2 intvolume: ' 7476' language: - iso: eng month: '01' oa_version: None page: 11 - 20 publication_status: published publisher: Springer publist_id: '3737' quality_controlled: '1' scopus_import: 1 status: public title: Interactive labeling of image segmentation hierarchies type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 7476 year: '2012' ... --- _id: '3120' abstract: - lang: eng text: We introduce a strategy based on Kustin-Miller unprojection that allows us to construct many hundreds of Gorenstein codimension 4 ideals with 9 × 16 resolutions (that is, nine equations and sixteen first syzygies). Our two basic games are called Tom and Jerry; the main application is the biregular construction of most of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type I projection. In every case, at least one Tom and one Jerry construction works, providing at least two deformation families of quasismooth Fano 3-folds having the same numerics but different topology. © 2012 Copyright Foundation Compositio Mathematica. acknowledgement: This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0. author: - first_name: Gavin full_name: Brown, Gavin last_name: Brown - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Miles full_name: Reid, Miles last_name: Reid citation: ama: Brown G, Kerber M, Reid M. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 2012;148(4):1171-1194. doi:10.1112/S0010437X11007226 apa: Brown, G., Kerber, M., & Reid, M. (2012). Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. Cambridge University Press. https://doi.org/10.1112/S0010437X11007226 chicago: Brown, Gavin, Michael Kerber, and Miles Reid. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” Compositio Mathematica. Cambridge University Press, 2012. https://doi.org/10.1112/S0010437X11007226. ieee: G. Brown, M. Kerber, and M. Reid, “Fano 3 folds in codimension 4 Tom and Jerry Part I,” Compositio Mathematica, vol. 148, no. 4. Cambridge University Press, pp. 1171–1194, 2012. ista: Brown G, Kerber M, Reid M. 2012. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 148(4), 1171–1194. mla: Brown, Gavin, et al. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” Compositio Mathematica, vol. 148, no. 4, Cambridge University Press, 2012, pp. 1171–94, doi:10.1112/S0010437X11007226. short: G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 1171–1194. date_created: 2018-12-11T12:01:30Z date_published: 2012-07-01T00:00:00Z date_updated: 2021-01-12T07:41:12Z day: '01' department: - _id: HeEd doi: 10.1112/S0010437X11007226 intvolume: ' 148' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1009.4313 month: '07' oa: 1 oa_version: Preprint page: 1171 - 1194 publication: Compositio Mathematica publication_status: published publisher: Cambridge University Press publist_id: '3579' quality_controlled: '1' scopus_import: 1 status: public title: Fano 3 folds in codimension 4 Tom and Jerry Part I type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 148 year: '2012' ... --- _id: '3133' abstract: - lang: eng text: 'This note contributes to the point calculus of persistent homology by extending Alexander duality from spaces to real-valued functions. Given a perfect Morse function f: S n+1 →[0, 1 and a decomposition S n+1 = U ∪ V into two (n + 1)-manifolds with common boundary M, we prove elementary relationships between the persistence diagrams of f restricted to U, to V, and to M. ' acknowledgement: "his research is partially supported by the National Science Foundation (NSF) under grant DBI-0820624, the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.\r\nThe authors thank an anonymous referee for suggesting the simplified proof of the Contravariant PE Theorem given in this paper. They also thank Frederick Cohen, Yuriy Mileyko and Amit Patel for helpful discussions." author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Edelsbrunner H, Kerber M. Alexander duality for functions: The persistent behavior of land and water and shore. In: Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry . ACM; 2012:249-258. doi:10.1145/2261250.2261287' apa: 'Edelsbrunner, H., & Kerber, M. (2012). Alexander duality for functions: The persistent behavior of land and water and shore. In Proceedings of the twenty-eighth annual symposium on Computational geometry (pp. 249–258). Chapel Hill, NC, USA: ACM. https://doi.org/10.1145/2261250.2261287' chicago: 'Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” In Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , 249–58. ACM, 2012. https://doi.org/10.1145/2261250.2261287.' ieee: 'H. Edelsbrunner and M. Kerber, “Alexander duality for functions: The persistent behavior of land and water and shore,” in Proceedings of the twenty-eighth annual symposium on Computational geometry , Chapel Hill, NC, USA, 2012, pp. 249–258.' ista: 'Edelsbrunner H, Kerber M. 2012. Alexander duality for functions: The persistent behavior of land and water and shore. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 249–258.' mla: 'Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–58, doi:10.1145/2261250.2261287.' short: H. Edelsbrunner, M. Kerber, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–258. conference: end_date: 2012-06-20 location: Chapel Hill, NC, USA name: 'SCG: Symposium on Computational Geometry' start_date: 2012-06-17 date_created: 2018-12-11T12:01:35Z date_published: 2012-06-20T00:00:00Z date_updated: 2021-01-12T07:41:17Z day: '20' department: - _id: HeEd doi: 10.1145/2261250.2261287 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1109.5052 month: '06' oa: 1 oa_version: Preprint page: 249 - 258 publication: 'Proceedings of the twenty-eighth annual symposium on Computational geometry ' publication_status: published publisher: ACM publist_id: '3564' quality_controlled: '1' scopus_import: 1 status: public title: 'Alexander duality for functions: The persistent behavior of land and water and shore' type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '3134' abstract: - lang: eng text: 'It has been an open question whether the sum of finitely many isotropic Gaussian kernels in n ≥ 2 dimensions can have more modes than kernels, until in 2003 Carreira-Perpiñán and Williams exhibited n +1 isotropic Gaussian kernels in ℝ n with n + 2 modes. We give a detailed analysis of this example, showing that it has exponentially many critical points and that the resilience of the extra mode grows like √n. In addition, we exhibit finite configurations of isotropic Gaussian kernels with superlinearly many modes. ' acknowledgement: This research is partially supported by the National Science Foun- dation (NSF) under grant DBI-0820624, by the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Brittany full_name: Fasy, Brittany last_name: Fasy - first_name: Günter full_name: Rote, Günter last_name: Rote citation: ama: 'Edelsbrunner H, Fasy B, Rote G. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In: Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry . ACM; 2012:91-100. doi:10.1145/2261250.2261265' apa: 'Edelsbrunner, H., Fasy, B., & Rote, G. (2012). Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In Proceedings of the twenty-eighth annual symposium on Computational geometry (pp. 91–100). Chapel Hill, NC, USA: ACM. https://doi.org/10.1145/2261250.2261265' chicago: 'Edelsbrunner, Herbert, Brittany Fasy, and Günter Rote. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” In Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , 91–100. ACM, 2012. https://doi.org/10.1145/2261250.2261265.' ieee: 'H. Edelsbrunner, B. Fasy, and G. Rote, “Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions,” in Proceedings of the twenty-eighth annual symposium on Computational geometry , Chapel Hill, NC, USA, 2012, pp. 91–100.' ista: 'Edelsbrunner H, Fasy B, Rote G. 2012. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 91–100.' mla: 'Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100, doi:10.1145/2261250.2261265.' short: H. Edelsbrunner, B. Fasy, G. Rote, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100. conference: end_date: 2012-06-20 location: Chapel Hill, NC, USA name: 'SCG: Symposium on Computational Geometry' start_date: 2012-06-17 date_created: 2018-12-11T12:01:35Z date_published: 2012-06-20T00:00:00Z date_updated: 2023-02-23T10:59:27Z day: '20' department: - _id: HeEd doi: 10.1145/2261250.2261265 language: - iso: eng month: '06' oa_version: None page: 91 - 100 publication: 'Proceedings of the twenty-eighth annual symposium on Computational geometry ' publication_status: published publisher: ACM publist_id: '3563' quality_controlled: '1' related_material: record: - id: '2815' relation: later_version status: public scopus_import: 1 status: public title: 'Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions' type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '3256' abstract: - lang: eng text: We use a distortion to define the dual complex of a cubical subdivision of ℝ n as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated by the topological analysis of high-dimensional digital image data, we consider such subdivisions defined by generalizations of quad- and oct-trees to n dimensions. Assuming the subdivision is balanced, we show that mapping each vertex to the center of the corresponding n-cube gives a geometric realization of the dual complex in ℝ n. acknowledgement: This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0057 and HR0011-09-0065 as well as the National Science Foundation (NSF) under grant DBI-0820624. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: Edelsbrunner H, Kerber M. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 2012;47(2):393-414. doi:10.1007/s00454-011-9382-4 apa: Edelsbrunner, H., & Kerber, M. (2012). Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-011-9382-4 chicago: Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” Discrete & Computational Geometry. Springer, 2012. https://doi.org/10.1007/s00454-011-9382-4. ieee: H. Edelsbrunner and M. Kerber, “Dual complexes of cubical subdivisions of ℝn,” Discrete & Computational Geometry, vol. 47, no. 2. Springer, pp. 393–414, 2012. ista: Edelsbrunner H, Kerber M. 2012. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 47(2), 393–414. mla: Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” Discrete & Computational Geometry, vol. 47, no. 2, Springer, 2012, pp. 393–414, doi:10.1007/s00454-011-9382-4. short: H. Edelsbrunner, M. Kerber, Discrete & Computational Geometry 47 (2012) 393–414. date_created: 2018-12-11T12:02:17Z date_published: 2012-03-01T00:00:00Z date_updated: 2021-01-12T07:42:10Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s00454-011-9382-4 file: - access_level: open_access checksum: 76486f3b2c9e7fd81342f3832ca387e7 content_type: application/pdf creator: system date_created: 2018-12-12T10:08:15Z date_updated: 2020-07-14T12:46:05Z file_id: '4675' file_name: IST-2016-543-v1+1_2012-J-08-HierarchyCubeComplex.pdf file_size: 203636 relation: main_file file_date_updated: 2020-07-14T12:46:05Z has_accepted_license: '1' intvolume: ' 47' issue: '2' language: - iso: eng month: '03' oa: 1 oa_version: Submitted Version page: 393 - 414 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '3398' pubrep_id: '543' quality_controlled: '1' scopus_import: 1 status: public title: Dual complexes of cubical subdivisions of ℝn type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 47 year: '2012' ... --- _id: '3265' abstract: - lang: eng text: We propose a mid-level statistical model for image segmentation that composes multiple figure-ground hypotheses (FG) obtained by applying constraints at different locations and scales, into larger interpretations (tilings) of the entire image. Inference is cast as optimization over sets of maximal cliques sampled from a graph connecting all non-overlapping figure-ground segment hypotheses. Potential functions over cliques combine unary, Gestalt-based figure qualities, and pairwise compatibilities among spatially neighboring segments, constrained by T-junctions and the boundary interface statistics of real scenes. Learning the model parameters is based on maximum likelihood, alternating between sampling image tilings and optimizing their potential function parameters. State of the art results are reported on the Berkeley and Stanford segmentation datasets, as well as VOC2009, where a 28% improvement was achieved. article_number: '6126486' author: - first_name: Adrian full_name: Ion, Adrian id: 29F89302-F248-11E8-B48F-1D18A9856A87 last_name: Ion - first_name: Joao full_name: Carreira, Joao last_name: Carreira - first_name: Cristian full_name: Sminchisescu, Cristian last_name: Sminchisescu citation: ama: 'Ion A, Carreira J, Sminchisescu C. Image segmentation by figure-ground composition into maximal cliques. In: IEEE; 2012. doi:10.1109/ICCV.2011.6126486' apa: 'Ion, A., Carreira, J., & Sminchisescu, C. (2012). Image segmentation by figure-ground composition into maximal cliques. Presented at the ICCV: International Conference on Computer Vision, Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126486' chicago: Ion, Adrian, Joao Carreira, and Cristian Sminchisescu. “Image Segmentation by Figure-Ground Composition into Maximal Cliques.” IEEE, 2012. https://doi.org/10.1109/ICCV.2011.6126486. ieee: 'A. Ion, J. Carreira, and C. Sminchisescu, “Image segmentation by figure-ground composition into maximal cliques,” presented at the ICCV: International Conference on Computer Vision, Barcelona, Spain, 2012.' ista: 'Ion A, Carreira J, Sminchisescu C. 2012. Image segmentation by figure-ground composition into maximal cliques. ICCV: International Conference on Computer Vision, 6126486.' mla: Ion, Adrian, et al. Image Segmentation by Figure-Ground Composition into Maximal Cliques. 6126486, IEEE, 2012, doi:10.1109/ICCV.2011.6126486. short: A. Ion, J. Carreira, C. Sminchisescu, in:, IEEE, 2012. conference: end_date: 2011-11-13 location: Barcelona, Spain name: 'ICCV: International Conference on Computer Vision' start_date: 2011-11-06 date_created: 2018-12-11T12:02:21Z date_published: 2012-01-12T00:00:00Z date_updated: 2021-01-12T07:42:15Z day: '12' department: - _id: HeEd doi: 10.1109/ICCV.2011.6126486 language: - iso: eng month: '01' oa_version: None publication_status: published publisher: IEEE publist_id: '3382' quality_controlled: '1' status: public title: Image segmentation by figure-ground composition into maximal cliques type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '3115' abstract: - lang: eng text: 'We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution P; then, P''s offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(nlogn)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. A variant of the algorithm, which we have implemented using the cgal library, is based on rational arithmetic and answers the same deconstruction problem up to an uncertainty parameter δ its running time additionally depends on δ. If the input shape is found to be approximable, this algorithm also computes an approximate solution for the problem. It also allows us to solve parameter-optimization problems induced by the offset-deconstruction problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution P with at most one more vertex than a vertex-minimal one.' acknowledgement: "We thank Eyal Flato (Plataine Ltd.) for raising the offset-deconstruction problem in connection with wood cutting. We also thank Tim Bretl (UIUC) for suggesting the digital-pen offset-deconstruction problem. This work has been supported in part by the Israel Science Foundation (grant no. 1102/11), by the German–Israeli Foundation (grant no. 969/07), by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University, and by the EU Project under Contract No. 255827 (CGL—Computational Geometry Learning).\r\n" author: - first_name: Eric full_name: Berberich, Eric last_name: Berberich - first_name: Dan full_name: Halperin, Dan last_name: Halperin - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Roza full_name: Pogalnikova, Roza last_name: Pogalnikova citation: ama: Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate offsets. Discrete & Computational Geometry. 2012;48(4):964-989. doi:10.1007/s00454-012-9441-5 apa: Berberich, E., Halperin, D., Kerber, M., & Pogalnikova, R. (2012). Deconstructing approximate offsets. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-012-9441-5 chicago: Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing Approximate Offsets.” Discrete & Computational Geometry. Springer, 2012. https://doi.org/10.1007/s00454-012-9441-5. ieee: E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing approximate offsets,” Discrete & Computational Geometry, vol. 48, no. 4. Springer, pp. 964–989, 2012. ista: Berberich E, Halperin D, Kerber M, Pogalnikova R. 2012. Deconstructing approximate offsets. Discrete & Computational Geometry. 48(4), 964–989. mla: Berberich, Eric, et al. “Deconstructing Approximate Offsets.” Discrete & Computational Geometry, vol. 48, no. 4, Springer, 2012, pp. 964–89, doi:10.1007/s00454-012-9441-5. short: E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, Discrete & Computational Geometry 48 (2012) 964–989. date_created: 2018-12-11T12:01:28Z date_published: 2012-12-01T00:00:00Z date_updated: 2023-02-23T11:22:30Z day: '01' department: - _id: HeEd doi: 10.1007/s00454-012-9441-5 external_id: arxiv: - '1109.2158' intvolume: ' 48' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1109.2158 month: '12' oa: 1 oa_version: Preprint page: 964 - 989 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '3584' quality_controlled: '1' related_material: record: - id: '3329' relation: earlier_version status: public scopus_import: 1 status: public title: Deconstructing approximate offsets type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2012' ... --- _id: '3331' abstract: - lang: eng text: Computing the topology of an algebraic plane curve C means computing a combinatorial graph that is isotopic to C and thus represents its topology in R2. We prove that, for a polynomial of degree n with integer coefficients bounded by 2ρ, the topology of the induced curve can be computed with bit operations ( indicates that we omit logarithmic factors). Our analysis improves the previous best known complexity bounds by a factor of n2. The improvement is based on new techniques to compute and refine isolating intervals for the real roots of polynomials, and on the consequent amortized analysis of the critical fibers of the algebraic curve. author: - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Michael full_name: Sagraloff, Michael last_name: Sagraloff citation: ama: Kerber M, Sagraloff M. A worst case bound for topology computation of algebraic curves. Journal of Symbolic Computation. 