--- _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' ...