[{"year":"2012","publication_status":"published","day":"01","publication":"Russian Mathematical Surveys","language":[{"iso":"eng"}],"page":"1167–1168","date_published":"2012-10-01T00:00:00Z","doi":"10.4213/rm9503","volume":67,"issue":"6","date_created":"2018-12-11T12:00:18Z","oa_version":"None","quality_controlled":"1","publisher":"Russian Academy of Sciences","month":"10","intvolume":" 67","date_updated":"2023-10-17T11:40:39Z","citation":{"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.","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.","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.","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"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"3831","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Strelkova","full_name":"Strelkova, Nataliya","first_name":"Nataliya"}],"article_processing_charge":"No","title":"On the configuration space for the shortest networks","department":[{"_id":"HeEd"}],"_id":"2912","type":"journal_article","status":"public"},{"month":"06","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1206.4652","open_access":"1"}],"scopus_import":"1","publisher":"ML Research Press","quality_controlled":"1","oa_version":"Preprint","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."}],"date_created":"2018-12-11T12:01:33Z","date_published":"2012-06-01T00:00:00Z","page":"211-218","publication":"Proceedings of the 29th International Conference on Machine Learning","language":[{"iso":"eng"}],"day":"01","year":"2012","publication_status":"published","status":"public","conference":{"name":"ICML: International Conference on Machine Learning","start_date":"2012-06-26","end_date":"2012-07-01","location":"Edinburgh, United Kingdom"},"type":"conference","_id":"3127","title":"The most persistent soft-clique in a set of sampled graphs","department":[{"_id":"ChLa"},{"_id":"HeEd"}],"article_processing_charge":"No","author":[{"first_name":"Novi","full_name":"Quadrianto, Novi","last_name":"Quadrianto"},{"full_name":"Lampert, Christoph","orcid":"0000-0001-8622-7887","last_name":"Lampert","first_name":"Christoph","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Chen","full_name":"Chen, Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao"}],"publist_id":"3572","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-10-17T11:55:06Z","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.","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.","short":"N. Quadrianto, C. Lampert, C. Chen, in:, Proceedings of the 29th International Conference on Machine Learning, ML Research Press, 2012, pp. 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.","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.","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."}},{"article_processing_charge":"No","publist_id":"3843","author":[{"last_name":"Pausinger","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"title":"Weak multipliers for generalized van der Corput sequences","citation":{"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","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","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.","short":"F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 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.","ista":"Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"729 - 749","date_created":"2018-12-11T12:00:15Z","doi":"10.5802/jtnb.819","date_published":"2012-01-01T00:00:00Z","year":"2012","has_accepted_license":"1","publication":"Journal de Theorie des Nombres des Bordeaux","day":"01","oa":1,"publisher":"Université de Bordeaux","quality_controlled":"1","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:52Z","date_updated":"2023-10-18T07:53:47Z","ddc":["510"],"article_type":"original","type":"journal_article","status":"public","_id":"2904","issue":"3","volume":24,"publication_status":"published","publication_identifier":{"eissn":["2118-8572"],"issn":["1246-7405"]},"language":[{"iso":"eng"}],"file":[{"file_size":819275,"date_updated":"2020-07-14T12:45:52Z","creator":"dernst","file_name":"JTNB_2012__24_3_729_0.pdf","date_created":"2020-05-11T12:40:39Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","checksum":"6954bfe9d7f4119fbdda7a11cf0f5c67","file_id":"7819"}],"scopus_import":"1","intvolume":" 24","month":"01","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."},{"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.","lang":"fre"}],"oa_version":"Published Version"},{"abstract":[{"text":"We present an algorithm for simplifying linear cartographic objects and results obtained with a computer program implementing this algorithm. ","lang":"eng"}],"oa_version":"Published Version","publisher":"Russian Academy of Sciences","quality_controlled":"1","oa":1,"main_file_link":[{"url":"http://mi.mathnet.ru/eng/mais280","open_access":"1"}],"month":"12","intvolume":" 19","year":"2012","publication_status":"published","day":"01","language":[{"iso":"rus"}],"publication":"Modeling and Analysis of Information Systems","page":"152 - 160","date_published":"2012-12-01T00:00:00Z","issue":"6","volume":19,"date_created":"2018-12-11T12:00:15Z","_id":"2902","type":"journal_article","article_type":"original","status":"public","citation":{"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.","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.","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.","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.","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.","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."},"date_updated":"2023-10-18T07:34:45Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"3845","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Oleg","full_name":"Musin, Oleg","last_name":"Musin"},{"full_name":"Ukhalov, Alexey","last_name":"Ukhalov","first_name":"Alexey"},{"last_name":"Yakimova","full_name":"Yakimova, Olga","first_name":"Olga"},{"full_name":"Alexeev, Vladislav","last_name":"Alexeev","first_name":"Vladislav"},{"full_name":"Bogaevskaya, Victoriya","last_name":"Bogaevskaya","first_name":"Victoriya"},{"first_name":"Andrey","full_name":"Gorohov, Andrey","last_name":"Gorohov"},{"first_name":"Margarita","full_name":"Preobrazhenskaya, Margarita","last_name":"Preobrazhenskaya"}],"article_processing_charge":"No","department":[{"_id":"HeEd"}],"title":"Fractal and computational geometry for generalizing cartographic objects"},{"scopus_import":1,"publisher":"Neural Information Processing Systems Foundation","quality_controlled":"1","intvolume":" 24","month":"12","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."