2012;47(3):239-258. doi:10.1016/j.jsc.2011.11.001 apa: Kerber, M., & Sagraloff, M. (2012). A worst case bound for topology computation of algebraic curves. Journal of Symbolic Computation. Elsevier. https://doi.org/10.1016/j.jsc.2011.11.001 chicago: Kerber, Michael, and Michael Sagraloff. “A Worst Case Bound for Topology Computation of Algebraic Curves.” Journal of Symbolic Computation. Elsevier, 2012. https://doi.org/10.1016/j.jsc.2011.11.001. ieee: M. Kerber and M. Sagraloff, “A worst case bound for topology computation of algebraic curves,” Journal of Symbolic Computation, vol. 47, no. 3. Elsevier, pp. 239–258, 2012. ista: Kerber M, Sagraloff M. 2012. A worst case bound for topology computation of algebraic curves. Journal of Symbolic Computation. 47(3), 239–258. mla: Kerber, Michael, and Michael Sagraloff. “A Worst Case Bound for Topology Computation of Algebraic Curves.” Journal of Symbolic Computation, vol. 47, no. 3, Elsevier, 2012, pp. 239–58, doi:10.1016/j.jsc.2011.11.001. short: M. Kerber, M. Sagraloff, Journal of Symbolic Computation 47 (2012) 239–258. date_created: 2018-12-11T12:02:43Z date_published: 2012-03-01T00:00:00Z date_updated: 2021-01-12T07:42:43Z day: '01' department: - _id: HeEd doi: 10.1016/j.jsc.2011.11.001 intvolume: ' 47' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1104.1510 month: '03' oa: 1 oa_version: Preprint page: 239 - 258 publication: ' Journal of Symbolic Computation' publication_status: published publisher: Elsevier publist_id: '3303' quality_controlled: '1' scopus_import: 1 status: public title: A worst case bound for topology computation of algebraic curves type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 47 year: '2012' ... --- _id: '3129' abstract: - lang: eng text: "Let K be a simplicial complex and g the rank of its p-th homology group Hp(K) defined with ℤ2 coefficients. We show that we can compute a basis H of Hp(K) and annotate each p-simplex of K with a binary vector of length g with the following property: the annotations, summed over all p-simplices in any p-cycle z, provide the coordinate vector of the homology class [z] in the basis H. The basis and the annotations for all simplices can be computed in O(n ω ) time, where n is the size of K and ω < 2.376 is a quantity so that two n×n matrices can be multiplied in O(n ω ) time. The precomputed annotations permit answering queries about the independence or the triviality of p-cycles efficiently.\r\n\r\nUsing annotations of edges in 2-complexes, we derive better algorithms for computing optimal basis and optimal homologous cycles in 1 - dimensional homology. Specifically, for computing an optimal basis of H1(K) , we improve the previously known time complexity from O(n 4) to O(n ω  + n 2 g ω − 1). Here n denotes the size of the 2-skeleton of K and g the rank of H1(K) . Computing an optimal cycle homologous to a given 1-cycle is NP-hard even for surfaces and an algorithm taking 2 O(g) nlogn time is known for surfaces. We extend this algorithm to work with arbitrary 2-complexes in O(n ω ) + 2 O(g) n 2logn time using annotations.\r\n" alternative_title: - LNCS author: - first_name: Oleksiy full_name: Busaryev, Oleksiy last_name: Busaryev - first_name: Sergio full_name: Cabello, Sergio last_name: Cabello - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Tamal full_name: Dey, Tamal last_name: Dey - first_name: Yusu full_name: Wang, Yusu last_name: Wang citation: ama: 'Busaryev O, Cabello S, Chen C, Dey T, Wang Y. Annotating simplices with a homology basis and its applications. In: Vol 7357. Springer; 2012:189-200. doi:10.1007/978-3-642-31155-0_17' apa: 'Busaryev, O., Cabello, S., Chen, C., Dey, T., & Wang, Y. (2012). Annotating simplices with a homology basis and its applications (Vol. 7357, pp. 189–200). Presented at the SWAT: Symposium and Workshops on Algorithm Theory, Helsinki, Finland: Springer. https://doi.org/10.1007/978-3-642-31155-0_17' chicago: Busaryev, Oleksiy, Sergio Cabello, Chao Chen, Tamal Dey, and Yusu Wang. “Annotating Simplices with a Homology Basis and Its Applications,” 7357:189–200. Springer, 2012. https://doi.org/10.1007/978-3-642-31155-0_17. ieee: 'O. Busaryev, S. Cabello, C. Chen, T. Dey, and Y. Wang, “Annotating simplices with a homology basis and its applications,” presented at the SWAT: Symposium and Workshops on Algorithm Theory, Helsinki, Finland, 2012, vol. 7357, pp. 189–200.' ista: 'Busaryev O, Cabello S, Chen C, Dey T, Wang Y. 2012. Annotating simplices with a homology basis and its applications. SWAT: Symposium and Workshops on Algorithm Theory, LNCS, vol. 7357, 189–200.' mla: Busaryev, Oleksiy, et al. Annotating Simplices with a Homology Basis and Its Applications. Vol. 7357, Springer, 2012, pp. 189–200, doi:10.1007/978-3-642-31155-0_17. short: O. Busaryev, S. Cabello, C. Chen, T. Dey, Y. Wang, in:, Springer, 2012, pp. 189–200. conference: end_date: 2012-07-06 location: Helsinki, Finland name: 'SWAT: Symposium and Workshops on Algorithm Theory' start_date: 2012-07-04 date_created: 2018-12-11T12:01:33Z date_published: 2012-06-19T00:00:00Z date_updated: 2021-01-12T07:41:15Z day: '19' department: - _id: HeEd doi: 10.1007/978-3-642-31155-0_17 external_id: arxiv: - '1107.3793' intvolume: ' 7357' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1107.3793 month: '06' oa: 1 oa_version: Preprint page: 189 - 200 publication_status: published publisher: Springer publist_id: '3569' quality_controlled: '1' scopus_import: 1 status: public title: Annotating simplices with a homology basis and its applications type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 7357 year: '2012' ... --- _id: '3159' abstract: - lang: eng text: The structure of hierarchical networks in biological and physical systems has long been characterized using the Horton-Strahler ordering scheme. The scheme assigns an integer order to each edge in the network based on the topology of branching such that the order increases from distal parts of the network (e.g., mountain streams or capillaries) to the "root" of the network (e.g., the river outlet or the aorta). However, Horton-Strahler ordering cannot be applied to networks with loops because they they create a contradiction in the edge ordering in terms of which edge precedes another in the hierarchy. Here, we present a generalization of the Horton-Strahler order to weighted planar reticular networks, where weights are assumed to correlate with the importance of network edges, e.g., weights estimated from edge widths may correlate to flow capacity. Our method assigns hierarchical levels not only to edges of the network, but also to its loops, and classifies the edges into reticular edges, which are responsible for loop formation, and tree edges. In addition, we perform a detailed and rigorous theoretical analysis of the sensitivity of the hierarchical levels to weight perturbations. In doing so, we show that the ordering of the reticular edges is more robust to noise in weight estimation than is the ordering of the tree edges. We discuss applications of this generalized Horton-Strahler ordering to the study of leaf venation and other biological networks. acknowledgement: "his work was supported by the National Science Foundation Plant Genome Research Program (grant 0820624 to H.E. and J.S.W.), the Defense Advanced Projects Research Agency (grant HR0011-09-1-0055 to H.E. and J.S.W.), and the European Science Foundation (under the Research Networking Programme on “Applied and Computational Algebraic Topology” run by H.E.). Joshua S. Weitz, Ph.D., holds a Career Award at the Scientific Interface from the Burroughs Wellcome Fund.\r\n\r\n\r\n\r\nDuring preparation of this manuscript the authors became aware of a related work by Katifori and Magnasco (arXiv:1110.1412v1), concurrently submitted and accepted for publication in PLoS ONE." article_number: e36715 author: - first_name: Yuriy full_name: Mileyko, Yuriy last_name: Mileyko - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Charles full_name: Price, Charles last_name: Price - first_name: Joshua full_name: Weitz, Joshua last_name: Weitz citation: ama: Mileyko Y, Edelsbrunner H, Price C, Weitz J. Hierarchical ordering of reticular networks. PLoS One. 2012;7(6). doi:10.1371/journal.pone.0036715 apa: Mileyko, Y., Edelsbrunner, H., Price, C., & Weitz, J. (2012). Hierarchical ordering of reticular networks. PLoS One. Public Library of Science. https://doi.org/10.1371/journal.pone.0036715 chicago: Mileyko, Yuriy, Herbert Edelsbrunner, Charles Price, and Joshua Weitz. “Hierarchical Ordering of Reticular Networks.” PLoS One. Public Library of Science, 2012. https://doi.org/10.1371/journal.pone.0036715. ieee: Y. Mileyko, H. Edelsbrunner, C. Price, and J. Weitz, “Hierarchical ordering of reticular networks,” PLoS One, vol. 7, no. 6. Public Library of Science, 2012. ista: Mileyko Y, Edelsbrunner H, Price C, Weitz J. 2012. Hierarchical ordering of reticular networks. PLoS One. 7(6), e36715. mla: Mileyko, Yuriy, et al. “Hierarchical Ordering of Reticular Networks.” PLoS One, vol. 7, no. 6, e36715, Public Library of Science, 2012, doi:10.1371/journal.pone.0036715. short: Y. Mileyko, H. Edelsbrunner, C. Price, J. Weitz, PLoS One 7 (2012). date_created: 2018-12-11T12:01:44Z date_published: 2012-06-06T00:00:00Z date_updated: 2021-01-12T07:41:28Z day: '06' ddc: - '510' department: - _id: HeEd doi: 10.1371/journal.pone.0036715 file: - access_level: open_access checksum: 515a98ad72e470752f03f13663dcaff8 content_type: application/pdf creator: kschuh date_created: 2019-02-05T12:38:43Z date_updated: 2020-07-14T12:46:01Z file_id: '5922' file_name: 2012_PLoS_Mileyko.PDF file_size: 541583 relation: main_file file_date_updated: 2020-07-14T12:46:01Z has_accepted_license: '1' intvolume: ' 7' issue: '6' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '06' oa: 1 oa_version: Published Version publication: PLoS One publication_status: published publisher: Public Library of Science publist_id: '3530' pubrep_id: '385' quality_controlled: '1' scopus_import: 1 status: public title: Hierarchical ordering of reticular networks tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 7 year: '2012' ... --- _id: '3310' abstract: - lang: eng text: The theory of persistent homology opens up the possibility to reason about topological features of a space or a function quantitatively and in combinatorial terms. We refer to this new angle at a classical subject within algebraic topology as a point calculus, which we present for the family of interlevel sets of a real-valued function. Our account of the subject is expository, devoid of proofs, and written for non-experts in algebraic topology. acknowledgement: Research by the third author is partially supported by the National Science Foundation (NSF) under grant DBI-0820624. author: - first_name: Paul full_name: Bendich, Paul id: 43F6EC54-F248-11E8-B48F-1D18A9856A87 last_name: Bendich - first_name: Sergio full_name: Cabello, Sergio last_name: Cabello - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: Bendich P, Cabello S, Edelsbrunner H. A point calculus for interlevel set homology. Pattern Recognition Letters. 2012;33(11):1436-1444. doi:10.1016/j.patrec.2011.10.007 apa: Bendich, P., Cabello, S., & Edelsbrunner, H. (2012). A point calculus for interlevel set homology. Pattern Recognition Letters. Elsevier. https://doi.org/10.1016/j.patrec.2011.10.007 chicago: Bendich, Paul, Sergio Cabello, and Herbert Edelsbrunner. “A Point Calculus for Interlevel Set Homology.” Pattern Recognition Letters. Elsevier, 2012. https://doi.org/10.1016/j.patrec.2011.10.007. ieee: P. Bendich, S. Cabello, and H. Edelsbrunner, “A point calculus for interlevel set homology,” Pattern Recognition Letters, vol. 33, no. 11. Elsevier, pp. 1436–1444, 2012. ista: Bendich P, Cabello S, Edelsbrunner H. 2012. A point calculus for interlevel set homology. Pattern Recognition Letters. 33(11), 1436–1444. mla: Bendich, Paul, et al. “A Point Calculus for Interlevel Set Homology.” Pattern Recognition Letters, vol. 33, no. 11, Elsevier, 2012, pp. 1436–44, doi:10.1016/j.patrec.2011.10.007. short: P. Bendich, S. Cabello, H. Edelsbrunner, Pattern Recognition Letters 33 (2012) 1436–1444. date_created: 2018-12-11T12:02:36Z date_published: 2012-08-01T00:00:00Z date_updated: 2021-01-12T07:42:34Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.patrec.2011.10.007 file: - access_level: open_access checksum: d65f79775b51258a604ca5ec741297cc content_type: application/pdf creator: system date_created: 2018-12-12T10:15:00Z date_updated: 2020-07-14T12:46:06Z file_id: '5116' file_name: IST-2016-542-v1+1_2012-J-01-Poinculus.pdf file_size: 280280 relation: main_file file_date_updated: 2020-07-14T12:46:06Z has_accepted_license: '1' intvolume: ' 33' issue: '11' language: - iso: eng month: '08' oa: 1 oa_version: Submitted Version page: 1436 - 1444 publication: Pattern Recognition Letters publication_status: published publisher: Elsevier publist_id: '3330' pubrep_id: '542' quality_controlled: '1' scopus_import: 1 status: public title: A point calculus for interlevel set homology type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 33 year: '2012' ... --- _id: '6588' abstract: - lang: eng text: First we note that the best polynomial approximation to vertical bar x vertical bar on the set, which consists of an interval on the positive half-axis and a point on the negative half-axis, can be given by means of the classical Chebyshev polynomials. Then we explore the cases when a solution of the related problem on two intervals can be given in elementary functions. acknowledgement: "This work is supported by the Austrian Science Fund (FWF), Project P22025-N18.\r\n" article_processing_charge: No article_type: original author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Pausinger F. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 2012;8(1):63-78. apa: Pausinger, F. (2012). Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. B. Verkin Institute for Low Temperature Physics and Engineering. chicago: Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.” Journal of Mathematical Physics, Analysis, Geometry. B. Verkin Institute for Low Temperature Physics and Engineering, 2012. ieee: F. Pausinger, “Elementary solutions of the Bernstein problem on two intervals,” Journal of Mathematical Physics, Analysis, Geometry, vol. 8, no. 1. B. Verkin Institute for Low Temperature Physics and Engineering, pp. 63–78, 2012. ista: Pausinger F. 2012. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 8(1), 63–78. mla: Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.” Journal of Mathematical Physics, Analysis, Geometry, vol. 8, no. 1, B. Verkin Institute for Low Temperature Physics and Engineering, 2012, pp. 63–78. short: F. Pausinger, Journal of Mathematical Physics, Analysis, Geometry 8 (2012) 63–78. date_created: 2019-06-27T08:16:56Z date_published: 2012-01-01T00:00:00Z date_updated: 2023-10-16T09:41:31Z day: '01' department: - _id: HeEd external_id: isi: - '000301173600004' intvolume: ' 8' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://mi.mathnet.ru/eng/jmag525 month: '01' oa: 1 oa_version: Published Version page: 63-78 publication: Journal of Mathematical Physics, Analysis, Geometry publication_identifier: issn: - 1812-9471 publication_status: published publisher: B. Verkin Institute for Low Temperature Physics and Engineering quality_controlled: '1' scopus_import: '1' status: public title: Elementary solutions of the Bernstein problem on two intervals type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8 year: '2012' ... --- _id: '2912' article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Nataliya full_name: Strelkova, Nataliya last_name: Strelkova citation: ama: Edelsbrunner H, Strelkova N. On the configuration space for the shortest networks. Russian Mathematical Surveys. 2012;67(6):1167–1168. doi:10.4213/rm9503 apa: Edelsbrunner, H., & Strelkova, N. (2012). On the configuration space for the shortest networks. Russian Mathematical Surveys. Russian Academy of Sciences. https://doi.org/10.4213/rm9503 chicago: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space for the Shortest Networks.” Russian Mathematical Surveys. Russian Academy of Sciences, 2012. https://doi.org/10.4213/rm9503. ieee: H. Edelsbrunner and N. Strelkova, “On the configuration space for the shortest networks,” Russian Mathematical Surveys, vol. 67, no. 6. Russian Academy of Sciences, pp. 1167–1168, 2012. ista: Edelsbrunner H, Strelkova N. 2012. On the configuration space for the shortest networks. Russian Mathematical Surveys. 67(6), 1167–1168. mla: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space for the Shortest Networks.” Russian Mathematical Surveys, vol. 67, no. 6, Russian Academy of Sciences, 2012, pp. 1167–1168, doi:10.4213/rm9503. short: H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168. date_created: 2018-12-11T12:00:18Z date_published: 2012-10-01T00:00:00Z date_updated: 2023-10-17T11:40:39Z day: '01' department: - _id: HeEd doi: 10.4213/rm9503 intvolume: ' 67' issue: '6' language: - iso: eng month: '10' oa_version: None page: 1167–1168 publication: Russian Mathematical Surveys publication_status: published publisher: Russian Academy of Sciences publist_id: '3831' quality_controlled: '1' status: public title: On the configuration space for the shortest networks type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 67 year: '2012' ... --- _id: '3127' abstract: - lang: eng text: "When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques.\r\n We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data, we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations." article_processing_charge: No author: - first_name: Novi full_name: Quadrianto, Novi last_name: Quadrianto - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen citation: ama: 'Quadrianto N, Lampert C, Chen C. The most persistent soft-clique in a set of sampled graphs. In: Proceedings of the 29th International Conference on Machine Learning. ML Research Press; 2012:211-218.' apa: 'Quadrianto, N., Lampert, C., & Chen, C. (2012). The most persistent soft-clique in a set of sampled graphs. In Proceedings of the 29th International Conference on Machine Learning (pp. 211–218). Edinburgh, United Kingdom: ML Research Press.' chicago: Quadrianto, Novi, Christoph Lampert, and Chao Chen. “The Most Persistent Soft-Clique in a Set of Sampled Graphs.” In Proceedings of the 29th International Conference on Machine Learning, 211–18. ML Research Press, 2012. ieee: N. Quadrianto, C. Lampert, and C. Chen, “The most persistent soft-clique in a set of sampled graphs,” in Proceedings of the 29th International Conference on Machine Learning, Edinburgh, United Kingdom, 2012, pp. 211–218. ista: 'Quadrianto N, Lampert C, Chen C. 2012. The most persistent soft-clique in a set of sampled graphs. Proceedings of the 29th International Conference on Machine Learning. ICML: International Conference on Machine Learning, 211–218.' mla: Quadrianto, Novi, et al. “The Most Persistent Soft-Clique in a Set of Sampled Graphs.” Proceedings of the 29th International Conference on Machine Learning, ML Research Press, 2012, pp. 211–18. short: N. Quadrianto, C. Lampert, C. Chen, in:, Proceedings of the 29th International Conference on Machine Learning, ML Research Press, 2012, pp. 211–218. conference: end_date: 2012-07-01 location: Edinburgh, United Kingdom name: 'ICML: International Conference on Machine Learning' start_date: 2012-06-26 date_created: 2018-12-11T12:01:33Z date_published: 2012-06-01T00:00:00Z date_updated: 2023-10-17T11:55:06Z day: '01' department: - _id: ChLa - _id: HeEd language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1206.4652 month: '06' oa: 1 oa_version: Preprint page: 211-218 publication: Proceedings of the 29th International Conference on Machine Learning publication_status: published publisher: ML Research Press publist_id: '3572' quality_controlled: '1' scopus_import: '1' status: public title: The most persistent soft-clique in a set of sampled graphs type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '2904' abstract: - lang: eng text: Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base b and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form P(i) = ai (mod b) for coprime integers a and b. We show that multipliers a that either divide b - 1 or b + 1 generate van der Corput sequences with weak distribution properties. We give explicit lower bounds for the asymptotic distribution behavior of these sequences and relate them to sequences generated from the identity permutation in smaller bases, which are, due to Faure, the weakest distributed generalized van der Corput sequences. - lang: fre text: Les suites de Van der Corput généralisées sont dessuites unidimensionnelles et infinies dans l’intervalle de l’unité.Elles sont générées par permutations des entiers de la basebetsont les éléments constitutifs des suites multi-dimensionnelles deHalton. Suites aux progrès récents d’Atanassov concernant le com-portement de distribution uniforme des suites de Halton nous nousintéressons aux permutations de la formuleP(i) =ai(modb)pour les entiers premiers entre euxaetb. Dans cet article nousidentifions des multiplicateursagénérant des suites de Van derCorput ayant une mauvaise distribution. Nous donnons les bornesinférieures explicites pour cette distribution asymptotique asso-ciée à ces suites et relions ces dernières aux suites générées parpermutation d’identité, qui sont, selon Faure, les moins bien dis-tribuées des suites généralisées de Van der Corput dans une basedonnée. article_processing_charge: No article_type: original author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Pausinger F. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 2012;24(3):729-749. doi:10.5802/jtnb.819 apa: Pausinger, F. (2012). Weak multipliers for generalized van der Corput sequences. Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux. https://doi.org/10.5802/jtnb.819 chicago: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux, 2012. https://doi.org/10.5802/jtnb.819. ieee: F. Pausinger, “Weak multipliers for generalized van der Corput sequences,” Journal de Theorie des Nombres des Bordeaux, vol. 24, no. 3. Université de Bordeaux, pp. 729–749, 2012. ista: Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749. mla: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” Journal de Theorie Des Nombres Des Bordeaux, vol. 24, no. 3, Université de Bordeaux, 2012, pp. 729–49, doi:10.5802/jtnb.819. short: F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749. date_created: 2018-12-11T12:00:15Z date_published: 2012-01-01T00:00:00Z date_updated: 2023-10-18T07:53:47Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.5802/jtnb.819 file: - access_level: open_access checksum: 6954bfe9d7f4119fbdda7a11cf0f5c67 content_type: application/pdf creator: dernst date_created: 2020-05-11T12:40:39Z date_updated: 2020-07-14T12:45:52Z file_id: '7819' file_name: JTNB_2012__24_3_729_0.pdf file_size: 819275 relation: main_file file_date_updated: 2020-07-14T12:45:52Z has_accepted_license: '1' intvolume: ' 24' issue: '3' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 729 - 749 publication: Journal de Theorie des Nombres des Bordeaux publication_identifier: eissn: - 2118-8572 issn: - 1246-7405 publication_status: published publisher: Université de Bordeaux publist_id: '3843' quality_controlled: '1' scopus_import: '1' status: public title: Weak multipliers for generalized van der Corput sequences type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2012' ... --- _id: '2902' abstract: - lang: eng text: 'We present an algorithm for simplifying linear cartographic objects and results obtained with a computer program implementing this algorithm. ' article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Oleg full_name: Musin, Oleg last_name: Musin - first_name: Alexey full_name: Ukhalov, Alexey last_name: Ukhalov - first_name: Olga full_name: Yakimova, Olga last_name: Yakimova - first_name: Vladislav full_name: Alexeev, Vladislav last_name: Alexeev - first_name: Victoriya full_name: Bogaevskaya, Victoriya last_name: Bogaevskaya - first_name: Andrey full_name: Gorohov, Andrey last_name: Gorohov - first_name: Margarita full_name: Preobrazhenskaya, Margarita last_name: Preobrazhenskaya citation: ama: Edelsbrunner H, Musin O, Ukhalov A, et al. Fractal and computational geometry for generalizing cartographic objects. Modeling and Analysis of Information Systems. 2012;19(6):152-160. apa: Edelsbrunner, H., Musin, O., Ukhalov, A., Yakimova, O., Alexeev, V., Bogaevskaya, V., … Preobrazhenskaya, M. (2012). Fractal and computational geometry for generalizing cartographic objects. Modeling and Analysis of Information Systems. Russian Academy of Sciences. chicago: Edelsbrunner, Herbert, Oleg Musin, Alexey Ukhalov, Olga Yakimova, Vladislav Alexeev, Victoriya Bogaevskaya, Andrey Gorohov, and Margarita Preobrazhenskaya. “Fractal and computational geometry for generalizing cartographic objects.” Modeling and Analysis of Information Systems. Russian Academy of Sciences, 2012. ieee: H. Edelsbrunner et al., “Fractal and computational geometry for generalizing cartographic objects,” Modeling and Analysis of Information Systems, vol. 19, no. 6. Russian Academy of Sciences, pp. 152–160, 2012. ista: Edelsbrunner H, Musin O, Ukhalov A, Yakimova O, Alexeev V, Bogaevskaya V, Gorohov A, Preobrazhenskaya M. 2012. Fractal and computational geometry for generalizing cartographic objects. Modeling and Analysis of Information Systems. 19(6), 152–160. mla: Edelsbrunner, Herbert, et al. “Fractal and computational geometry for generalizing cartographic objects.” Modeling and Analysis of Information Systems, vol. 19, no. 6, Russian Academy of Sciences, 2012, pp. 152–60. short: H. Edelsbrunner, O. Musin, A. Ukhalov, O. Yakimova, V. Alexeev, V. Bogaevskaya, A. Gorohov, M. Preobrazhenskaya, Modeling and Analysis of Information Systems 19 (2012) 152–160. date_created: 2018-12-11T12:00:15Z date_published: 2012-12-01T00:00:00Z date_updated: 2023-10-18T07:34:45Z day: '01' department: - _id: HeEd intvolume: ' 19' issue: '6' language: - iso: rus main_file_link: - open_access: '1' url: http://mi.mathnet.ru/eng/mais280 month: '12' oa: 1 oa_version: Published Version page: 152 - 160 publication: Modeling and Analysis of Information Systems publication_status: published publisher: Russian Academy of Sciences publist_id: '3845' quality_controlled: '1' status: public title: Fractal and computational geometry for generalizing cartographic objects type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 19 year: '2012' ... --- _id: '3266' abstract: - lang: eng text: We present a joint image segmentation and labeling model (JSL) which, given a bag of figure-ground segment hypotheses extracted at multiple image locations and scales, constructs a joint probability distribution over both the compatible image interpretations (tilings or image segmentations) composed from those segments, and over their labeling into categories. The process of drawing samples from the joint distribution can be interpreted as first sampling tilings, modeled as maximal cliques, from a graph connecting spatially non-overlapping segments in the bag [1], followed by sampling labels for those segments, conditioned on the choice of a particular tiling. We learn the segmentation and labeling parameters jointly, based on Maximum Likelihood with a novel Incremental Saddle Point estimation procedure. The partition function over tilings and labelings is increasingly more accurately approximated by including incorrect configurations that a not-yet-competent model rates probable during learning. We show that the proposed methodologymatches the current state of the art in the Stanford dataset [2], as well as in VOC2010, where 41.7% accuracy on the test set is achieved. author: - first_name: Adrian full_name: Ion, Adrian id: 29F89302-F248-11E8-B48F-1D18A9856A87 last_name: Ion - first_name: Joao full_name: Carreira, Joao last_name: Carreira - first_name: Cristian full_name: Sminchisescu, Cristian last_name: Sminchisescu citation: ama: 'Ion A, Carreira J, Sminchisescu C. Probabilistic joint image segmentation and labeling. In: NIPS Proceedings. Vol 24. Neural Information Processing Systems Foundation; 2011:1827-1835.' apa: 'Ion, A., Carreira, J., & Sminchisescu, C. (2011). Probabilistic joint image segmentation and labeling. In NIPS Proceedings (Vol. 24, pp. 1827–1835). Granada, Spain: Neural Information Processing Systems Foundation.' chicago: Ion, Adrian, Joao Carreira, and Cristian Sminchisescu. “Probabilistic Joint Image Segmentation and Labeling.” In NIPS Proceedings, 24:1827–35. Neural Information Processing Systems Foundation, 2011. ieee: A. Ion, J. Carreira, and C. Sminchisescu, “Probabilistic joint image segmentation and labeling,” in NIPS Proceedings, Granada, Spain, 2011, vol. 24, pp. 1827–1835. ista: 'Ion A, Carreira J, Sminchisescu C. 2011. Probabilistic joint image segmentation and labeling. NIPS Proceedings. NIPS: Neural Information Processing Systems vol. 24, 1827–1835.' mla: Ion, Adrian, et al. “Probabilistic Joint Image Segmentation and Labeling.” NIPS Proceedings, vol. 24, Neural Information Processing Systems Foundation, 2011, pp. 1827–35. short: A. Ion, J. Carreira, C. Sminchisescu, in:, NIPS Proceedings, Neural Information Processing Systems Foundation, 2011, pp. 1827–1835. conference: end_date: 2011-12-14 location: Granada, Spain name: 'NIPS: Neural Information Processing Systems' start_date: 2011-12-12 date_created: 2018-12-11T12:02:21Z date_published: 2011-12-01T00:00:00Z date_updated: 2021-01-12T07:42:15Z day: '01' department: - _id: HeEd intvolume: ' 24' language: - iso: eng month: '12' oa_version: None page: 1827 - 1835 publication: NIPS Proceedings publication_status: published publisher: Neural Information Processing Systems Foundation publist_id: '3381' quality_controlled: '1' scopus_import: 1 status: public title: Probabilistic joint image segmentation and labeling type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2011' ... --- _id: '3269' abstract: - lang: eng text: The unintentional scattering of light between neighboring surfaces in complex projection environments increases the brightness and decreases the contrast, disrupting the appearance of the desired imagery. To achieve satisfactory projection results, the inverse problem of global illumination must be solved to cancel this secondary scattering. In this paper, we propose a global illumination cancellation method that minimizes the perceptual difference between the desired imagery and the actual total illumination in the resulting physical environment. Using Gauss-Newton and active set methods, we design a fast solver for the bound constrained nonlinear least squares problem raised by the perceptual error metrics. Our solver is further accelerated with a CUDA implementation and multi-resolution method to achieve 1–2 fps for problems with approximately 3000 variables. We demonstrate the global illumination cancellation algorithm with our multi-projector system. Results show that our method preserves the color fidelity of the desired imagery significantly better than previous methods. article_processing_charge: No article_type: original author: - first_name: Yu full_name: Sheng, Yu last_name: Sheng - first_name: Barbara full_name: Cutler, Barbara last_name: Cutler - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Joshua full_name: Nasman, Joshua last_name: Nasman citation: ama: Sheng Y, Cutler B, Chen C, Nasman J. Perceptual global illumination cancellation in complex projection environments. Computer Graphics Forum. 2011;30(4):1261-1268. doi:10.1111/j.1467-8659.2011.01985.x apa: Sheng, Y., Cutler, B., Chen, C., & Nasman, J. (2011). Perceptual global illumination cancellation in complex projection environments. Computer Graphics Forum. Wiley-Blackwell. https://doi.org/10.1111/j.1467-8659.2011.01985.x chicago: Sheng, Yu, Barbara Cutler, Chao Chen, and Joshua Nasman. “Perceptual Global Illumination Cancellation in Complex Projection Environments.” Computer Graphics Forum. Wiley-Blackwell, 2011. https://doi.org/10.1111/j.1467-8659.2011.01985.x. ieee: Y. Sheng, B. Cutler, C. Chen, and J. Nasman, “Perceptual global illumination cancellation in complex projection environments,” Computer Graphics Forum, vol. 30, no. 4. Wiley-Blackwell, pp. 1261–1268, 2011. ista: Sheng Y, Cutler B, Chen C, Nasman J. 2011. Perceptual global illumination cancellation in complex projection environments. Computer Graphics Forum. 30(4), 1261–1268. mla: Sheng, Yu, et al. “Perceptual Global Illumination Cancellation in Complex Projection Environments.” Computer Graphics Forum, vol. 30, no. 4, Wiley-Blackwell, 2011, pp. 1261–68, doi:10.1111/j.1467-8659.2011.01985.x. short: Y. Sheng, B. Cutler, C. Chen, J. Nasman, Computer Graphics Forum 30 (2011) 1261–1268. date_created: 2018-12-11T12:02:22Z date_published: 2011-07-19T00:00:00Z date_updated: 2021-01-12T07:42:16Z day: '19' department: - _id: HeEd doi: 10.1111/j.1467-8659.2011.01985.x intvolume: ' 30' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://www.cs.cmu.edu/%7Eshengyu/download/egsr2011_paper.pdf month: '07' oa: 1 oa_version: Published Version page: 1261 - 1268 publication: Computer Graphics Forum publication_status: published publisher: Wiley-Blackwell publist_id: '3377' quality_controlled: '1' scopus_import: 1 status: public title: Perceptual global illumination cancellation in complex projection environments type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2011' ... --- _id: '3267' abstract: - lang: eng text: 'We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We study the problem with different measures: volume, diameter and radius. For volume, that is, the 1-norm of a cycle, two main results are presented. First, we prove that the problem is NP-hard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NP-hard to approximate even when the Betti number is O(1). The latter result leads to the inapproximability of the problem of computing the nonbounding cycle with the smallest volume and computing cycles representing a homology basis with the minimal total volume. As for the other two measures defined by pairwise geodesic distance, diameter and radius, we show that the localization problem is NP-hard for diameter but is polynomial for radius. Our work is restricted to homology over the ℤ2 field.' author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Daniel full_name: Freedman, Daniel last_name: Freedman citation: ama: Chen C, Freedman D. Hardness results for homology localization. Discrete & Computational Geometry. 2011;45(3):425-448. doi:10.1007/s00454-010-9322-8 apa: Chen, C., & Freedman, D. (2011). Hardness results for homology localization. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-010-9322-8 chicago: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” Discrete & Computational Geometry. Springer, 2011. https://doi.org/10.1007/s00454-010-9322-8. ieee: C. Chen and D. Freedman, “Hardness results for homology localization,” Discrete & Computational Geometry, vol. 45, no. 3. Springer, pp. 425–448, 2011. ista: Chen C, Freedman D. 2011. Hardness results for homology localization. Discrete & Computational Geometry. 45(3), 425–448. mla: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” Discrete & Computational Geometry, vol. 45, no. 3, Springer, 2011, pp. 425–48, doi:10.1007/s00454-010-9322-8. short: C. Chen, D. Freedman, Discrete & Computational Geometry 45 (2011) 425–448. date_created: 2018-12-11T12:02:21Z date_published: 2011-01-14T00:00:00Z date_updated: 2023-02-21T16:07:10Z day: '14' department: - _id: HeEd doi: 10.1007/s00454-010-9322-8 intvolume: ' 45' issue: '3' language: - iso: eng month: '01' oa_version: None page: 425 - 448 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '3379' quality_controlled: '1' related_material: record: - id: '10909' relation: earlier_version status: public scopus_import: 1 status: public title: Hardness results for homology localization type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 45 year: '2011' ... --- _id: '3335' abstract: - lang: eng text: We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend the information beyond conventional cosmological studies of topology in terms of genus and Euler characteristic. The richer information content of Betti numbers goes along the availability of fast algorithms to compute them. For continuous density fields, we determine the scale-dependence of Betti numbers by invoking the cosmologically familiar filtration of sublevel or superlevel sets defined by density thresholds. For the discrete galaxy distribution, however, the analysis is based on the alpha shapes of the particles. These simplicial complexes constitute an ordered sequence of nested subsets of the Delaunay tessellation, a filtration defined by the scale parameter, α. As they are homotopy equivalent to the sublevel sets of the distance field, they are an excellent tool for assessing the topological structure of a discrete point distribution. In order to develop an intuitive understanding for the behavior of Betti numbers as a function of α, and their relation to the morphological patterns in the Cosmic Web, we first study them within the context of simple heuristic Voronoi clustering models. These can be tuned to consist of specific morphological elements of the Cosmic Web, i.e. clusters, filaments, or sheets. To elucidate the relative prominence of the various Betti numbers in different stages of morphological evolution, we introduce the concept of alpha tracks. Subsequently, we address the topology of structures emerging in the standard LCDM scenario and in cosmological scenarios with alternative dark energy content. The evolution of the Betti numbers is shown to reflect the hierarchical evolution of the Cosmic Web. We also demonstrate that the scale-dependence of the Betti numbers yields a promising measure of cosmological parameters, with a potential to help in determining the nature of dark energy and to probe primordial non-Gaussianities. We also discuss the expected Betti numbers as a function of the density threshold for superlevel sets of a Gaussian random field. Finally, we introduce the concept of persistent homology. It measures scale levels of the mass distribution and allows us to separate small from large scale features. Within the context of the hierarchical cosmic structure formation, persistence provides a natural formalism for a multiscale topology study of the Cosmic Web. alternative_title: - LNCS author: - first_name: Rien full_name: Van De Weygaert, Rien last_name: Van De Weygaert - first_name: Gert full_name: Vegter, Gert last_name: Vegter - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Bernard full_name: Jones, Bernard last_name: Jones - first_name: Pratyush full_name: Pranav, Pratyush last_name: Pranav - first_name: Changbom full_name: Park, Changbom last_name: Park - first_name: Wojciech full_name: Hellwing, Wojciech last_name: Hellwing - first_name: Bob full_name: Eldering, Bob last_name: Eldering - first_name: Nico full_name: Kruithof, Nico last_name: Kruithof - first_name: Patrick full_name: Bos, Patrick last_name: Bos - first_name: Johan full_name: Hidding, Johan last_name: Hidding - first_name: Job full_name: Feldbrugge, Job last_name: Feldbrugge - first_name: Eline full_name: Ten Have, Eline last_name: Ten Have - first_name: Matti full_name: Van Engelen, Matti last_name: Van Engelen - first_name: Manuel full_name: Caroli, Manuel last_name: Caroli - first_name: Monique full_name: Teillaud, Monique last_name: Teillaud citation: ama: 'Van De Weygaert R, Vegter G, Edelsbrunner H, et al. Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web. In: Gavrilova M, Tan K, Mostafavi M, eds. Transactions on Computational Science XIV. Vol 6970. Special Issue on Voronoi Diagrams and Delaunay Triangulation. Springer; 2011:60-101. doi:10.1007/978-3-642-25249-5_3' apa: 'Van De Weygaert, R., Vegter, G., Edelsbrunner, H., Jones, B., Pranav, P., Park, C., … Teillaud, M. (2011). Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web. In M. Gavrilova, K. Tan, & M. Mostafavi (Eds.), Transactions on Computational Science XIV (Vol. 6970, pp. 60–101). Springer. https://doi.org/10.1007/978-3-642-25249-5_3' chicago: 'Van De Weygaert, Rien, Gert Vegter, Herbert Edelsbrunner, Bernard Jones, Pratyush Pranav, Changbom Park, Wojciech Hellwing, et al. “Alpha, Betti and the Megaparsec Universe: On the Topology of the Cosmic Web.” In Transactions on Computational Science XIV, edited by Marina Gavrilova, Kenneth Tan, and Mir Mostafavi, 6970:60–101. Special Issue on Voronoi Diagrams and Delaunay Triangulation. Springer, 2011. https://doi.org/10.1007/978-3-642-25249-5_3.' ieee: 'R. Van De Weygaert et al., “Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web,” in Transactions on Computational Science XIV, vol. 6970, M. Gavrilova, K. Tan, and M. Mostafavi, Eds. Springer, 2011, pp. 60–101.' ista: 'Van De Weygaert R, Vegter G, Edelsbrunner H, Jones B, Pranav P, Park C, Hellwing W, Eldering B, Kruithof N, Bos P, Hidding J, Feldbrugge J, Ten Have E, Van Engelen M, Caroli M, Teillaud M. 2011.Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web. In: Transactions on Computational Science XIV. LNCS, vol. 6970, 60–101.' mla: 'Van De Weygaert, Rien, et al. “Alpha, Betti and the Megaparsec Universe: On the Topology of the Cosmic Web.” Transactions on Computational Science XIV, edited by Marina Gavrilova et al., vol. 6970, Springer, 2011, pp. 60–101, doi:10.1007/978-3-642-25249-5_3.' short: R. Van De Weygaert, G. Vegter, H. Edelsbrunner, B. Jones, P. Pranav, C. Park, W. Hellwing, B. Eldering, N. Kruithof, P. Bos, J. Hidding, J. Feldbrugge, E. Ten Have, M. Van Engelen, M. Caroli, M. Teillaud, in:, M. Gavrilova, K. Tan, M. Mostafavi (Eds.), Transactions on Computational Science XIV, Springer, 2011, pp. 60–101. date_created: 2018-12-11T12:02:44Z date_published: 2011-11-09T00:00:00Z date_updated: 2021-01-12T07:42:44Z day: '09' department: - _id: HeEd doi: 10.1007/978-3-642-25249-5_3 editor: - first_name: Marina full_name: Gavrilova, Marina last_name: Gavrilova - first_name: Kenneth full_name: Tan, Kenneth last_name: Tan - first_name: Mir full_name: Mostafavi, Mir last_name: Mostafavi external_id: arxiv: - '1306.3640' intvolume: ' 6970' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1306.3640 month: '11' oa: 1 oa_version: Preprint page: 60 - 101 publication: Transactions on Computational Science XIV publication_status: published publisher: Springer publist_id: '3295' quality_controlled: '1' scopus_import: 1 series_title: Special Issue on Voronoi Diagrams and Delaunay Triangulation status: public title: 'Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web' type: book_chapter user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 6970 year: '2011' ... --- _id: '3329' abstract: - lang: eng text: 'We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance µ in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution shape P; then, P''s offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(n log n)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. An alternative algorithm, based purely on rational arithmetic, answers the same deconstruction problem, up to an uncertainty parameter, and its running time depends on the parameter δ (in addition to the other input parameters: n, δ and the radius of the disk). If the input shape is found to be approximable, the rational-arithmetic algorithm also computes an approximate solution shape for the problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution shape P with at most one more vertex than a vertex-minimal one. Our study is motivated by applications from two different domains. However, since the offset operation has numerous uses, we anticipate that the reverse question that we study here will be still more broadly applicable. We present results obtained with our implementation of the rational-arithmetic algorithm.' author: - first_name: Eric full_name: Berberich, Eric last_name: Berberich - first_name: Dan full_name: Halperin, Dan last_name: Halperin - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Roza full_name: Pogalnikova, Roza last_name: Pogalnikova citation: ama: 'Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate offsets. In: Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry. ACM; 2011:187-196. doi:10.1145/1998196.1998225' apa: 'Berberich, E., Halperin, D., Kerber, M., & Pogalnikova, R. (2011). Deconstructing approximate offsets. In Proceedings of the twenty-seventh annual symposium on Computational geometry (pp. 187–196). Paris, France: ACM. https://doi.org/10.1145/1998196.1998225' chicago: Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing Approximate Offsets.” In Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry, 187–96. ACM, 2011. https://doi.org/10.1145/1998196.1998225. ieee: E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing approximate offsets,” in Proceedings of the twenty-seventh annual symposium on Computational geometry, Paris, France, 2011, pp. 187–196. ista: 'Berberich E, Halperin D, Kerber M, Pogalnikova R. 2011. Deconstructing approximate offsets. Proceedings of the twenty-seventh annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 187–196.' mla: Berberich, Eric, et al. “Deconstructing Approximate Offsets.” Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry, ACM, 2011, pp. 187–96, doi:10.1145/1998196.1998225. short: E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, in:, Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry, ACM, 2011, pp. 187–196. conference: end_date: 2011-06-15 location: Paris, France name: 'SCG: Symposium on Computational Geometry' start_date: 2011-06-13 date_created: 2018-12-11T12:02:42Z date_published: 2011-06-13T00:00:00Z date_updated: 2023-02-23T11:12:57Z day: '13' department: - _id: HeEd doi: 10.1145/1998196.1998225 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1109.2158 month: '06' oa: 1 oa_version: Preprint page: 187 - 196 publication: Proceedings of the twenty-seventh annual symposium on Computational geometry publication_status: published publisher: ACM publist_id: '3306' quality_controlled: '1' related_material: record: - id: '3115' relation: later_version status: public scopus_import: 1 status: public title: Deconstructing approximate offsets type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3332' abstract: - lang: eng text: Given an algebraic hypersurface O in ℝd, how many simplices are necessary for a simplicial complex isotopic to O? We address this problem and the variant where all vertices of the complex must lie on O. We give asymptotically tight worst-case bounds for algebraic plane curves. Our results gradually improve known bounds in higher dimensions; however, the question for tight bounds remains unsolved for d ≥ 3. article_processing_charge: No article_type: original author: - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Michael full_name: Sagraloff, Michael last_name: Sagraloff citation: ama: Kerber M, Sagraloff M. A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics. 2011;27(3):419-430. doi:10.1007/s00373-011-1020-7 apa: Kerber, M., & Sagraloff, M. (2011). A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics. Springer. https://doi.org/10.1007/s00373-011-1020-7 chicago: Kerber, Michael, and Michael Sagraloff. “A Note on the Complexity of Real Algebraic Hypersurfaces.” Graphs and Combinatorics. Springer, 2011. https://doi.org/10.1007/s00373-011-1020-7. ieee: M. Kerber and M. Sagraloff, “A note on the complexity of real algebraic hypersurfaces,” Graphs and Combinatorics, vol. 27, no. 3. Springer, pp. 419–430, 2011. ista: Kerber M, Sagraloff M. 2011. A note on the complexity of real algebraic hypersurfaces. Graphs and Combinatorics. 27(3), 419–430. mla: Kerber, Michael, and Michael Sagraloff. “A Note on the Complexity of Real Algebraic Hypersurfaces.” Graphs and Combinatorics, vol. 27, no. 3, Springer, 2011, pp. 419–30, doi:10.1007/s00373-011-1020-7. short: M. Kerber, M. Sagraloff, Graphs and Combinatorics 27 (2011) 419–430. date_created: 2018-12-11T12:02:43Z date_published: 2011-03-17T00:00:00Z date_updated: 2021-01-12T07:42:43Z day: '17' ddc: - '500' department: - _id: HeEd doi: 10.1007/s00373-011-1020-7 file: - access_level: open_access checksum: a63a1e3e885dcc68f1e3dea68dfbe213 content_type: application/pdf creator: dernst date_created: 2020-05-19T16:11:36Z date_updated: 2020-07-14T12:46:08Z file_id: '7869' file_name: 2011_GraphsCombi_Kerber.pdf file_size: 143976 relation: main_file file_date_updated: 2020-07-14T12:46:08Z has_accepted_license: '1' intvolume: ' 27' issue: '3' language: - iso: eng month: '03' oa: 1 oa_version: Submitted Version page: 419 - 430 publication: Graphs and Combinatorics publication_status: published publisher: Springer publist_id: '3301' quality_controlled: '1' scopus_import: 1 status: public title: A note on the complexity of real algebraic hypersurfaces type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 27 year: '2011' ... --- _id: '3330' abstract: - lang: eng text: We consider the problem of approximating all real roots of a square-free polynomial f. Given isolating intervals, our algorithm refines each of them to a width at most 2-L, that is, each of the roots is approximated to L bits after the binary point. Our method provides a certified answer for arbitrary real polynomials, only requiring finite approximations of the polynomial coefficient and choosing a suitable working precision adaptively. In this way, we get a correct algorithm that is simple to implement and practically efficient. Our algorithm uses the quadratic interval refinement method; we adapt that method to be able to cope with inaccuracies when evaluating f, without sacrificing its quadratic convergence behavior. We prove a bound on the bit complexity of our algorithm in terms of degree, coefficient size and discriminant. Our bound improves previous work on integer polynomials by a factor of deg f and essentially matches best known theoretical bounds on root approximation which are obtained by very sophisticated algorithms. article_processing_charge: No author: - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Michael full_name: Sagraloff, Michael last_name: Sagraloff citation: ama: 'Kerber M, Sagraloff M. Root refinement for real polynomials. In: Springer; 2011:209-216. doi:10.1145/1993886.1993920' apa: 'Kerber, M., & Sagraloff, M. (2011). Root refinement for real polynomials (pp. 209–216). Presented at the ISSAC: International Symposium on Symbolic and Algebraic Computation, California, USA: Springer. https://doi.org/10.1145/1993886.1993920' chicago: Kerber, Michael, and Michael Sagraloff. “Root Refinement for Real Polynomials,” 209–16. Springer, 2011. https://doi.org/10.1145/1993886.1993920. ieee: 'M. Kerber and M. Sagraloff, “Root refinement for real polynomials,” presented at the ISSAC: International Symposium on Symbolic and Algebraic Computation, California, USA, 2011, pp. 209–216.' ista: 'Kerber M, Sagraloff M. 2011. Root refinement for real polynomials. ISSAC: International Symposium on Symbolic and Algebraic Computation, 209–216.' mla: Kerber, Michael, and Michael Sagraloff. Root Refinement for Real Polynomials. Springer, 2011, pp. 209–16, doi:10.1145/1993886.1993920. short: M. Kerber, M. Sagraloff, in:, Springer, 2011, pp. 209–216. conference: end_date: 2011-06-11 location: California, USA name: 'ISSAC: International Symposium on Symbolic and Algebraic Computation' start_date: 2011-06-08 date_created: 2018-12-11T12:02:43Z date_published: 2011-06-08T00:00:00Z date_updated: 2021-01-12T07:42:42Z day: '08' department: - _id: HeEd doi: 10.1145/1993886.1993920 external_id: arxiv: - '1104.1362' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1104.1362 month: '06' oa: 1 oa_version: Preprint page: 209 - 216 publication_status: published publisher: Springer publist_id: '3304' quality_controlled: '1' scopus_import: 1 status: public title: Root refinement for real polynomials type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3328' abstract: - lang: eng text: 'We report on a generic uni- and bivariate algebraic kernel that is publicly available with CGAL 3.7. It comprises complete, correct, though efficient state-of-the-art implementations on polynomials, roots of polynomial systems, and the support to analyze algebraic curves defined by bivariate polynomials. The kernel design is generic, that is, various number types and substeps can be exchanged. It is accompanied with a ready-to-use interface to enable arrangements induced by algebraic curves, that have already been used as basis for various geometric applications, as arrangements on Dupin cyclides or the triangulation of algebraic surfaces. We present two novel applications: arrangements of rotated algebraic curves and Boolean set operations on polygons bounded by segments of algebraic curves. We also provide experiments showing that our general implementation is competitive and even often clearly outperforms existing implementations that are explicitly tailored for specific types of non-linear curves that are available in CGAL.' article_processing_charge: No author: - first_name: Eric full_name: Berberich, Eric last_name: Berberich - first_name: Michael full_name: Hemmer, Michael last_name: Hemmer - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Berberich E, Hemmer M, Kerber M. A generic algebraic kernel for non linear geometric applications. In: ACM; 2011:179-186. doi:10.1145/1998196.1998224' apa: 'Berberich, E., Hemmer, M., & Kerber, M. (2011). A generic algebraic kernel for non linear geometric applications (pp. 179–186). Presented at the SCG: Symposium on Computational Geometry, Paris, France: ACM. https://doi.org/10.1145/1998196.1998224' chicago: Berberich, Eric, Michael Hemmer, and Michael Kerber. “A Generic Algebraic Kernel for Non Linear Geometric Applications,” 179–86. ACM, 2011. https://doi.org/10.1145/1998196.1998224. ieee: 'E. Berberich, M. Hemmer, and M. Kerber, “A generic algebraic kernel for non linear geometric applications,” presented at the SCG: Symposium on Computational Geometry, Paris, France, 2011, pp. 179–186.' ista: 'Berberich E, Hemmer M, Kerber M. 2011. A generic algebraic kernel for non linear geometric applications. SCG: Symposium on Computational Geometry, 179–186.' mla: Berberich, Eric, et al. A Generic Algebraic Kernel for Non Linear Geometric Applications. ACM, 2011, pp. 179–86, doi:10.1145/1998196.1998224. short: E. Berberich, M. Hemmer, M. Kerber, in:, ACM, 2011, pp. 179–186. conference: end_date: 2011-06-15 location: Paris, France name: 'SCG: Symposium on Computational Geometry' start_date: 2011-06-13 date_created: 2018-12-11T12:02:42Z date_published: 2011-06-13T00:00:00Z date_updated: 2021-01-12T07:42:41Z day: '13' department: - _id: HeEd doi: 10.1145/1998196.1998224 language: - iso: eng main_file_link: - open_access: '1' url: https://hal.inria.fr/inria-00480031/file/RR-7274.pdf month: '06' oa: 1 oa_version: Published Version page: 179 - 186 publication_status: published publisher: ACM publist_id: '3307' quality_controlled: '1' scopus_import: 1 status: public title: A generic algebraic kernel for non linear geometric applications type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3334' article_type: letter_note author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: János full_name: Pach, János last_name: Pach - first_name: Günter full_name: Ziegler, Günter last_name: Ziegler citation: ama: Edelsbrunner H, Pach J, Ziegler G. Letter from the new editors-in-chief. Discrete & Computational Geometry. 