}],"oa_version":"None","page":"1827 - 1835","date_created":"2018-12-11T12:02:21Z","volume":24,"date_published":"2011-12-01T00:00:00Z","publication_status":"published","year":"2011","publication":"NIPS Proceedings","language":[{"iso":"eng"}],"day":"01","conference":{"end_date":"2011-12-14","location":"Granada, Spain","start_date":"2011-12-12","name":"NIPS: Neural Information Processing Systems"},"type":"conference","status":"public","_id":"3266","publist_id":"3381","author":[{"id":"29F89302-F248-11E8-B48F-1D18A9856A87","first_name":"Adrian","full_name":"Ion, Adrian","last_name":"Ion"},{"last_name":"Carreira","full_name":"Carreira, Joao","first_name":"Joao"},{"full_name":"Sminchisescu, Cristian","last_name":"Sminchisescu","first_name":"Cristian"}],"title":"Probabilistic joint image segmentation and labeling","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T07:42:15Z","citation":{"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.","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.","short":"A. Ion, J. Carreira, C. Sminchisescu, in:, NIPS Proceedings, Neural Information Processing Systems Foundation, 2011, pp. 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.","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.","mla":"Ion, Adrian, et al. “Probabilistic Joint Image Segmentation and Labeling.” NIPS Proceedings, vol. 24, Neural Information Processing Systems Foundation, 2011, pp. 1827–35."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T07:42:16Z","status":"public","type":"journal_article","article_type":"original","_id":"3269","issue":"4","volume":30,"language":[{"iso":"eng"}],"publication_status":"published","month":"07","intvolume":" 30","scopus_import":1,"main_file_link":[{"url":"http://www.cs.cmu.edu/%7Eshengyu/download/egsr2011_paper.pdf","open_access":"1"}],"oa_version":"Published Version","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."}],"title":"Perceptual global illumination cancellation in complex projection environments","author":[{"full_name":"Sheng, Yu","last_name":"Sheng","first_name":"Yu"},{"first_name":"Barbara","full_name":"Cutler, Barbara","last_name":"Cutler"},{"last_name":"Chen","full_name":"Chen, Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao"},{"first_name":"Joshua","full_name":"Nasman, Joshua","last_name":"Nasman"}],"publist_id":"3377","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","short":"Y. Sheng, B. Cutler, C. Chen, J. Nasman, Computer Graphics Forum 30 (2011) 1261–1268.","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.","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","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","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."},"doi":"10.1111/j.1467-8659.2011.01985.x","date_published":"2011-07-19T00:00:00Z","date_created":"2018-12-11T12:02:22Z","page":"1261 - 1268","day":"19","publication":"Computer Graphics Forum","year":"2011","publisher":"Wiley-Blackwell","quality_controlled":"1","oa":1},{"status":"public","type":"journal_article","_id":"3267","department":[{"_id":"HeEd"}],"title":"Hardness results for homology localization","author":[{"full_name":"Chen, Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao"},{"first_name":"Daniel","last_name":"Freedman","full_name":"Freedman, Daniel"}],"publist_id":"3379","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","apa":"Chen, C., & Freedman, D. (2011). Hardness results for homology localization. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-010-9322-8","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","ieee":"C. Chen and D. Freedman, “Hardness results for homology localization,” Discrete & Computational Geometry, vol. 45, no. 3. Springer, pp. 425–448, 2011.","short":"C. Chen, D. Freedman, Discrete & Computational Geometry 45 (2011) 425–448."},"date_updated":"2023-02-21T16:07:10Z","month":"01","intvolume":" 45","scopus_import":1,"publisher":"Springer","quality_controlled":"1","oa_version":"None","abstract":[{"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.","lang":"eng"}],"volume":45,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"10909"}]},"doi":"10.1007/s00454-010-9322-8","date_published":"2011-01-14T00:00:00Z","issue":"3","date_created":"2018-12-11T12:02:21Z","page":"425 - 448","day":"14","language":[{"iso":"eng"}],"publication":"Discrete & Computational Geometry","publication_status":"published","year":"2011"},{"publication_status":"published","language":[{"iso":"eng"}],"volume":6970,"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."}],"oa_version":"Preprint","main_file_link":[{"url":"http://arxiv.org/abs/1306.3640","open_access":"1"}],"alternative_title":["LNCS"],"scopus_import":1,"intvolume":" 6970","month":"11","date_updated":"2021-01-12T07:42:44Z","department":[{"_id":"HeEd"}],"series_title":"Special Issue on Voronoi Diagrams and Delaunay Triangulation","_id":"3335","type":"book_chapter","status":"public","year":"2011","publication":"Transactions on Computational Science XIV","day":"09","page":"60 - 101","date_created":"2018-12-11T12:02:44Z","doi":"10.1007/978-3-642-25249-5_3","date_published":"2011-11-09T00:00:00Z","oa":1,"publisher":"Springer","quality_controlled":"1","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","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.","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.","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.","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.","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."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1306.3640"]},"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"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Jones, Bernard","last_name":"Jones","first_name":"Bernard"},{"first_name":"Pratyush","last_name":"Pranav","full_name":"Pranav, Pratyush"},{"last_name":"Park","full_name":"Park, Changbom","first_name":"Changbom"},{"full_name":"Hellwing, Wojciech","last_name":"Hellwing","first_name":"Wojciech"},{"first_name":"Bob","last_name":"Eldering","full_name":"Eldering, Bob"},{"last_name":"Kruithof","full_name":"Kruithof, Nico","first_name":"Nico"},{"full_name":"Bos, Patrick","last_name":"Bos","first_name":"Patrick"},{"last_name":"Hidding","full_name":"Hidding, Johan","first_name":"Johan"},{"first_name":"Job","full_name":"Feldbrugge, Job","last_name":"Feldbrugge"},{"first_name":"Eline","last_name":"Ten Have","full_name":"Ten Have, Eline"},{"full_name":"Van Engelen, Matti","last_name":"Van Engelen","first_name":"Matti"},{"last_name":"Caroli","full_name":"Caroli, Manuel","first_name":"Manuel"},{"first_name":"Monique","last_name":"Teillaud","full_name":"Teillaud, Monique"}],"publist_id":"3295","editor":[{"last_name":"Gavrilova","full_name":"Gavrilova, Marina","first_name":"Marina"},{"first_name":"Kenneth","full_name":"Tan, Kenneth","last_name":"Tan"},{"full_name":"Mostafavi, Mir","last_name":"Mostafavi","first_name":"Mir"}],"title":"Alpha, Betti and the Megaparsec Universe: On the topology of the Cosmic Web"},{"abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","publisher":"ACM","scopus_import":1,"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1109.2158"}],"oa":1,"month":"06","year":"2011","publication_status":"published","day":"13","language":[{"iso":"eng"}],"publication":"Proceedings of the twenty-seventh annual symposium on Computational geometry","page":"187 - 196","related_material":{"record":[{"relation":"later_version","status":"public","id":"3115"}]},"date_published":"2011-06-13T00:00:00Z","doi":"10.1145/1998196.1998225","date_created":"2018-12-11T12:02:42Z","_id":"3329","type":"conference","conference":{"name":"SCG: Symposium on Computational Geometry","location":"Paris, France","end_date":"2011-06-15","start_date":"2011-06-13"},"status":"public","citation":{"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.","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.","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.","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","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","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."},"date_updated":"2023-02-23T11:12:57Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publist_id":"3306","author":[{"first_name":"Eric","full_name":"Berberich, Eric","last_name":"Berberich"},{"full_name":"Halperin, Dan","last_name":"Halperin","first_name":"Dan"},{"first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber"},{"first_name":"Roza","full_name":"Pogalnikova, Roza","last_name":"Pogalnikova"}],"title":"Deconstructing approximate offsets","department":[{"_id":"HeEd"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","short":"M. Kerber, M. Sagraloff, Graphs and Combinatorics 27 (2011) 419–430.","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."},"title":"A note on the complexity of real algebraic hypersurfaces","article_processing_charge":"No","publist_id":"3301","author":[{"last_name":"Kerber","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael"},{"last_name":"Sagraloff","full_name":"Sagraloff, Michael","first_name":"Michael"}],"oa":1,"publisher":"Springer","quality_controlled":"1","publication":"Graphs and Combinatorics","day":"17","year":"2011","has_accepted_license":"1","date_created":"2018-12-11T12:02:43Z","date_published":"2011-03-17T00:00:00Z","doi":"10.1007/s00373-011-1020-7","page":"419 - 430","_id":"3332","status":"public","article_type":"original","type":"journal_article","ddc":["500"],"date_updated":"2021-01-12T07:42:43Z","file_date_updated":"2020-07-14T12:46:08Z","department":[{"_id":"HeEd"}],"oa_version":"Submitted Version","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."}],"intvolume":" 27","month":"03","scopus_import":1,"language":[{"iso":"eng"}],"file":[{"file_id":"7869","checksum":"a63a1e3e885dcc68f1e3dea68dfbe213","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2020-05-19T16:11:36Z","file_name":"2011_GraphsCombi_Kerber.pdf","creator":"dernst","date_updated":"2020-07-14T12:46:08Z","file_size":143976}],"publication_status":"published","issue":"3","volume":27},{"day":"08","language":[{"iso":"eng"}],"year":"2011","publication_status":"published","doi":"10.1145/1993886.1993920","date_published":"2011-06-08T00:00:00Z","date_created":"2018-12-11T12:02:43Z","page":"209 - 216","oa_version":"Preprint","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."}],"month":"06","scopus_import":1,"publisher":"Springer","quality_controlled":"1","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1104.1362","open_access":"1"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T07:42:42Z","citation":{"ista":"Kerber M, Sagraloff M. 2011. Root refinement for real polynomials. ISSAC: International Symposium on Symbolic and Algebraic Computation, 209–216.","chicago":"Kerber, Michael, and Michael Sagraloff. “Root Refinement for Real Polynomials,” 209–16. Springer, 2011. https://doi.org/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","ama":"Kerber M, Sagraloff M. Root refinement for real polynomials. In: Springer; 2011:209-216. doi: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.","short":"M. Kerber, M. Sagraloff, in:, Springer, 2011, pp. 209–216.","mla":"Kerber, Michael, and Michael Sagraloff. Root Refinement for Real Polynomials. Springer, 2011, pp. 209–16, doi:10.1145/1993886.1993920."