2011;45(1):1-2. doi:10.1007/s00454-010-9313-9 apa: Edelsbrunner, H., Pach, J., & Ziegler, G. (2011). Letter from the new editors-in-chief. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-010-9313-9 chicago: Edelsbrunner, Herbert, János Pach, and Günter Ziegler. “Letter from the New Editors-in-Chief.” Discrete & Computational Geometry. Springer, 2011. https://doi.org/10.1007/s00454-010-9313-9. ieee: H. Edelsbrunner, J. Pach, and G. Ziegler, “Letter from the new editors-in-chief,” Discrete & Computational Geometry, vol. 45, no. 1. Springer, pp. 1–2, 2011. ista: Edelsbrunner H, Pach J, Ziegler G. 2011. Letter from the new editors-in-chief. Discrete & Computational Geometry. 45(1), 1–2. mla: Edelsbrunner, Herbert, et al. “Letter from the New Editors-in-Chief.” Discrete & Computational Geometry, vol. 45, no. 1, Springer, 2011, pp. 1–2, doi:10.1007/s00454-010-9313-9. short: H. Edelsbrunner, J. Pach, G. Ziegler, Discrete & Computational Geometry 45 (2011) 1–2. date_created: 2018-12-11T12:02:44Z date_published: 2011-01-01T00:00:00Z date_updated: 2021-01-12T07:42:44Z day: '01' department: - _id: HeEd doi: 10.1007/s00454-010-9313-9 intvolume: ' 45' issue: '1' language: - iso: eng month: '01' oa_version: None page: 1 - 2 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '3297' quality_controlled: '1' scopus_import: 1 status: public title: Letter from the new editors-in-chief type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 45 year: '2011' ... --- _id: '3367' abstract: - lang: eng text: In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ>0, it returns only those homology classes with persistence at least Γ. Instead of the classical reduction via column operations, our algorithm performs rank computations on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0,1), the running time is O(C(1-δ)ΓR(n)log n), where C(1-δ)Γ is the number of homology classes with persistence at least (1-δ)Γ, n is the total number of simplices, and R(n) is the complexity of computing the rank of an n x n matrix with O(n) nonzero entries. Depending on the choice of the rank algorithm, this yields a deterministic O(C(1-δ)Γn2.376) algorithm, a O(C(1-δ)Γn2.28) Las-Vegas algorithm, or a O(C(1-δ)Γn2+ε) Monte-Carlo algorithm for an arbitrary ε>0. article_processing_charge: No author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Chen C, Kerber M. An output sensitive algorithm for persistent homology. In: ACM; 2011:207-216. doi:10.1145/1998196.1998228' apa: 'Chen, C., & Kerber, M. (2011). An output sensitive algorithm for persistent homology (pp. 207–216). Presented at the SoCG: Symposium on Computational Geometry, Paris, France: ACM. https://doi.org/10.1145/1998196.1998228' chicago: Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology,” 207–16. ACM, 2011. https://doi.org/10.1145/1998196.1998228. ieee: 'C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,” presented at the SoCG: Symposium on Computational Geometry, Paris, France, 2011, pp. 207–216.' ista: 'Chen C, Kerber M. 2011. An output sensitive algorithm for persistent homology. SoCG: Symposium on Computational Geometry, 207–216.' mla: Chen, Chao, and Michael Kerber. An Output Sensitive Algorithm for Persistent Homology. ACM, 2011, pp. 207–16, doi:10.1145/1998196.1998228. short: C. Chen, M. Kerber, in:, ACM, 2011, pp. 207–216. conference: end_date: 2011-06-15 location: Paris, France name: 'SoCG: Symposium on Computational Geometry' start_date: 2011-06-13 date_created: 2018-12-11T12:02:56Z date_published: 2011-06-13T00:00:00Z date_updated: 2023-02-23T11:05:04Z day: '13' department: - _id: HeEd doi: 10.1145/1998196.1998228 language: - iso: eng month: '06' oa_version: None page: 207 - 216 publication_status: published publisher: ACM publist_id: '3245' quality_controlled: '1' related_material: record: - id: '2939' relation: later_version status: public scopus_import: 1 status: public title: An output sensitive algorithm for persistent homology type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3781' abstract: - lang: eng text: We bound the difference in length of two curves in terms of their total curvatures and the Fréchet distance. The bound is independent of the dimension of the ambient Euclidean space, it improves upon a bound by Cohen-Steiner and Edelsbrunner, and it generalizes a result by Fáry and Chakerian. acknowledgement: Funded by Graduate Aid in Areas of National Need (GAANN) Fellowship. author: - first_name: Brittany Terese full_name: Fasy, Brittany Terese id: F65D502E-E68D-11E9-9252-C644099818F6 last_name: Fasy citation: ama: Fasy BT. The difference in length of curves in R^n. Acta Sci Math (Szeged). 2011;77(1-2):359-367. apa: Fasy, B. T. (2011). The difference in length of curves in R^n. Acta Sci. Math. (Szeged). Szegedi Tudományegyetem. chicago: Fasy, Brittany Terese. “The Difference in Length of Curves in R^n.” Acta Sci. Math. (Szeged). Szegedi Tudományegyetem, 2011. ieee: B. T. Fasy, “The difference in length of curves in R^n,” Acta Sci. Math. (Szeged), vol. 77, no. 1–2. Szegedi Tudományegyetem, pp. 359–367, 2011. ista: Fasy BT. 2011. The difference in length of curves in R^n. Acta Sci. Math. (Szeged). 77(1–2), 359–367. mla: Fasy, Brittany Terese. “The Difference in Length of Curves in R^n.” Acta Sci. Math. (Szeged), vol. 77, no. 1–2, Szegedi Tudományegyetem, 2011, pp. 359–67. short: B.T. Fasy, Acta Sci. Math. (Szeged) 77 (2011) 359–367. date_created: 2018-12-11T12:05:08Z date_published: 2011-01-01T00:00:00Z date_updated: 2021-01-12T07:52:09Z day: '01' department: - _id: HeEd intvolume: ' 77' issue: 1-2 language: - iso: eng month: '01' oa_version: None page: 359 - 367 publication: Acta Sci. Math. (Szeged) publication_status: published publisher: Szegedi Tudományegyetem publist_id: '2446' quality_controlled: '1' status: public title: The difference in length of curves in R^n type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 77 year: '2011' ... --- _id: '3796' abstract: - lang: eng text: We address the problem of covering ℝ n with congruent balls, while minimizing the number of balls that contain an average point. Considering the 1-parameter family of lattices defined by stretching or compressing the integer grid in diagonal direction, we give a closed formula for the covering density that depends on the distortion parameter. We observe that our family contains the thinnest lattice coverings in dimensions 2 to 5. We also consider the problem of packing congruent balls in ℝ n , for which we give a closed formula for the packing density as well. Again we observe that our family contains optimal configurations, this time densest packings in dimensions 2 and 3. alternative_title: - LNCS author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Edelsbrunner H, Kerber M. Covering and packing with spheres by diagonal distortion in R^n. In: Calude C, Rozenberg G, Salomaa A, eds. Rainbow of Computer Science. Vol 6570. Dedicated to Hermann Maurer on the Occasion of His 70th Birthday. Springer; 2011:20-35. doi:10.1007/978-3-642-19391-0_2' apa: Edelsbrunner, H., & Kerber, M. (2011). Covering and packing with spheres by diagonal distortion in R^n. In C. Calude, G. Rozenberg, & A. Salomaa (Eds.), Rainbow of Computer Science (Vol. 6570, pp. 20–35). Springer. https://doi.org/10.1007/978-3-642-19391-0_2 chicago: Edelsbrunner, Herbert, and Michael Kerber. “Covering and Packing with Spheres by Diagonal Distortion in R^n.” In Rainbow of Computer Science, edited by Cristian Calude, Grzegorz Rozenberg, and Arto Salomaa, 6570:20–35. Dedicated to Hermann Maurer on the Occasion of His 70th Birthday. Springer, 2011. https://doi.org/10.1007/978-3-642-19391-0_2. ieee: H. Edelsbrunner and M. Kerber, “Covering and packing with spheres by diagonal distortion in R^n,” in Rainbow of Computer Science, vol. 6570, C. Calude, G. Rozenberg, and A. Salomaa, Eds. Springer, 2011, pp. 20–35. ista: 'Edelsbrunner H, Kerber M. 2011.Covering and packing with spheres by diagonal distortion in R^n. In: Rainbow of Computer Science. LNCS, vol. 6570, 20–35.' mla: Edelsbrunner, Herbert, and Michael Kerber. “Covering and Packing with Spheres by Diagonal Distortion in R^n.” Rainbow of Computer Science, edited by Cristian Calude et al., vol. 6570, Springer, 2011, pp. 20–35, doi:10.1007/978-3-642-19391-0_2. short: H. Edelsbrunner, M. Kerber, in:, C. Calude, G. Rozenberg, A. Salomaa (Eds.), Rainbow of Computer Science, Springer, 2011, pp. 20–35. date_created: 2018-12-11T12:05:13Z date_published: 2011-05-03T00:00:00Z date_updated: 2021-01-12T07:52:15Z day: '03' ddc: - '000' department: - _id: HeEd doi: 10.1007/978-3-642-19391-0_2 editor: - first_name: Cristian full_name: Calude, Cristian last_name: Calude - first_name: Grzegorz full_name: Rozenberg, Grzegorz last_name: Rozenberg - first_name: Arto full_name: Salomaa, Arto last_name: Salomaa file: - access_level: open_access checksum: aaf22b4d7bd4277ffe8db532119cf474 content_type: application/pdf creator: system date_created: 2018-12-12T10:07:42Z date_updated: 2020-07-14T12:46:16Z file_id: '4640' file_name: IST-2016-539-v1+1_2011-B-01-CoveringPacking.pdf file_size: 436875 relation: main_file file_date_updated: 2020-07-14T12:46:16Z has_accepted_license: '1' intvolume: ' 6570' language: - iso: eng month: '05' oa: 1 oa_version: Submitted Version page: 20 - 35 publication: Rainbow of Computer Science publication_status: published publisher: Springer publist_id: '2427' pubrep_id: '539' quality_controlled: '1' series_title: Dedicated to Hermann Maurer on the Occasion of His 70th Birthday status: public title: Covering and packing with spheres by diagonal distortion in R^n type: book_chapter user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 6570 year: '2011' ... --- _id: '3965' abstract: - lang: eng text: The elevation function on a smoothly embedded 2-manifold in R-3 reflects the multiscale topography of cavities and protrusions as local maxima. The function has been useful in identifying coarse docking configurations for protein pairs. Transporting the concept from the smooth to the piecewise linear category, this paper describes an algorithm for finding all local maxima. While its worst-case running time is the same as of the algorithm used in prior work, its performance in practice is orders of magnitudes superior. We cast light on this improvement by relating the running time to the total absolute Gaussian curvature of the 2-manifold. author: - first_name: Bei full_name: Wang, Bei last_name: Wang - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Dmitriy full_name: Morozov, Dmitriy last_name: Morozov citation: ama: Wang B, Edelsbrunner H, Morozov D. Computing elevation maxima by searching the Gauss sphere. Journal of Experimental Algorithmics. 2011;16(2.2):1-13. doi:10.1145/1963190.1970375 apa: Wang, B., Edelsbrunner, H., & Morozov, D. (2011). Computing elevation maxima by searching the Gauss sphere. Journal of Experimental Algorithmics. ACM. https://doi.org/10.1145/1963190.1970375 chicago: Wang, Bei, Herbert Edelsbrunner, and Dmitriy Morozov. “Computing Elevation Maxima by Searching the Gauss Sphere.” Journal of Experimental Algorithmics. ACM, 2011. https://doi.org/10.1145/1963190.1970375. ieee: B. Wang, H. Edelsbrunner, and D. Morozov, “Computing elevation maxima by searching the Gauss sphere,” Journal of Experimental Algorithmics, vol. 16, no. 2.2. ACM, pp. 1–13, 2011. ista: Wang B, Edelsbrunner H, Morozov D. 2011. Computing elevation maxima by searching the Gauss sphere. Journal of Experimental Algorithmics. 16(2.2), 1–13. mla: Wang, Bei, et al. “Computing Elevation Maxima by Searching the Gauss Sphere.” Journal of Experimental Algorithmics, vol. 16, no. 2.2, ACM, 2011, pp. 1–13, doi:10.1145/1963190.1970375. short: B. Wang, H. Edelsbrunner, D. Morozov, Journal of Experimental Algorithmics 16 (2011) 1–13. date_created: 2018-12-11T12:06:09Z date_published: 2011-05-01T00:00:00Z date_updated: 2021-01-12T07:53:31Z day: '01' department: - _id: HeEd doi: 10.1145/1963190.1970375 intvolume: ' 16' issue: '2.2' language: - iso: eng month: '05' oa_version: None page: 1 - 13 publication: Journal of Experimental Algorithmics publication_status: published publisher: ACM publist_id: '2161' quality_controlled: '1' scopus_import: 1 status: public title: Computing elevation maxima by searching the Gauss sphere type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2011' ... --- _id: '3271' abstract: - lang: eng text: In this paper we present an efficient framework for computation of persis- tent homology of cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is adapted to the setting of cubical complexes. The proposed approach enables efficient application of persistent homology in domains where the data is naturally given in a cubical form. By avoiding triangulation of the data, we significantly reduce the size of the complex. We also present a data-structure de- signed to compactly store and quickly manipulate cubical complexes. By means of numerical experiments, we show high speed and memory efficiency of our ap- proach. We compare our framework to other available implementations, showing its superiority. Finally, we report performance on selected 3D and 4D data-sets. alternative_title: - Theory, Algorithms, and Applications author: - first_name: Hubert full_name: Wagner, Hubert last_name: Wagner - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Erald full_name: Vuçini, Erald last_name: Vuçini citation: ama: 'Wagner H, Chen C, Vuçini E. Efficient computation of persistent homology for cubical data. In: Peikert R, Hauser H, Carr H, Fuchs R, eds. Topological Methods in Data Analysis and Visualization II. Springer; 2011:91-106. doi:10.1007/978-3-642-23175-9_7' apa: Wagner, H., Chen, C., & Vuçini, E. (2011). Efficient computation of persistent homology for cubical data. In R. Peikert, H. Hauser, H. Carr, & R. Fuchs (Eds.), Topological Methods in Data Analysis and Visualization II (pp. 91–106). Springer. https://doi.org/10.1007/978-3-642-23175-9_7 chicago: Wagner, Hubert, Chao Chen, and Erald Vuçini. “Efficient Computation of Persistent Homology for Cubical Data.” In Topological Methods in Data Analysis and Visualization II, edited by Ronald Peikert, Helwig Hauser, Hamish Carr, and Raphael Fuchs, 91–106. Springer, 2011. https://doi.org/10.1007/978-3-642-23175-9_7. ieee: H. Wagner, C. Chen, and E. Vuçini, “Efficient computation of persistent homology for cubical data,” in Topological Methods in Data Analysis and Visualization II, R. Peikert, H. Hauser, H. Carr, and R. Fuchs, Eds. Springer, 2011, pp. 91–106. ista: 'Wagner H, Chen C, Vuçini E. 2011.Efficient computation of persistent homology for cubical data. In: Topological Methods in Data Analysis and Visualization II. Theory, Algorithms, and Applications, , 91–106.' mla: Wagner, Hubert, et al. “Efficient Computation of Persistent Homology for Cubical Data.” Topological Methods in Data Analysis and Visualization II, edited by Ronald Peikert et al., Springer, 2011, pp. 91–106, doi:10.1007/978-3-642-23175-9_7. short: H. Wagner, C. Chen, E. Vuçini, in:, R. Peikert, H. Hauser, H. Carr, R. Fuchs (Eds.), Topological Methods in Data Analysis and Visualization II, Springer, 2011, pp. 91–106. date_created: 2018-12-11T12:02:23Z date_published: 2011-11-14T00:00:00Z date_updated: 2021-01-12T07:42:18Z day: '14' department: - _id: HeEd doi: 10.1007/978-3-642-23175-9_7 editor: - first_name: Ronald full_name: Peikert, Ronald last_name: Peikert - first_name: Helwig full_name: Hauser, Helwig last_name: Hauser - first_name: Hamish full_name: Carr, Hamish last_name: Carr - first_name: Raphael full_name: Fuchs, Raphael last_name: Fuchs language: - iso: eng month: '11' oa_version: None page: 91 - 106 publication: Topological Methods in Data Analysis and Visualization II publication_status: published publisher: Springer publist_id: '3375' quality_controlled: '1' scopus_import: 1 status: public title: Efficient computation of persistent homology for cubical data type: book_chapter user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3270' abstract: - lang: eng text: 'The persistence diagram of a filtered simplicial com- plex is usually computed by reducing the boundary matrix of the complex. We introduce a simple op- timization technique: by processing the simplices of the complex in decreasing dimension, we can “kill” columns (i.e., set them to zero) without reducing them. This technique completely avoids reduction on roughly half of the columns. We demonstrate that this idea significantly improves the running time of the reduction algorithm in practice. We