},"department":[{"_id":"HeEd"}],"title":"Root refinement for real polynomials","publist_id":"3304","author":[{"orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","last_name":"Kerber","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael"},{"last_name":"Sagraloff","full_name":"Sagraloff, Michael","first_name":"Michael"}],"external_id":{"arxiv":["1104.1362"]},"article_processing_charge":"No","_id":"3330","status":"public","type":"conference","conference":{"name":"ISSAC: International Symposium on Symbolic and Algebraic Computation","location":"California, USA","end_date":"2011-06-11","start_date":"2011-06-08"}},{"_id":"3328","conference":{"name":"SCG: Symposium on Computational Geometry","start_date":"2011-06-13","end_date":"2011-06-15","location":"Paris, France"},"type":"conference","status":"public","citation":{"short":"E. Berberich, M. Hemmer, M. Kerber, in:, ACM, 2011, pp. 179–186.","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.","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","mla":"Berberich, Eric, et al. A Generic Algebraic Kernel for Non Linear Geometric Applications. ACM, 2011, pp. 179–86, doi:10.1145/1998196.1998224.","ista":"Berberich E, Hemmer M, Kerber M. 2011. A generic algebraic kernel for non linear geometric applications. SCG: Symposium on Computational Geometry, 179–186.","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."},"date_updated":"2021-01-12T07:42:41Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","publist_id":"3307","author":[{"first_name":"Eric","last_name":"Berberich","full_name":"Berberich, Eric"},{"first_name":"Michael","last_name":"Hemmer","full_name":"Hemmer, Michael"},{"first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","last_name":"Kerber"}],"department":[{"_id":"HeEd"}],"title":"A generic algebraic kernel for non linear geometric applications","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."}],"oa_version":"Published Version","main_file_link":[{"open_access":"1","url":"https://hal.inria.fr/inria-00480031/file/RR-7274.pdf"}],"oa":1,"scopus_import":1,"publisher":"ACM","quality_controlled":"1","month":"06","publication_status":"published","year":"2011","language":[{"iso":"eng"}],"day":"13","page":"179 - 186","date_created":"2018-12-11T12:02:42Z","doi":"10.1145/1998196.1998224","date_published":"2011-06-13T00:00:00Z"},{"citation":{"short":"H. Edelsbrunner, J. Pach, G. Ziegler, Discrete & Computational Geometry 45 (2011) 1–2.","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.","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","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","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.","ista":"Edelsbrunner H, Pach J, Ziegler G. 2011. Letter from the new editors-in-chief. Discrete & Computational Geometry. 45(1), 1–2.","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."},"date_updated":"2021-01-12T07:42:44Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Pach, János","last_name":"Pach","first_name":"János"},{"full_name":"Ziegler, Günter","last_name":"Ziegler","first_name":"Günter"}],"publist_id":"3297","department":[{"_id":"HeEd"}],"title":"Letter from the new editors-in-chief","_id":"3334","article_type":"letter_note","type":"journal_article","status":"public","publication_status":"published","year":"2011","day":"01","publication":"Discrete & Computational Geometry","language":[{"iso":"eng"}],"page":"1 - 2","volume":45,"issue":"1","doi":"10.1007/s00454-010-9313-9","date_published":"2011-01-01T00:00:00Z","date_created":"2018-12-11T12:02:44Z","oa_version":"None","quality_controlled":"1","scopus_import":1,"publisher":"Springer","month":"01","intvolume":" 45"},{"_id":"3367","type":"conference","conference":{"end_date":"2011-06-15","location":"Paris, France","start_date":"2011-06-13","name":"SoCG: Symposium on Computational Geometry"},"status":"public","date_updated":"2023-02-23T11:05:04Z","citation":{"mla":"Chen, Chao, and Michael Kerber. An Output Sensitive Algorithm for Persistent Homology. ACM, 2011, pp. 207–16, doi:10.1145/1998196.1998228.","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","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.","short":"C. Chen, M. Kerber, in:, ACM, 2011, pp. 207–216.","chicago":"Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology,” 207–16. ACM, 2011. https://doi.org/10.1145/1998196.1998228.","ista":"Chen C, Kerber M. 2011. An output sensitive algorithm for persistent homology. SoCG: Symposium on Computational Geometry, 207–216."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"3245","author":[{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao","last_name":"Chen","full_name":"Chen, Chao"},{"first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber"}],"article_processing_charge":"No","title":"An output sensitive algorithm for persistent homology","department":[{"_id":"HeEd"}],"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."}],"oa_version":"None","quality_controlled":"1","publisher":"ACM","scopus_import":1,"month":"06","year":"2011","publication_status":"published","day":"13","language":[{"iso":"eng"}],"page":"207 - 216","date_published":"2011-06-13T00:00:00Z","doi":"10.1145/1998196.1998228","related_material":{"record":[{"relation":"later_version","status":"public","id":"2939"}]},"date_created":"2018-12-11T12:02:56Z"},{"year":"2011","publication_status":"published","day":"01","publication":"Acta Sci. Math. (Szeged)","language":[{"iso":"eng"}],"page":"359 - 367","issue":"1-2","volume":77,"date_published":"2011-01-01T00:00:00Z","date_created":"2018-12-11T12:05:08Z","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."}],"oa_version":"None","acknowledgement":"Funded by Graduate Aid in Areas of National Need (GAANN) Fellowship.","publisher":"Szegedi Tudományegyetem","quality_controlled":"1","month":"01","intvolume":" 77","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.","short":"B.T. Fasy, Acta Sci. Math. (Szeged) 77 (2011) 359–367.","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.","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.","ista":"Fasy BT. 2011. The difference in length of curves in R^n. Acta Sci. Math. (Szeged). 77(1–2), 359–367.","chicago":"Fasy, Brittany Terese. “The Difference in Length of Curves in R^n.” Acta Sci. Math. (Szeged). Szegedi Tudományegyetem, 2011."},"date_updated":"2021-01-12T07:52:09Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Fasy","full_name":"Fasy, Brittany Terese","id":"F65D502E-E68D-11E9-9252-C644099818F6","first_name":"Brittany Terese"}],"publist_id":"2446","title":"The difference in length of curves in R^n","department":[{"_id":"HeEd"}],"_id":"3781","type":"journal_article","status":"public"},{"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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","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.","short":"H. Edelsbrunner, M. Kerber, in:, C. Calude, G. Rozenberg, A. Salomaa (Eds.), Rainbow of Computer Science, Springer, 2011, pp. 20–35."},"title":"Covering and packing with spheres by diagonal distortion in R^n","editor":[{"last_name":"Calude","full_name":"Calude, Cristian","first_name":"Cristian"},{"last_name":"Rozenberg","full_name":"Rozenberg, Grzegorz","first_name":"Grzegorz"},{"first_name":"Arto","full_name":"Salomaa, Arto","last_name":"Salomaa"}],"author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","last_name":"Kerber"}],"publist_id":"2427","day":"03","publication":"Rainbow of Computer Science","has_accepted_license":"1","year":"2011","doi":"10.1007/978-3-642-19391-0_2","date_published":"2011-05-03T00:00:00Z","date_created":"2018-12-11T12:05:13Z","page":"20 - 35","quality_controlled":"1","publisher":"Springer","oa":1,"ddc":["000"],"date_updated":"2021-01-12T07:52:15Z","file_date_updated":"2020-07-14T12:46:16Z","department":[{"_id":"HeEd"}],"_id":"3796","series_title":"Dedicated to Hermann Maurer on the Occasion of His 70th Birthday","status":"public","pubrep_id":"539","type":"book_chapter","file":[{"date_updated":"2020-07-14T12:46:16Z","file_size":436875,"creator":"system","date_created":"2018-12-12T10:07:42Z","file_name":"IST-2016-539-v1+1_2011-B-01-CoveringPacking.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"aaf22b4d7bd4277ffe8db532119cf474","file_id":"4640"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":6570,"oa_version":"Submitted Version","abstract":[{"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.","lang":"eng"}],"month":"05","intvolume":" 6570","alternative_title":["LNCS"]},{"date_published":"2011-05-01T00:00:00Z","issue":"2.2","volume":16,"doi":"10.1145/1963190.1970375","date_created":"2018-12-11T12:06:09Z","page":"1 - 13","day":"01","language":[{"iso":"eng"}],"publication":"Journal of Experimental Algorithmics","publication_status":"published","year":"2011","month":"05","intvolume":" 16","publisher":"ACM","quality_controlled":"1","scopus_import":1,"oa_version":"None","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."}],"department":[{"_id":"HeEd"}],"title":"Computing elevation maxima by searching the Gauss sphere","publist_id":"2161","author":[{"last_name":"Wang","full_name":"Wang, Bei","first_name":"Bei"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Dmitriy","full_name":"Morozov, Dmitriy","last_name":"Morozov"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T07:53:31Z","citation":{"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","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","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.","short":"B. Wang, H. Edelsbrunner, D. Morozov, Journal of Experimental Algorithmics 16 (2011) 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.","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.","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."},"status":"public","type":"journal_article","_id":"3965"},{"title":"Efficient computation of persistent homology for cubical data","department":[{"_id":"HeEd"}],"editor":[{"first_name":"Ronald","last_name":"Peikert","full_name":"Peikert, Ronald"},{"first_name":"Helwig","last_name":"Hauser","full_name":"Hauser, Helwig"},{"first_name":"Hamish","last_name":"Carr","full_name":"Carr, Hamish"},{"first_name":"Raphael","last_name":"Fuchs","full_name":"Fuchs, Raphael"}],"publist_id":"3375","author":[{"last_name":"Wagner","full_name":"Wagner, Hubert","first_name":"Hubert"},{"full_name":"Chen, Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao"},{"full_name":"Vuçini, Erald","last_name":"Vuçini","first_name":"Erald"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T07:42:18Z","citation":{"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.","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.","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","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.","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."},"status":"public","type":"book_chapter","_id":"3271","doi":"10.1007/978-3-642-23175-9_7","date_published":"2011-11-14T00:00:00Z","date_created":"2018-12-11T12:02:23Z","page":"91 - 106","day":"14","publication":"Topological Methods in Data Analysis and Visualization II","language":[{"iso":"eng"}],"year":"2011","publication_status":"published","month":"11","publisher":"Springer","alternative_title":["Theory, Algorithms, and Applications"],"quality_controlled":"1","scopus_import":1,"oa_version":"None","abstract":[{"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.","lang":"eng"}]},{"page":"197 - 200","date_published":"2011-01-01T00:00:00Z","date_created":"2018-12-11T12:02:22Z","publication_status":"published","year":"2011","day":"01","language":[{"iso":"eng"}],"publisher":"TU Dortmund","quality_controlled":"1","month":"01","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."}],"oa_version":"None","publist_id":"3376","author":[{"full_name":"Chen, Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao"},{"last_name":"Kerber","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael"}],"department":[{"_id":"HeEd"}],"title":"Persistent homology computation with a twist","date_updated":"2021-01-12T07:42:17Z","citation":{"mla":"Chen, Chao, and Michael Kerber. Persistent Homology Computation with a Twist. TU Dortmund, 2011, pp. 197–200.","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.","short":"C. Chen, M. Kerber, in:, TU Dortmund, 2011, pp. 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.","ama":"Chen C, Kerber M. Persistent homology computation with a twist. In: TU Dortmund; 2011:197-200.","chicago":"Chen, Chao, and Michael Kerber. “Persistent Homology Computation with a Twist,” 197–200. TU Dortmund, 2011.","ista":"Chen C, Kerber M. 2011. Persistent homology computation with a twist. EuroCG: European Workshop on Computational Geometry, 197–200."