also give an output-sensitive complexity analysis for the new al- gorithm which yields to sub-cubic asymptotic bounds under certain assumptions.' author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Chen C, Kerber M. Persistent homology computation with a twist. In: TU Dortmund; 2011:197-200.' apa: 'Chen, C., & Kerber, M. (2011). Persistent homology computation with a twist (pp. 197–200). Presented at the EuroCG: European Workshop on Computational Geometry, Morschach, Switzerland: TU Dortmund.' chicago: Chen, Chao, and Michael Kerber. “Persistent Homology Computation with a Twist,” 197–200. TU Dortmund, 2011. ieee: 'C. Chen and M. Kerber, “Persistent homology computation with a twist,” presented at the EuroCG: European Workshop on Computational Geometry, Morschach, Switzerland, 2011, pp. 197–200.' ista: 'Chen C, Kerber M. 2011. Persistent homology computation with a twist. EuroCG: European Workshop on Computational Geometry, 197–200.' mla: Chen, Chao, and Michael Kerber. Persistent Homology Computation with a Twist. TU Dortmund, 2011, pp. 197–200. short: C. Chen, M. Kerber, in:, TU Dortmund, 2011, pp. 197–200. conference: end_date: 2011-03-30 location: Morschach, Switzerland name: 'EuroCG: European Workshop on Computational Geometry' start_date: 2011-03-28 date_created: 2018-12-11T12:02:22Z date_published: 2011-01-01T00:00:00Z date_updated: 2021-01-12T07:42:17Z day: '01' department: - _id: HeEd language: - iso: eng month: '01' oa_version: None page: 197 - 200 publication_status: published publisher: TU Dortmund publist_id: '3376' quality_controlled: '1' status: public title: Persistent homology computation with a twist type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3312' abstract: - lang: eng text: We study the 3D reconstruction of plant roots from multiple 2D images. To meet the challenge caused by the delicate nature of thin branches, we make three innovations to cope with the sensitivity to image quality and calibration. First, we model the background as a harmonic function to improve the segmentation of the root in each 2D image. Second, we develop the concept of the regularized visual hull which reduces the effect of jittering and refraction by ensuring consistency with one 2D image. Third, we guarantee connectedness through adjustments to the 3D reconstruction that minimize global error. Our software is part of a biological phenotype/genotype study of agricultural root systems. It has been tested on more than 40 plant roots and results are promising in terms of reconstruction quality and efficiency. acknowledgement: This research is supported by the National Science Foundation (NSF) under grant DBI-0820624. article_number: '6126475' article_processing_charge: No author: - first_name: Ying full_name: Zheng, Ying last_name: Zheng - first_name: Steve full_name: Gu, Steve last_name: Gu - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Carlo full_name: Tomasi, Carlo last_name: Tomasi - first_name: Philip full_name: Benfey, Philip last_name: Benfey citation: ama: Zheng Y, Gu S, Edelsbrunner H, Tomasi C, Benfey P. Detailed Reconstruction of 3D Plant Root Shape. IEEE; 2011. doi:10.1109/ICCV.2011.6126475 apa: 'Zheng, Y., Gu, S., Edelsbrunner, H., Tomasi, C., & Benfey, P. (2011). Detailed reconstruction of 3D plant root shape. Proceedings of the IEEE International Conference on Computer Vision. Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126475' chicago: Zheng, Ying, Steve Gu, Herbert Edelsbrunner, Carlo Tomasi, and Philip Benfey. Detailed Reconstruction of 3D Plant Root Shape. Proceedings of the IEEE International Conference on Computer Vision. IEEE, 2011. https://doi.org/10.1109/ICCV.2011.6126475. ieee: Y. Zheng, S. Gu, H. Edelsbrunner, C. Tomasi, and P. Benfey, Detailed reconstruction of 3D plant root shape. IEEE, 2011. ista: Zheng Y, Gu S, Edelsbrunner H, Tomasi C, Benfey P. 2011. Detailed reconstruction of 3D plant root shape, IEEE,p. mla: Zheng, Ying, et al. “Detailed Reconstruction of 3D Plant Root Shape.” Proceedings of the IEEE International Conference on Computer Vision, 6126475, IEEE, 2011, doi:10.1109/ICCV.2011.6126475. short: Y. Zheng, S. Gu, H. Edelsbrunner, C. Tomasi, P. Benfey, Detailed Reconstruction of 3D Plant Root Shape, IEEE, 2011. conference: end_date: 2011-11-13 location: Barcelona, Spain name: 'ICCV: International Conference on Computer Vision' start_date: 2011-11-06 date_created: 2018-12-11T12:02:36Z date_published: 2011-12-31T00:00:00Z date_updated: 2020-07-14T23:03:43Z day: '31' ddc: - '000' department: - _id: HeEd doi: 10.1109/ICCV.2011.6126475 file: - access_level: open_access checksum: 30a33564b7b45a7ee31610898267fd0e content_type: application/pdf creator: system date_created: 2018-12-12T10:09:04Z date_updated: 2020-07-14T12:46:07Z file_id: '4727' file_name: IST-2016-541-v1+1_2011-P-07-RootReconstruction.pdf file_size: 5622728 relation: main_file file_date_updated: 2020-07-14T12:46:07Z has_accepted_license: '1' language: - iso: eng month: '12' oa: 1 oa_version: Submitted Version publication: Proceedings of the IEEE International Conference on Computer Vision publication_status: published publisher: IEEE publist_id: '3328' pubrep_id: '541' quality_controlled: '1' status: public title: Detailed reconstruction of 3D plant root shape type: conference_poster user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3313' abstract: - lang: eng text: Interpreting an image as a function on a compact sub- set of the Euclidean plane, we get its scale-space by diffu- sion, spreading the image over the entire plane. This gener- ates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian ker- nel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods. article_number: '6126271' author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Chen C, Edelsbrunner H. Diffusion runs low on persistence fast. In: Proceedings of the IEEE International Conference on Computer Vision. IEEE; 2011. doi:10.1109/ICCV.2011.6126271' apa: 'Chen, C., & Edelsbrunner, H. (2011). Diffusion runs low on persistence fast. In Proceedings of the IEEE International Conference on Computer Vision. Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126271' chicago: Chen, Chao, and Herbert Edelsbrunner. “Diffusion Runs Low on Persistence Fast.” In Proceedings of the IEEE International Conference on Computer Vision. IEEE, 2011. https://doi.org/10.1109/ICCV.2011.6126271. ieee: C. Chen and H. Edelsbrunner, “Diffusion runs low on persistence fast,” in Proceedings of the IEEE International Conference on Computer Vision, Barcelona, Spain, 2011. ista: 'Chen C, Edelsbrunner H. 2011. Diffusion runs low on persistence fast. Proceedings of the IEEE International Conference on Computer Vision. ICCV: International Conference on Computer Vision, 6126271.' mla: Chen, Chao, and Herbert Edelsbrunner. “Diffusion Runs Low on Persistence Fast.” Proceedings of the IEEE International Conference on Computer Vision, 6126271, IEEE, 2011, doi:10.1109/ICCV.2011.6126271. short: C. Chen, H. Edelsbrunner, in:, Proceedings of the IEEE International Conference on Computer Vision, IEEE, 2011. conference: end_date: 2011-11-13 location: Barcelona, Spain name: 'ICCV: International Conference on Computer Vision' start_date: 2011-11-06 date_created: 2018-12-11T12:02:37Z date_published: 2011-11-06T00:00:00Z date_updated: 2021-01-12T07:42:35Z day: '06' ddc: - '000' department: - _id: HeEd doi: 10.1109/ICCV.2011.6126271 file: - access_level: open_access checksum: 6984684081ba123808b344f9f2e64a8f content_type: application/pdf creator: system date_created: 2018-12-12T10:17:28Z date_updated: 2020-07-14T12:46:07Z file_id: '5282' file_name: IST-2016-540-v1+1_2011-P-08-RunEmpty.pdf file_size: 614050 relation: main_file file_date_updated: 2020-07-14T12:46:07Z has_accepted_license: '1' language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version publication: Proceedings of the IEEE International Conference on Computer Vision publication_status: published publisher: IEEE publist_id: '3327' pubrep_id: '540' quality_controlled: '1' scopus_import: 1 status: public title: Diffusion runs low on persistence fast type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3311' abstract: - lang: eng text: Alpha shapes have been conceived in 1981 as an attempt to define the shape of a finite set of point in the plane. Since then, connections to diverse areas in the sciences and engineering have developed, including to pattern recognition, digital shape sampling and processing, and structural molecular biology. This survey begins with a historical account and discusses geometric, algorithmic, topological, and combinatorial aspects of alpha shapes in this sequence. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Edelsbrunner H. Alpha shapes - a survey. In: van de Weygaert R, Vegter G, Ritzerveld J, Icke V, eds. Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings. Springer.' apa: 'Edelsbrunner, H. (n.d.). Alpha shapes - a survey. In R. van de Weygaert, G. Vegter, J. Ritzerveld, & V. Icke (Eds.), Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings. Springer.' chicago: 'Edelsbrunner, Herbert. “Alpha Shapes - a Survey.” In Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, edited by R van de Weygaert, G Vegter, J Ritzerveld, and V Icke. Springer, n.d.' ieee: 'H. Edelsbrunner, “Alpha shapes - a survey,” in Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, R. van de Weygaert, G. Vegter, J. Ritzerveld, and V. Icke, Eds. Springer.' ista: 'Edelsbrunner H.Alpha shapes - a survey. In: Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings. .' mla: 'Edelsbrunner, Herbert. “Alpha Shapes - a Survey.” Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, edited by R van de Weygaert et al., Springer.' short: 'H. Edelsbrunner, in:, R. van de Weygaert, G. Vegter, J. Ritzerveld, V. Icke (Eds.), Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, Springer, n.d.' date_created: 2018-12-11T12:02:36Z date_published: 2011-12-31T00:00:00Z date_updated: 2022-05-24T07:56:30Z day: '31' ddc: - '510' department: - _id: HeEd editor: - first_name: R full_name: van de Weygaert, R last_name: van de Weygaert - first_name: G full_name: Vegter, G last_name: Vegter - first_name: J full_name: Ritzerveld, J last_name: Ritzerveld - first_name: V full_name: Icke, V last_name: Icke file: - access_level: open_access checksum: a592ea438351e7280eea993a7713ab8f content_type: application/pdf creator: dernst date_created: 2022-05-24T07:55:05Z date_updated: 2022-05-24T07:55:05Z file_id: '11408' file_name: 2010_AlphaShapes.pdf file_size: 475254 relation: main_file success: 1 file_date_updated: 2022-05-24T07:55:05Z has_accepted_license: '1' language: - iso: eng month: '12' oa: 1 oa_version: Submitted Version publication: 'Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings' publication_status: inpress publisher: Springer publist_id: '3329' quality_controlled: '1' status: public title: Alpha shapes - a survey type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '3377' abstract: - lang: eng text: By definition, transverse intersections are stable under in- finitesimal perturbations. Using persistent homology, we ex- tend this notion to sizeable perturbations. Specifically, we assign to each homology class of the intersection its robust- ness, the magnitude of a perturbation necessary to kill it, and prove that robustness is stable. Among the applications of this result is a stable notion of robustness for fixed points of continuous mappings and a statement of stability for con- tours of smooth mappings. acknowledgement: This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0007 and HR0011-05-1-0057. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Dmitriy full_name: Morozov, Dmitriy last_name: Morozov - first_name: Amit full_name: Patel, Amit id: 34A254A0-F248-11E8-B48F-1D18A9856A87 last_name: Patel citation: ama: Edelsbrunner H, Morozov D, Patel A. Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. 2011;11(3):345-361. doi:10.1007/s10208-011-9090-8 apa: Edelsbrunner, H., Morozov, D., & Patel, A. (2011). Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-011-9090-8 chicago: Edelsbrunner, Herbert, Dmitriy Morozov, and Amit Patel. “Quantifying Transversality by Measuring the Robustness of Intersections.” Foundations of Computational Mathematics. Springer, 2011. https://doi.org/10.1007/s10208-011-9090-8. ieee: H. Edelsbrunner, D. Morozov, and A. Patel, “Quantifying transversality by measuring the robustness of intersections,” Foundations of Computational Mathematics, vol. 11, no. 3. Springer, pp. 345–361, 2011. ista: Edelsbrunner H, Morozov D, Patel A. 2011. Quantifying transversality by measuring the robustness of intersections. Foundations of Computational Mathematics. 11(3), 345–361. mla: Edelsbrunner, Herbert, et al. “Quantifying Transversality by Measuring the Robustness of Intersections.” Foundations of Computational Mathematics, vol. 11, no. 3, Springer, 2011, pp. 345–61, doi:10.1007/s10208-011-9090-8. short: H. Edelsbrunner, D. Morozov, A. Patel, Foundations of Computational Mathematics 11 (2011) 345–361. date_created: 2018-12-11T12:02:59Z date_published: 2011-06-01T00:00:00Z date_updated: 2021-01-12T07:43:04Z day: '01' department: - _id: HeEd doi: 10.1007/s10208-011-9090-8 intvolume: ' 11' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/0911.2142 month: '06' oa: 1 oa_version: Submitted Version page: 345 - 361 publication: Foundations of Computational Mathematics publication_status: published publisher: Springer publist_id: '3230' quality_controlled: '1' scopus_import: 1 status: public title: Quantifying transversality by measuring the robustness of intersections type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 11 year: '2011' ... --- _id: '3378' abstract: - lang: eng text: The theory of intersection homology was developed to study the singularities of a topologically stratified space. This paper in- corporates this theory into the already developed framework of persistent homology. We demonstrate that persistent intersec- tion homology gives useful information about the relationship between an embedded stratified space and its singularities. We give, and prove the correctness of, an algorithm for the computa- tion of the persistent intersection homology groups of a filtered simplicial complex equipped with a stratification by subcom- plexes. We also derive, from Poincare ́ Duality, some structural results about persistent intersection homology. acknowledgement: This research was partially supported by the Defense Advanced Research Projects Agency (DARPA) under grant HR0011-05-1-0007. author: - first_name: Paul full_name: Bendich, Paul id: 43F6EC54-F248-11E8-B48F-1D18A9856A87 last_name: Bendich - first_name: John full_name: Harer, John last_name: Harer citation: ama: Bendich P, Harer J. Persistent intersection homology. Foundations of Computational Mathematics. 2011;11(3):305-336. doi:10.1007/s10208-010-9081-1 apa: Bendich, P., & Harer, J. (2011). Persistent intersection homology. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-010-9081-1 chicago: Bendich, Paul, and John Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics. Springer, 2011. https://doi.org/10.1007/s10208-010-9081-1. ieee: P. Bendich and J. Harer, “Persistent intersection homology,” Foundations of Computational Mathematics, vol. 11, no. 3. Springer, pp. 305–336, 2011. ista: Bendich P, Harer J. 2011. Persistent intersection homology. Foundations of Computational Mathematics. 