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","type":"conference","conference":{"location":"Morschach, Switzerland","end_date":"2011-03-30","start_date":"2011-03-28","name":"EuroCG: European Workshop on Computational Geometry"},"status":"public","_id":"3270"},{"_id":"3312","conference":{"start_date":"2011-11-06","location":"Barcelona, Spain","end_date":"2011-11-13","name":"ICCV: International Conference on Computer Vision"},"type":"conference_poster","pubrep_id":"541","status":"public","date_updated":"2020-07-14T23:03:43Z","ddc":["000"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:46:07Z","abstract":[{"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.","lang":"eng"}],"oa_version":"Submitted Version","month":"12","publication_status":"published","language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"4727","checksum":"30a33564b7b45a7ee31610898267fd0e","creator":"system","file_size":5622728,"date_updated":"2020-07-14T12:46:07Z","file_name":"IST-2016-541-v1+1_2011-P-07-RootReconstruction.pdf","date_created":"2018-12-12T10:09:04Z"}],"article_number":"6126475","citation":{"ieee":"Y. Zheng, S. Gu, H. Edelsbrunner, C. Tomasi, and P. Benfey, Detailed reconstruction of 3D plant root shape. IEEE, 2011.","short":"Y. Zheng, S. Gu, H. Edelsbrunner, C. Tomasi, P. Benfey, Detailed Reconstruction of 3D Plant Root Shape, IEEE, 2011.","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","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","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.","ista":"Zheng Y, Gu S, Edelsbrunner H, Tomasi C, Benfey P. 2011. Detailed reconstruction of 3D plant root shape, IEEE,p.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","publist_id":"3328","author":[{"last_name":"Zheng","full_name":"Zheng, Ying","first_name":"Ying"},{"full_name":"Gu, Steve","last_name":"Gu","first_name":"Steve"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Tomasi","full_name":"Tomasi, Carlo","first_name":"Carlo"},{"full_name":"Benfey, Philip","last_name":"Benfey","first_name":"Philip"}],"title":"Detailed reconstruction of 3D plant root shape","acknowledgement":"This research is supported by the National Science Foundation (NSF) under grant DBI-0820624.","oa":1,"quality_controlled":"1","publisher":"IEEE","year":"2011","has_accepted_license":"1","publication":"Proceedings of the IEEE International Conference on Computer Vision","day":"31","date_created":"2018-12-11T12:02:36Z","doi":"10.1109/ICCV.2011.6126475","date_published":"2011-12-31T00:00:00Z"},{"oa":1,"quality_controlled":"1","publisher":"IEEE","year":"2011","has_accepted_license":"1","publication":"Proceedings of the IEEE International Conference on Computer Vision","day":"06","date_created":"2018-12-11T12:02:37Z","date_published":"2011-11-06T00:00:00Z","doi":"10.1109/ICCV.2011.6126271","article_number":"6126271","citation":{"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.","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.","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","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","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.","short":"C. Chen, H. Edelsbrunner, in:, Proceedings of the IEEE International Conference on Computer Vision, IEEE, 2011.","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."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Chen","full_name":"Chen, Chao","first_name":"Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"publist_id":"3327","title":"Diffusion runs low on persistence fast","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."}],"oa_version":"Submitted Version","scopus_import":1,"month":"11","publication_status":"published","language":[{"iso":"eng"}],"file":[{"date_created":"2018-12-12T10:17:28Z","file_name":"IST-2016-540-v1+1_2011-P-08-RunEmpty.pdf","creator":"system","date_updated":"2020-07-14T12:46:07Z","file_size":614050,"checksum":"6984684081ba123808b344f9f2e64a8f","file_id":"5282","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"_id":"3313","conference":{"end_date":"2011-11-13","location":"Barcelona, Spain","start_date":"2011-11-06","name":"ICCV: International Conference on Computer Vision"},"type":"conference","pubrep_id":"540","status":"public","date_updated":"2021-01-12T07:42:35Z","ddc":["000"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:46:07Z"},{"oa_version":"Submitted Version","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."}],"month":"12","oa":1,"publisher":"Springer","quality_controlled":"1","language":[{"iso":"eng"}],"publication":"Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings","day":"31","file":[{"file_name":"2010_AlphaShapes.pdf","date_created":"2022-05-24T07:55:05Z","creator":"dernst","file_size":475254,"date_updated":"2022-05-24T07:55:05Z","success":1,"file_id":"11408","checksum":"a592ea438351e7280eea993a7713ab8f","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"year":"2011","publication_status":"inpress","has_accepted_license":"1","date_created":"2018-12-11T12:02:36Z","date_published":"2011-12-31T00:00:00Z","_id":"3311","status":"public","type":"book_chapter","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2022-05-24T07:56:30Z","citation":{"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.","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.","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.","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.","ista":"Edelsbrunner H.Alpha shapes - a survey. In: Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings. .","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."},"file_date_updated":"2022-05-24T07:55:05Z","department":[{"_id":"HeEd"}],"title":"Alpha shapes - a survey","editor":[{"first_name":"R","full_name":"van de Weygaert, R","last_name":"van de Weygaert"},{"first_name":"G","last_name":"Vegter","full_name":"Vegter, G"},{"full_name":"Ritzerveld, J","last_name":"Ritzerveld","first_name":"J"},{"first_name":"V","last_name":"Icke","full_name":"Icke, V"}],"article_processing_charge":"No","publist_id":"3329","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}]},{"citation":{"short":"H. Edelsbrunner, D. Morozov, A. Patel, Foundations of Computational Mathematics 11 (2011) 345–361.","ieee":"H. Edelsbrunner, D. Morozov, and A. Patel, “Quantifying transversality by measuring the robustness of intersections,” Foundations of Computational Mathematics, vol. 11, no. 3. 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Foundations of Computational Mathematics. 11(3), 345–361.","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."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dmitriy","full_name":"Morozov, Dmitriy","last_name":"Morozov"},{"full_name":"Patel, Amit","last_name":"Patel","id":"34A254A0-F248-11E8-B48F-1D18A9856A87","first_name":"Amit"}],"publist_id":"3230","title":"Quantifying transversality by measuring the robustness of intersections","year":"2011","publication":"Foundations of Computational Mathematics","day":"01","page":"345 - 361","date_created":"2018-12-11T12:02:59Z","date_published":"2011-06-01T00:00:00Z","doi":"10.1007/s10208-011-9090-8","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.","oa":1,"publisher":"Springer","quality_controlled":"1","date_updated":"2021-01-12T07:43:04Z","department":[{"_id":"HeEd"}],"_id":"3377","type":"journal_article","status":"public","publication_status":"published","language":[{"iso":"eng"}],"volume":11,"issue":"3","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."}],"oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0911.2142"}],"scopus_import":1,"intvolume":" 11","month":"06"},{"day":"01","language":[{"iso":"eng"}],"publication":"Foundations of Computational Mathematics","publication_status":"published","year":"2011","issue":"3","doi":"10.1007/s10208-010-9081-1","date_published":"2011-06-01T00:00:00Z","volume":11,"date_created":"2018-12-11T12:02:59Z","page":"305 - 336","oa_version":"None","acknowledgement":"This research was partially supported by the Defense Advanced Research Projects Agency (DARPA) under grant HR0011-05-1-0007.","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."}],"month":"06","intvolume":" 11","scopus_import":1,"quality_controlled":"1","publisher":"Springer","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T07:43:04Z","citation":{"chicago":"Bendich, Paul, and John Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics. Springer, 2011. https://doi.org/10.1007/s10208-010-9081-1.","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.","apa":"Bendich, P., & Harer, J. (2011). Persistent intersection homology. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-010-9081-1","ama":"Bendich P, Harer J. Persistent intersection homology. Foundations of Computational Mathematics. 2011;11(3):305-336. doi:10.1007/s10208-010-9081-1","short":"P. Bendich, J. Harer, Foundations of Computational Mathematics 11 (2011) 305–336.","ieee":"P. Bendich and J. Harer, “Persistent intersection homology,” Foundations of Computational Mathematics, vol. 11, no. 3. Springer, pp. 305–336, 2011."},"department":[{"_id":"HeEd"}],"title":"Persistent intersection homology","publist_id":"3229","author":[{"first_name":"Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","full_name":"Bendich, Paul","last_name":"Bendich"},{"first_name":"John","full_name":"Harer, John","last_name":"Harer"}],"_id":"3378","status":"public","type":"journal_article"},{"_id":"3336","type":"conference","conference":{"name":"CVPR: Conference on Computer Vision and Pattern Recognition","start_date":"2011-06-20","end_date":"2011-06-25","location":"Colorado Springs, CO, United States"},"status":"public","citation":{"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.","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.","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.","short":"C. Chen, D. Freedman, C. Lampert, in:, CVPR: Computer Vision and Pattern Recognition, IEEE, 2011, pp. 2089–2096.","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"},"date_updated":"2023-02-23T12:23:56Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"3294","author":[{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao","full_name":"Chen, Chao","last_name":"Chen"},{"first_name":"Daniel","last_name":"Freedman","full_name":"Freedman, Daniel"},{"full_name":"Lampert, Christoph","orcid":"0000-0001-8622-7887","last_name":"Lampert","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","first_name":"Christoph"}],"article_processing_charge":"No","title":"Enforcing topological constraints in random field image segmentation","department":[{"_id":"HeEd"},{"_id":"ChLa"}],"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."}],"oa_version":"None","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.","scopus_import":"1","publisher":"IEEE","quality_controlled":"1","month":"07","publication_identifier":{"eisbn":["978-1-4577-0395-9"],"isbn":["978-1-4577-0394-2"]},"year":"2011","publication_status":"published","day":"22","language":[{"iso":"eng"}],"publication":"CVPR: Computer Vision and Pattern Recognition","page":"2089 - 2096","date_published":"2011-07-22T00:00:00Z","related_material":{"record":[{"relation":"earlier_version","id":"5386","status":"public"}]},"doi":"10.1109/CVPR.2011.5995503","date_created":"2018-12-11T12:02:45Z"},{"article_processing_charge":"No","author":[{"full_name":"Gonzalez-Diaz, Rocio","last_name":"Gonzalez-Diaz","first_name":"Rocio"},{"full_name":"Ion, Adrian","last_name":"Ion","id":"29F89302-F248-11E8-B48F-1D18A9856A87","first_name":"Adrian"},{"full_name":"Jimenez, Maria Jose","last_name":"Jimenez","first_name":"Maria Jose"},{"last_name":"Poyatos","full_name":"Poyatos, Regina","first_name":"Regina"}],"title":"Incremental-decremental algorithm for computing AT-models and persistent homology","citation":{"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.","ama":"Gonzalez-Diaz R, Ion A, Jimenez MJ, Poyatos R. 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Poyatos, in:, Computer Analysis of Images and Patterns, Springer Nature, 2011, pp. 286–293.","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.","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."