11(3), 305–336. mla: Bendich, Paul, and John Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics, vol. 11, no. 3, Springer, 2011, pp. 305–36, doi:10.1007/s10208-010-9081-1. short: P. Bendich, J. Harer, Foundations of Computational Mathematics 11 (2011) 305–336. date_created: 2018-12-11T12:02:59Z date_published: 2011-06-01T00:00:00Z date_updated: 2021-01-12T07:43:04Z day: '01' department: - _id: HeEd doi: 10.1007/s10208-010-9081-1 intvolume: ' 11' issue: '3' language: - iso: eng month: '06' oa_version: None page: 305 - 336 publication: Foundations of Computational Mathematics publication_status: published publisher: Springer publist_id: '3229' quality_controlled: '1' scopus_import: 1 status: public title: Persistent intersection homology type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 11 year: '2011' ... --- _id: '3336' abstract: - lang: eng text: 'We introduce TopoCut: a new way to integrate knowledge about topological properties (TPs) into random field image segmentation model. Instead of including TPs as additional constraints during minimization of the energy function, we devise an efficient algorithm for modifying the unary potentials such that the resulting segmentation is guaranteed with the desired properties. Our method is more flexible in the sense that it handles more topology constraints than previous methods, which were only able to enforce pairwise or global connectivity. In particular, our method is very fast, making it for the first time possible to enforce global topological properties in practical image segmentation tasks.' acknowledgement: The first author is supported by the Austrian Science Fund (FWF) grant No. P20134-N13. The authors would like to thank Sebastian Nowozin for helpful discussions. article_processing_charge: No author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Daniel full_name: Freedman, Daniel last_name: Freedman - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: 'Chen C, Freedman D, Lampert C. Enforcing topological constraints in random field image segmentation. In: CVPR: Computer Vision and Pattern Recognition. IEEE; 2011:2089-2096. doi:10.1109/CVPR.2011.5995503' apa: 'Chen, C., Freedman, D., & Lampert, C. (2011). Enforcing topological constraints in random field image segmentation. In CVPR: Computer Vision and Pattern Recognition (pp. 2089–2096). Colorado Springs, CO, United States: IEEE. https://doi.org/10.1109/CVPR.2011.5995503' chicago: 'Chen, Chao, Daniel Freedman, and Christoph Lampert. “Enforcing Topological Constraints in Random Field Image Segmentation.” In CVPR: Computer Vision and Pattern Recognition, 2089–96. IEEE, 2011. https://doi.org/10.1109/CVPR.2011.5995503.' ieee: 'C. Chen, D. Freedman, and C. Lampert, “Enforcing topological constraints in random field image segmentation,” in CVPR: Computer Vision and Pattern Recognition, Colorado Springs, CO, United States, 2011, pp. 2089–2096.' ista: 'Chen C, Freedman D, Lampert C. 2011. Enforcing topological constraints in random field image segmentation. CVPR: Computer Vision and Pattern Recognition. CVPR: Conference on Computer Vision and Pattern Recognition, 2089–2096.' mla: 'Chen, Chao, et al. “Enforcing Topological Constraints in Random Field Image Segmentation.” CVPR: Computer Vision and Pattern Recognition, IEEE, 2011, pp. 2089–96, doi:10.1109/CVPR.2011.5995503.' short: 'C. Chen, D. Freedman, C. Lampert, in:, CVPR: Computer Vision and Pattern Recognition, IEEE, 2011, pp. 2089–2096.' conference: end_date: 2011-06-25 location: Colorado Springs, CO, United States name: 'CVPR: Conference on Computer Vision and Pattern Recognition' start_date: 2011-06-20 date_created: 2018-12-11T12:02:45Z date_published: 2011-07-22T00:00:00Z date_updated: 2023-02-23T12:23:56Z day: '22' department: - _id: HeEd - _id: ChLa doi: 10.1109/CVPR.2011.5995503 language: - iso: eng month: '07' oa_version: None page: 2089 - 2096 publication: 'CVPR: Computer Vision and Pattern Recognition' publication_identifier: eisbn: - 978-1-4577-0395-9 isbn: - 978-1-4577-0394-2 publication_status: published publisher: IEEE publist_id: '3294' quality_controlled: '1' related_material: record: - id: '5386' relation: earlier_version status: public scopus_import: '1' status: public title: Enforcing topological constraints in random field image segmentation type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2011' ... --- _id: '9648' abstract: - lang: eng text: In this paper, we establish a correspondence between the incremental algorithm for computing AT-models [8,9] and the one for computing persistent homology [6,14,15]. We also present a decremental algorithm for computing AT-models that allows to extend the persistence computation to a wider setting. Finally, we show how to combine incremental and decremental techniques for persistent homology computation. alternative_title: - LNCS article_processing_charge: No author: - first_name: Rocio full_name: Gonzalez-Diaz, Rocio last_name: Gonzalez-Diaz - first_name: Adrian full_name: Ion, Adrian id: 29F89302-F248-11E8-B48F-1D18A9856A87 last_name: Ion - first_name: Maria Jose full_name: Jimenez, Maria Jose last_name: Jimenez - first_name: Regina full_name: Poyatos, Regina last_name: Poyatos citation: ama: 'Gonzalez-Diaz R, Ion A, Jimenez MJ, Poyatos R. Incremental-decremental algorithm for computing AT-models and persistent homology. In: Computer Analysis of Images and Patterns. Vol 6854. Springer Nature; 2011:286-293. doi:10.1007/978-3-642-23672-3_35' apa: 'Gonzalez-Diaz, R., Ion, A., Jimenez, M. J., & Poyatos, R. (2011). Incremental-decremental algorithm for computing AT-models and persistent homology. In Computer Analysis of Images and Patterns (Vol. 6854, pp. 286–293). Seville, Spain: Springer Nature. https://doi.org/10.1007/978-3-642-23672-3_35' chicago: Gonzalez-Diaz, Rocio, Adrian Ion, Maria Jose Jimenez, and Regina Poyatos. “Incremental-Decremental Algorithm for Computing AT-Models and Persistent Homology.” In Computer Analysis of Images and Patterns, 6854:286–93. Springer Nature, 2011. https://doi.org/10.1007/978-3-642-23672-3_35. ieee: R. Gonzalez-Diaz, A. Ion, M. J. Jimenez, and R. Poyatos, “Incremental-decremental algorithm for computing AT-models and persistent homology,” in Computer Analysis of Images and Patterns, Seville, Spain, 2011, vol. 6854, pp. 286–293. ista: 'Gonzalez-Diaz R, Ion A, Jimenez MJ, Poyatos R. 2011. Incremental-decremental algorithm for computing AT-models and persistent homology. Computer Analysis of Images and Patterns. CAIP: International Conference on Computer Analysis of Images and Patterns, LNCS, vol. 6854, 286–293.' mla: Gonzalez-Diaz, Rocio, et al. “Incremental-Decremental Algorithm for Computing AT-Models and Persistent Homology.” Computer Analysis of Images and Patterns, vol. 6854, Springer Nature, 2011, pp. 286–93, doi:10.1007/978-3-642-23672-3_35. short: R. Gonzalez-Diaz, A. Ion, M.J. Jimenez, R. Poyatos, in:, Computer Analysis of Images and Patterns, Springer Nature, 2011, pp. 286–293. conference: end_date: 2011-08-31 location: Seville, Spain name: 'CAIP: International Conference on Computer Analysis of Images and Patterns' start_date: 2011-08-29 date_created: 2021-07-11T22:01:19Z date_published: 2011-08-01T00:00:00Z date_updated: 2021-08-12T13:53:17Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-642-23672-3_35 intvolume: ' 6854' language: - iso: eng main_file_link: - open_access: '1' url: http://hdl.handle.net/11441/30766 month: '08' oa: 1 oa_version: Published Version page: 286-293 publication: Computer Analysis of Images and Patterns publication_identifier: eissn: - '16113349' isbn: - '9783642236716' issn: - '03029743' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Incremental-decremental algorithm for computing AT-models and persistent homology type: conference user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 6854 year: '2011' ... --- _id: '10907' abstract: - lang: eng text: This paper presents a method to create a model of an articulated object using the planar motion in an initialization video. The model consists of rigid parts connected by points of articulation. The rigid parts are described by the positions of salient feature-points tracked throughout the video. Following a filtering step that identifies points that belong to different objects, rigid parts are found by a grouping process in a graph pyramid. Valid articulation points are selected by verifying multiple hypotheses for each pair of parts. acknowledgement: This work has been partially supported by the Austrian Science Fund under grants S9103-N13 and P18716-N13. alternative_title: - LNCS article_processing_charge: No author: - first_name: Nicole M. full_name: Artner, Nicole M. last_name: Artner - first_name: Adrian full_name: Ion, Adrian id: 29F89302-F248-11E8-B48F-1D18A9856A87 last_name: Ion - first_name: Walter G. full_name: Kropatsch, Walter G. last_name: Kropatsch citation: ama: 'Artner NM, Ion A, Kropatsch WG. Spatio-temporal extraction of articulated models in a graph pyramid. In: Jiang X, Ferrer M, Torsello A, eds. Graph-Based Representations in Pattern Recognition. Vol 6658. LNIP. Berlin, Heidelberg: Springer; 2011:215-224. doi:10.1007/978-3-642-20844-7_22' apa: 'Artner, N. M., Ion, A., & Kropatsch, W. G. (2011). Spatio-temporal extraction of articulated models in a graph pyramid. In X. Jiang, M. Ferrer, & A. Torsello (Eds.), Graph-Based Representations in Pattern Recognition (Vol. 6658, pp. 215–224). Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-642-20844-7_22' chicago: 'Artner, Nicole M., Adrian Ion, and Walter G. Kropatsch. “Spatio-Temporal Extraction of Articulated Models in a Graph Pyramid.” In Graph-Based Representations in Pattern Recognition, edited by Xiaoyi Jiang, Miquel Ferrer, and Andrea Torsello, 6658:215–24. LNIP. Berlin, Heidelberg: Springer, 2011. https://doi.org/10.1007/978-3-642-20844-7_22.' ieee: N. M. Artner, A. Ion, and W. G. Kropatsch, “Spatio-temporal extraction of articulated models in a graph pyramid,” in Graph-Based Representations in Pattern Recognition, Münster, Germany, 2011, vol. 6658, pp. 215–224. ista: 'Artner NM, Ion A, Kropatsch WG. 2011. Spatio-temporal extraction of articulated models in a graph pyramid. Graph-Based Representations in Pattern Recognition. GbRPR: Graph-based Representations in Pattern RecognitionLNIP, LNCS, vol. 6658, 215–224.' mla: Artner, Nicole M., et al. “Spatio-Temporal Extraction of Articulated Models in a Graph Pyramid.” Graph-Based Representations in Pattern Recognition, edited by Xiaoyi Jiang et al., vol. 6658, Springer, 2011, pp. 215–24, doi:10.1007/978-3-642-20844-7_22. short: N.M. Artner, A. Ion, W.G. Kropatsch, in:, X. Jiang, M. Ferrer, A. Torsello (Eds.), Graph-Based Representations in Pattern Recognition, Springer, Berlin, Heidelberg, 2011, pp. 215–224. conference: end_date: 2011-05-20 location: Münster, Germany name: 'GbRPR: Graph-based Representations in Pattern Recognition' start_date: 2011-05-18 date_created: 2022-03-21T08:08:35Z date_published: 2011-06-01T00:00:00Z date_updated: 2023-09-05T14:10:15Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-642-20844-7_22 editor: - first_name: Xiaoyi full_name: Jiang, Xiaoyi last_name: Jiang - first_name: Miquel full_name: Ferrer, Miquel last_name: Ferrer - first_name: Andrea full_name: Torsello, Andrea last_name: Torsello intvolume: ' 6658' language: - iso: eng month: '06' oa_version: None page: 215-224 place: Berlin, Heidelberg publication: Graph-Based Representations in Pattern Recognition publication_identifier: eisbn: - '9783642208447' eissn: - 1611-3349 isbn: - '9783642208430' issn: - 0302-9743 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' series_title: LNIP status: public title: Spatio-temporal extraction of articulated models in a graph pyramid type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 6658 year: '2011' ... --- _id: '10909' abstract: - lang: eng text: We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We focus on the volume measure, that is, the 1-norm of a cycle. Two main results are presented. First, we prove the problem is NP-hard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NP-hard to approximate even when the Betti number is O(1). A side effect is the inapproximability of the problem of computing the nonbounding cycle with the smallest volume, and computing cycles representing a homology basis with the minimal total volume. We also discuss other geometric measures (diameter and radius) and show their disadvantages in homology localization. Our work is restricted to homology over the ℤ2 field. acknowledgement: Partially supported by the Austrian Science Fund under grantFSP-S9103-N04 and P20134-N13. article_processing_charge: No author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Daniel full_name: Freedman, Daniel last_name: Freedman citation: ama: 'Chen C, Freedman D. Hardness results for homology localization. In: Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics; 2010:1594-1604. doi:10.1137/1.9781611973075.129' apa: 'Chen, C., & Freedman, D. (2010). Hardness results for homology localization. In Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 1594–1604). Austin, TX, United States: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611973075.129' chicago: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” In Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms, 1594–1604. Society for Industrial and Applied Mathematics, 2010. https://doi.org/10.1137/1.9781611973075.129. ieee: C. Chen and D. Freedman, “Hardness results for homology localization,” in Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms, Austin, TX, United States, 2010, pp. 1594–1604. ista: 'Chen C, Freedman D. 2010. Hardness results for homology localization. Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 1594–1604.' mla: Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2010, pp. 1594–604, doi:10.1137/1.9781611973075.129. short: C. Chen, D. Freedman, in:, Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2010, pp. 1594–1604. conference: end_date: 2010-01-19 location: Austin, TX, United States name: 'SODA: Symposium on Discrete Algorithms' start_date: 2010-01-17 date_created: 2022-03-21T08:24:07Z date_published: 2010-02-01T00:00:00Z date_updated: 2023-02-23T11:19:46Z day: '01' department: - _id: HeEd doi: 10.1137/1.9781611973075.129 language: - iso: eng month: '02' oa_version: None page: 1594-1604 publication: Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms publication_identifier: eisbn: - '9781611973075' publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' related_material: record: - id: '3267' relation: later_version status: public scopus_import: '1' status: public title: Hardness results for homology localization type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2010' ... --- _id: '3782' abstract: - lang: eng text: In cortex surface segmentation, the extracted surface is required to have a particular topology, namely, a two-sphere. We present a new method for removing topology noise of a curve or surface within the level set framework, and thus produce a cortical surface with correct topology. We define a new energy term which quantifies topology noise. We then show how to minimize this term by computing its functional derivative with respect to the level set function. This method differs from existing methods in that it is inherently continuous and not digital; and in the way that our energy directly relates to the topology of the underlying curve or surface, versus existing knot-based measures which are related in a more indirect fashion. The proposed flow is validated empirically. acknowledgement: "Partially supported by the Austri an Science Fund unde r grant P20134-N13.\r\nWe thank Helena Molina-Abril for very helpful discussion. We thank anonymous reviewers for helpful comments." alternative_title: - LNCS author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Daniel full_name: Freedman, Daniel last_name: Freedman citation: ama: 'Chen C, Freedman D. Topology noise removal for curve  and surface evolution. In: Conference Proceedings MCV 2010. Vol 6533. Springer; 2010:31-42. doi:10.1007/978-3-642-18421-5_4' apa: 'Chen, C., & Freedman, D. (2010). Topology noise removal for curve  and surface evolution. In Conference proceedings MCV 2010 (Vol. 6533, pp. 31–42). Beijing, China: Springer. https://doi.org/10.1007/978-3-642-18421-5_4' chicago: Chen, Chao, and Daniel Freedman. “Topology Noise Removal for Curve  and Surface Evolution.” In Conference Proceedings MCV 2010, 6533:31–42. Springer, 2010. https://doi.org/10.1007/978-3-642-18421-5_4. ieee: C. Chen and D. Freedman, “Topology noise removal for curve  and surface evolution,” in Conference proceedings MCV 2010, Beijing, China, 2010, vol. 6533, pp. 31–42. ista: 'Chen C, Freedman D. 2010. Topology noise removal for curve  and surface evolution. Conference proceedings MCV 2010. MCV: Medical Computer Vision, LNCS, vol. 6533, 31–42.' mla: Chen, Chao, and Daniel Freedman. “Topology Noise Removal for Curve  and Surface Evolution.” Conference Proceedings MCV 2010, vol. 6533, Springer, 2010, pp. 31–42, doi:10.1007/978-3-642-18421-5_4. short: C. Chen, D. Freedman, in:, Conference Proceedings MCV 2010, Springer, 2010, pp. 31–42. conference: end_date: 2010-09-20 location: Beijing, China name: 'MCV: Medical Computer Vision' start_date: 2010-09-20 date_created: 2018-12-11T12:05:08Z date_published: 2010-12-31T00:00:00Z date_updated: 2021-01-12T07:52:10Z day: '31' department: - _id: HeEd doi: 10.1007/978-3-642-18421-5_4 intvolume: ' 6533' language: - iso: eng month: '12' oa_version: None page: 31 - 42 publication: ' Conference proceedings MCV 2010' publication_status: published publisher: Springer publist_id: '2445' quality_controlled: '1' scopus_import: 1 status: public title: Topology noise removal for curve and surface evolution type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 6533 year: '2010' ... --- _id: '3795' abstract: - lang: eng text: 'The (apparent) contour of a smooth mapping from a 2-manifold to the plane, f: M → R2 , is the set of critical values, that is, the image of the points at which the gradients of the two component functions are linearly dependent. Assuming M is compact and orientable and measuring difference with the erosion distance, we prove that the contour is stable.' acknowledgement: This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0007 and HR0011-05-1-0057. alternative_title: - Mathematics and Visualization author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Dmitriy full_name: Morozov, Dmitriy last_name: Morozov - first_name: Amit full_name: Patel, Amit id: 34A254A0-F248-11E8-B48F-1D18A9856A87 last_name: Patel citation: ama: 'Edelsbrunner H, Morozov D, Patel A. The stability of the apparent contour of an orientable 2-manifold. In: Topological Data Analysis and Visualization: Theory, Algorithms and Applications. Springer; 2010:27-42. doi:10.1007/978-3-642-15014-2_3' apa: 'Edelsbrunner, H., Morozov, D., & Patel, A. (2010). The stability of the apparent contour of an orientable 2-manifold. In Topological Data Analysis and Visualization: Theory, Algorithms and Applications (pp. 27–42). Springer. https://doi.org/10.1007/978-3-642-15014-2_3' chicago: 'Edelsbrunner, Herbert, Dmitriy Morozov, and Amit Patel. “The Stability of the Apparent Contour of an Orientable 2-Manifold.” In Topological Data Analysis and Visualization: Theory, Algorithms and Applications, 27–42. Springer, 2010. https://doi.org/10.1007/978-3-642-15014-2_3.' ieee: 'H. Edelsbrunner, D. Morozov, and A. Patel, “The stability of the apparent contour of an orientable 2-manifold,” in Topological Data Analysis and Visualization: Theory, Algorithms and Applications, Springer, 2010, pp. 27–42.' ista: 'Edelsbrunner H, Morozov D, Patel A. 2010.The stability of the apparent contour of an orientable 2-manifold. In: Topological Data Analysis and Visualization: Theory, Algorithms and Applications. Mathematics and Visualization, , 27–42.' mla: 'Edelsbrunner, Herbert, et al. “The Stability of the Apparent Contour of an Orientable 2-Manifold.” Topological Data Analysis and Visualization: Theory, Algorithms and Applications, Springer, 2010, pp. 27–42, doi:10.1007/978-3-642-15014-2_3.' short: 'H. Edelsbrunner, D. Morozov, A. Patel, in:, Topological Data Analysis and Visualization: Theory, Algorithms and Applications, Springer, 2010, pp. 27–42.' date_created: 2018-12-11T12:05:13Z date_published: 2010-12-22T00:00:00Z date_updated: 2021-01-12T07:52:15Z day: '22' ddc: - '000' department: - _id: HeEd doi: 10.1007/978-3-642-15014-2_3 file: - access_level: open_access checksum: f03a44c3d1c3e2d4fedb3b94404f3fd5 content_type: application/pdf creator: system date_created: 2018-12-12T10:11:40Z date_updated: 2020-07-14T12:46:16Z file_id: '4896' file_name: IST-2016-538-v1+1_2011-B-02-ApparentContour.pdf file_size: 210710 relation: main_file file_date_updated: 2020-07-14T12:46:16Z has_accepted_license: '1' language: - iso: eng month: '12' oa: 1 oa_version: Submitted Version page: 27 - 42 publication: 'Topological Data Analysis and Visualization: Theory, Algorithms and Applications' publication_status: published publisher: Springer publist_id: '2428' pubrep_id: '538' quality_controlled: '1' scopus_import: 1 status: public title: The stability of the apparent contour of an orientable 2-manifold type: book_chapter user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2010' ... --- _id: '3848' abstract: - lang: eng text: We define the robustness of a level set homology class of a function f:XR as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theoretic framework, we compute the robustness for each class, using a connection to extended persistent homology. The special case X=R3 has ramifications in medical imaging and scientific visualization. alternative_title: - LNCS author: - first_name: Paul full_name: Bendich, Paul id: 43F6EC54-F248-11E8-B48F-1D18A9856A87 last_name: Bendich - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Dmitriy full_name: Morozov, Dmitriy last_name: Morozov - first_name: Amit full_name: Patel, Amit id: 34A254A0-F248-11E8-B48F-1D18A9856A87 last_name: Patel citation: ama: 'Bendich P, Edelsbrunner H, Morozov D, Patel A. The robustness of level sets. In: Vol 6346. Springer; 2010:1-10. doi:10.1007/978-3-642-15775-2_1' apa: 'Bendich, P., Edelsbrunner, H., Morozov, D., & Patel, A. (2010). The robustness of level sets (Vol. 6346, pp. 1–10). Presented at the ESA: European Symposium on Algorithms, Liverpool, UK: Springer. https://doi.org/10.1007/978-3-642-15775-2_1' chicago: Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “The Robustness of Level Sets,” 6346:1–10. Springer, 2010. https://doi.org/10.1007/978-3-642-15775-2_1. ieee: 'P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “The robustness of level sets,” presented at the ESA: European Symposium on Algorithms, Liverpool, UK, 2010, vol. 6346, pp. 1–10.' ista: 'Bendich P, Edelsbrunner H, Morozov D, Patel A. 2010. The robustness of level sets. ESA: European Symposium on Algorithms, LNCS, vol. 6346, 1–10.' mla: Bendich, Paul, et al. The Robustness of Level Sets. Vol. 6346, Springer, 2010, pp. 1–10, doi:10.1007/978-3-642-15775-2_1. short: P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, in:, Springer, 2010, pp. 1–10. conference: end_date: 2010-09-08 location: Liverpool, UK name: 'ESA: European Symposium on Algorithms' start_date: 2010-09-06 date_created: 2018-12-11T12:05:30Z date_published: 2010-09-01T00:00:00Z date_updated: 2021-01-12T07:52:38Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-642-15775-2_1 intvolume: ' 6346' language: - iso: eng month: '09' oa_version: None page: 1 - 10 publication_status: published publisher: Springer publist_id: '2336' quality_controlled: '1' scopus_import: 1 status: public title: The robustness of level sets type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 6346 year: '2010' ... --- _id: '3853' abstract: - lang: eng text: 'Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic meanpayoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions.' alternative_title: - LNCS author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Laurent full_name: Doyen, Laurent last_name: Doyen - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000−0002−2985−7724 - first_name: Philippe full_name: Rannou, Philippe last_name: Rannou citation: ama: 'Chatterjee K, Doyen L, Edelsbrunner H, Henzinger TA, Rannou P. Mean-payoff automaton expressions. In: Vol 6269. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2010:269-283. doi:10.1007/978-3-642-15375-4_19' apa: 'Chatterjee, K., Doyen, L., Edelsbrunner, H., Henzinger, T. A., & Rannou, P. (2010). Mean-payoff automaton expressions (Vol. 6269, pp. 269–283). Presented at the CONCUR: Concurrency Theory, Paris, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.1007/978-3-642-15375-4_19' chicago: Chatterjee, Krishnendu, Laurent Doyen, Herbert Edelsbrunner, Thomas A Henzinger, and Philippe Rannou. “Mean-Payoff Automaton Expressions,” 6269:269–83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2010. https://doi.org/10.1007/978-3-642-15375-4_19. ieee: 'K. Chatterjee, L. Doyen, H. Edelsbrunner, T. A. Henzinger, and P. Rannou, “Mean-payoff automaton expressions,” presented at the CONCUR: Concurrency Theory, Paris, France, 2010, vol. 6269, pp. 269–283.' ista: 'Chatterjee K, Doyen L, Edelsbrunner H, Henzinger TA, Rannou P. 2010. Mean-payoff automaton expressions. CONCUR: Concurrency Theory, LNCS, vol. 6269, 269–283.' mla: Chatterjee, Krishnendu, et al. Mean-Payoff Automaton Expressions. Vol. 6269, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2010, pp. 269–83, doi:10.1007/978-3-642-15375-4_19. short: K. Chatterjee, L. Doyen, H. Edelsbrunner, T.A. Henzinger, P. Rannou, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2010, pp. 269–283. conference: end_date: 2010-09-03 location: Paris, France name: 'CONCUR: Concurrency Theory' start_date: 2010-08-31 date_created: 2018-12-11T12:05:31Z date_published: 2010-11-18T00:00:00Z date_updated: 2021-01-12T07:52:40Z day: '18' ddc: - '000' - '005' department: - _id: KrCh - _id: HeEd - _id: ToHe doi: 10.1007/978-3-642-15375-4_19 ec_funded: 1 file: - access_level: open_access checksum: 4f753ae99d076553fb8733e2c8b390e2 content_type: application/pdf creator: system date_created: 2018-12-12T10:15:41Z date_updated: 2020-07-14T12:46:17Z file_id: '5163' file_name: IST-2012-62-v1+1_Mean-payoff_automaton_expressions.pdf file_size: 233260 relation: main_file file_date_updated: 2020-07-14T12:46:17Z has_accepted_license: '1' intvolume: ' 6269' language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version page: 269 - 283 project: - _id: 25EFB36C-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '215543' name: COMponent-Based Embedded Systems design Techniques - _id: 25F1337C-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '214373' name: Design for Embedded Systems publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '2328' pubrep_id: '62' quality_controlled: '1' scopus_import: 1 status: public title: Mean-payoff automaton expressions type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 6269 year: '2010' ... --- _id: '3849' abstract: - lang: eng text: Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classes. Prior work has shown that the homology and robustness information can be read off the extended persistence diagram of the function. This paper extends these results to a non-uniform error model in which perturbations vary in their magnitude across the domain. alternative_title: - LNCS author: - first_name: Paul full_name: Bendich, Paul id: 43F6EC54-F248-11E8-B48F-1D18A9856A87 last_name: Bendich - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Amit full_name: Patel, Amit id: 34A254A0-F248-11E8-B48F-1D18A9856A87 last_name: Patel citation: ama: 'Bendich P, Edelsbrunner H, Kerber M, Patel A. Persistent homology under non-uniform error. In: Vol 6281. Springer; 2010:12-23. doi:10.1007/978-3-642-15155-2_2' apa: 'Bendich, P., Edelsbrunner, H., Kerber, M., & Patel, A. (2010). Persistent homology under non-uniform error (Vol. 6281, pp. 12–23). Presented at the MFCS: Mathematical Foundations of Computer Science, Brno, Czech Republic: Springer. https://doi.org/10.1007/978-3-642-15155-2_2' chicago: Bendich, Paul, Herbert Edelsbrunner, Michael Kerber, and Amit Patel. “Persistent Homology under Non-Uniform Error,” 6281:12–23. Springer, 2010. https://doi.org/10.1007/978-3-642-15155-2_2. ieee: 'P. Bendich, H. Edelsbrunner, M. Kerber, and A. Patel, “Persistent homology under non-uniform error,” presented at the MFCS: Mathematical Foundations of Computer Science, Brno, Czech Republic, 2010, vol. 6281, pp. 12–23.' ista: 'Bendich P, Edelsbrunner H, Kerber M, Patel A. 2010. Persistent homology under non-uniform error. MFCS: Mathematical Foundations of Computer Science, LNCS, vol. 6281, 12–23.' mla: Bendich, Paul, et al. Persistent Homology under Non-Uniform Error. Vol. 6281, Springer, 2010, pp. 12–23, doi:10.1007/978-3-642-15155-2_2. short: P. Bendich, H. Edelsbrunner, M. Kerber, A. Patel, in:, Springer, 2010, pp. 12–23. conference: end_date: 2010-08-27 location: Brno, Czech Republic name: 'MFCS: Mathematical Foundations of Computer Science' start_date: 2010-08-23 date_created: 2018-12-11T12:05:30Z date_published: 2010-08-10T00:00:00Z date_updated: 2021-01-12T07:52:38Z day: '10' ddc: - '000' department: - _id: HeEd doi: 10.1007/978-3-642-15155-2_2 file: - access_level: open_access checksum: af61e1c2bb42f3d556179d4692caeb1b content_type: application/pdf creator: system date_created: 2018-12-12T10:13:13Z date_updated: 2020-07-14T12:46:17Z file_id: '4994' file_name: IST-2016-537-v1+1_2010-P-05-NonuniformError.pdf file_size: 142357 relation: main_file file_date_updated: 2020-07-14T12:46:17Z has_accepted_license: '1' intvolume: ' 6281' language: - iso: eng month: '08' oa: 1 oa_version: Submitted Version page: 12 - 23 publication_status: published publisher: Springer publist_id: '2333' pubrep_id: '537' quality_controlled: '1' scopus_import: 1 status: public title: Persistent homology under non-uniform error type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 6281 year: '2010' ... --- _id: '3850' abstract: - lang: eng text: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape with a disk of fixed radius? If it does, we also seek a preferably simple solution shape P;P’s offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give a decision algorithm for fixed radius in O(nlogn) time that handles any polygonal shape. For convex shapes, the complexity drops to O(n), which is also the time required to compute a solution shape P with at most one more vertex than a vertex-minimal one. author: - first_name: Eric full_name: Berberich, Eric last_name: Berberich - first_name: Dan full_name: Halperin, Dan last_name: Halperin - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Roza full_name: Pogalnikova, Roza last_name: Pogalnikova citation: ama: 'Berberich E, Halperin D, Kerber M, Pogalnikova R. Polygonal reconstruction from approximate offsets. In: TU Dortmund; 2010:12-23.' apa: 'Berberich, E., Halperin, D., Kerber, M., & Pogalnikova, R. (2010). Polygonal reconstruction from approximate offsets (pp. 12–23). Presented at the EuroCG: European Workshop on Computational Geometry, Dortmund, Germany: TU Dortmund.' chicago: Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Polygonal Reconstruction from Approximate Offsets,” 12–23. TU Dortmund, 2010. ieee: 'E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Polygonal reconstruction from approximate offsets,” presented at the EuroCG: European Workshop on Computational Geometry, Dortmund, Germany, 2010, pp. 12–23.' ista: 'Berberich E, Halperin D, Kerber M, Pogalnikova R. 2010. Polygonal reconstruction from approximate offsets. EuroCG: European Workshop on Computational Geometry, 12–23.' mla: Berberich, Eric, et al. Polygonal Reconstruction from Approximate Offsets. TU Dortmund, 2010, pp. 12–23. short: E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, in:, TU Dortmund, 2010, pp. 12–23. conference: end_date: 2010-03-24 location: Dortmund, Germany name: 'EuroCG: European Workshop on Computational Geometry' start_date: 2010-03-22 date_created: 2018-12-11T12:05:30Z date_published: 2010-01-01T00:00:00Z date_updated: 2021-01-12T07:52:39Z day: '01' department: - _id: HeEd language: - iso: eng month: '01' oa_version: None page: 12 - 23 publication_status: published publisher: TU Dortmund publist_id: '2334' quality_controlled: '1' status: public title: Polygonal reconstruction from approximate offsets type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2010' ... --- _id: '3901' abstract: - lang: eng text: We are interested in 3-dimensional images given as arrays of voxels with intensity values. Extending these values to acontinuous function, we study the robustness of homology classes in its level and interlevel sets, that is, the amount of perturbationneeded to destroy these classes. The structure of the homology classes and their robustness, over all level and interlevel sets, can bevisualized by a triangular diagram of dots obtained by computing the extended persistence of the function. We give a fast hierarchicalalgorithm using the dual complexes of oct-tree approximations of the function. In addition, we show that for balanced oct-trees, thedual complexes are geometrically realized in $R^3$ and can thus be used to construct level and interlevel sets. We apply these tools tostudy 3-dimensional images of plant root systems. author: - first_name: Paul full_name: Bendich, Paul id: 43F6EC54-F248-11E8-B48F-1D18A9856A87 last_name: Bendich - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: Bendich P, Edelsbrunner H, Kerber M. Computing robustness and persistence for images. IEEE Transactions of Visualization and Computer Graphics. 2010;16(6):1251-1260. doi:10.1109/TVCG.2010.139 apa: Bendich, P., Edelsbrunner, H., & Kerber, M. (2010). Computing robustness and persistence for images. IEEE Transactions of Visualization and Computer Graphics. IEEE. https://doi.org/10.1109/TVCG.2010.139 chicago: Bendich, Paul, Herbert Edelsbrunner, and Michael Kerber. “Computing Robustness and Persistence for Images.” IEEE Transactions of Visualization and Computer Graphics. IEEE, 2010. https://doi.org/10.1109/TVCG.2010.139. ieee: P. Bendich, H. Edelsbrunner, and M. Kerber, “Computing robustness and persistence for images,” IEEE Transactions of Visualization and Computer Graphics, vol. 16, no. 6. IEEE, pp. 1251–1260, 2010. ista: Bendich P, Edelsbrunner H, Kerber M. 2010. Computing robustness and persistence for images. IEEE Transactions of Visualization and Computer Graphics. 16(6), 1251–1260. mla: Bendich, Paul, et al. “Computing Robustness and Persistence for Images.” IEEE Transactions of Visualization and Computer Graphics, vol. 16, no. 6, IEEE, 2010, pp. 1251–60, doi:10.1109/TVCG.2010.139. short: P. Bendich, H. Edelsbrunner, M. Kerber, IEEE Transactions of Visualization and Computer Graphics 16 (2010) 1251–1260. date_created: 2018-12-11T12:05:47Z date_published: 2010-10-28T00:00:00Z date_updated: 2021-01-12T07:53:04Z day: '28' ddc: - '000' department: - _id: HeEd doi: 10.1109/TVCG.2010.139 file: - access_level: open_access checksum: f6d813c04f4b46023cec6b9a17f15472 content_type: application/pdf creator: system date_created: 2018-12-12T10:17:10Z date_updated: 2020-07-14T12:46:21Z file_id: '5262' file_name: IST-2016-536-v1+1_2010-J-02-PersistenceforImages.pdf file_size: 721994 relation: main_file file_date_updated: 2020-07-14T12:46:21Z has_accepted_license: '1' intvolume: ' 16' issue: '6' language: - iso: eng month: '10' oa: 1 oa_version: Submitted Version page: 1251 - 1260 publication: IEEE Transactions of Visualization and Computer Graphics publication_status: published publisher: IEEE publist_id: '2253' pubrep_id: '536' quality_controlled: '1' scopus_import: 1 status: public title: Computing robustness and persistence for images type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2010' ... --- _id: '3968' abstract: - lang: eng text: We describe an algorithm for segmenting three-dimensional medical imaging data modeled as a continuous function on a 3-manifold. It is related to watershed algorithms developed in image processing but is closer to its mathematical roots, which are Morse theory and homological algebra. It allows for the implicit treatment of an underlying mesh, thus combining the structural integrity of its mathematical foundations with the computational efficiency of image processing. acknowledgement: This research was partially supported by Geomagic, Inc., and by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0007 and HR0011-05-1-0057. alternative_title: - LNCS author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: John full_name: Harer, John last_name: Harer citation: ama: 'Edelsbrunner H, Harer J. The persistent Morse complex segmentation of a 3-manifold. In: Vol 5903. Springer; 2009:36-50. doi:10.1007/978-3-642-10470-1_4' apa: 'Edelsbrunner, H., & Harer, J. (2009). The persistent Morse complex segmentation of a 3-manifold (Vol. 5903, pp. 36–50). Presented at the 3DPH: Modelling the Physiological Human, Zermatt, Switzerland: Springer. https://doi.org/10.1007/978-3-642-10470-1_4' chicago: Edelsbrunner, Herbert, and John Harer. “The Persistent Morse Complex Segmentation of a 3-Manifold,” 5903:36–50. Springer, 2009. https://doi.org/10.1007/978-3-642-10470-1_4. ieee: 'H. Edelsbrunner and J. Harer, “The persistent Morse complex segmentation of a 3-manifold,” presented at the 3DPH: Modelling the Physiological Human, Zermatt, Switzerland, 2009, vol. 5903, pp. 36–50.' ista: 'Edelsbrunner H, Harer J. 2009. The persistent Morse complex segmentation of a 3-manifold. 3DPH: Modelling the Physiological Human, LNCS, vol. 5903, 36–50.' mla: Edelsbrunner, Herbert, and John Harer. The Persistent Morse Complex Segmentation of a 3-Manifold. Vol. 5903, Springer, 2009, pp. 36–50, doi:10.1007/978-3-642-10470-1_4. short: H. Edelsbrunner, J. Harer, in:, Springer, 2009, pp. 36–50. conference: end_date: 2009-12-02 location: Zermatt, Switzerland name: '3DPH: Modelling the Physiological Human' start_date: 2009-11-29 date_created: 2018-12-11T12:06:10Z date_published: 2009-11-17T00:00:00Z date_updated: 2021-01-12T07:53:32Z day: '17' ddc: - '000' department: - _id: HeEd doi: 10.1007/978-3-642-10470-1_4 file: - access_level: open_access checksum: 11fc85bcc19bab1f020e706a4b8a4660 content_type: application/pdf creator: system date_created: 2018-12-12T10:08:33Z date_updated: 2020-07-14T12:46:21Z file_id: '4694' file_name: IST-2016-535-v1+1_2009-P-04-3ManifoldSegmentation.pdf file_size: 165090 relation: main_file file_date_updated: 2020-07-14T12:46:21Z has_accepted_license: '1' intvolume: ' 5903' language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version page: 36 - 50 publication_status: published publisher: Springer publist_id: '2160' pubrep_id: '535' quality_controlled: '1' scopus_import: 1 status: public title: The persistent Morse complex segmentation of a 3-manifold type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 5903 year: '2009' ...