},"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","page":"286-293","date_created":"2021-07-11T22:01:19Z","doi":"10.1007/978-3-642-23672-3_35","date_published":"2011-08-01T00:00:00Z","year":"2011","publication":"Computer Analysis of Images and Patterns","day":"01","oa":1,"quality_controlled":"1","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"date_updated":"2021-08-12T13:53:17Z","conference":{"location":"Seville, Spain","end_date":"2011-08-31","start_date":"2011-08-29","name":"CAIP: International Conference on Computer Analysis of Images and Patterns"},"type":"conference","status":"public","_id":"9648","volume":6854,"publication_status":"published","publication_identifier":{"isbn":["9783642236716"],"eissn":["16113349"],"issn":["03029743"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://hdl.handle.net/11441/30766"}],"alternative_title":["LNCS"],"scopus_import":"1","intvolume":" 6854","month":"08","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."}],"oa_version":"Published Version"},{"intvolume":" 6658","month":"06","place":"Berlin, Heidelberg","alternative_title":["LNCS"],"scopus_import":"1","oa_version":"None","abstract":[{"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.","lang":"eng"}],"volume":6658,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783642208430"],"eisbn":["9783642208447"]},"status":"public","conference":{"start_date":"2011-05-18","end_date":"2011-05-20","location":"Münster, Germany","name":"GbRPR: Graph-based Representations in Pattern Recognition"},"type":"conference","_id":"10907","series_title":"LNIP","department":[{"_id":"HeEd"}],"date_updated":"2023-09-05T14:10:15Z","publisher":"Springer","quality_controlled":"1","acknowledgement":"This work has been partially supported by the Austrian Science Fund under grants S9103-N13 and P18716-N13.","date_created":"2022-03-21T08:08:35Z","doi":"10.1007/978-3-642-20844-7_22","date_published":"2011-06-01T00:00:00Z","page":"215-224","publication":"Graph-Based Representations in Pattern Recognition","day":"01","year":"2011","editor":[{"full_name":"Jiang, Xiaoyi","last_name":"Jiang","first_name":"Xiaoyi"},{"first_name":"Miquel","last_name":"Ferrer","full_name":"Ferrer, Miquel"},{"full_name":"Torsello, Andrea","last_name":"Torsello","first_name":"Andrea"}],"title":"Spatio-temporal extraction of articulated models in a graph pyramid","article_processing_charge":"No","author":[{"first_name":"Nicole M.","last_name":"Artner","full_name":"Artner, Nicole M."},{"first_name":"Adrian","id":"29F89302-F248-11E8-B48F-1D18A9856A87","full_name":"Ion, Adrian","last_name":"Ion"},{"first_name":"Walter G.","last_name":"Kropatsch","full_name":"Kropatsch, Walter G."}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","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.","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","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.","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.","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."}},{"publisher":"Society for Industrial and Applied Mathematics","scopus_import":"1","quality_controlled":"1","month":"02","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.","oa_version":"None","page":"1594-1604","date_created":"2022-03-21T08:24:07Z","date_published":"2010-02-01T00:00:00Z","doi":"10.1137/1.9781611973075.129","related_material":{"record":[{"id":"3267","status":"public","relation":"later_version"}]},"publication_status":"published","year":"2010","publication_identifier":{"eisbn":["9781611973075"]},"language":[{"iso":"eng"}],"publication":"Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms","day":"01","conference":{"name":"SODA: Symposium on Discrete Algorithms","start_date":"2010-01-17","location":"Austin, TX, United States","end_date":"2010-01-19"},"type":"conference","status":"public","_id":"10909","article_processing_charge":"No","author":[{"full_name":"Chen, Chao","last_name":"Chen","first_name":"Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Freedman","full_name":"Freedman, Daniel","first_name":"Daniel"}],"title":"Hardness results for homology localization","department":[{"_id":"HeEd"}],"date_updated":"2023-02-23T11:19:46Z","citation":{"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.","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.","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.","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"_id":"3782","status":"public","type":"conference","conference":{"name":"MCV: Medical Computer Vision","end_date":"2010-09-20","location":"Beijing, China","start_date":"2010-09-20"},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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","short":"C. Chen, D. Freedman, in:, Conference Proceedings MCV 2010, Springer, 2010, pp. 31–42.","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."},"date_updated":"2021-01-12T07:52:10Z","title":"Topology noise removal for curve and surface evolution","department":[{"_id":"HeEd"}],"author":[{"full_name":"Chen, Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao"},{"first_name":"Daniel","full_name":"Freedman, Daniel","last_name":"Freedman"}],"publist_id":"2445","oa_version":"None","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.","abstract":[{"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.","lang":"eng"}],"month":"12","intvolume":" 6533","scopus_import":1,"publisher":"Springer","alternative_title":["LNCS"],"quality_controlled":"1","day":"31","language":[{"iso":"eng"}],"publication":" Conference proceedings MCV 2010","publication_status":"published","year":"2010","volume":6533,"doi":"10.1007/978-3-642-18421-5_4","date_published":"2010-12-31T00:00:00Z","date_created":"2018-12-11T12:05:08Z","page":"31 - 42"},{"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:46:16Z","date_updated":"2021-01-12T07:52:15Z","ddc":["000"],"type":"book_chapter","pubrep_id":"538","status":"public","_id":"3795","publication_status":"published","language":[{"iso":"eng"}],"file":[{"checksum":"f03a44c3d1c3e2d4fedb3b94404f3fd5","file_id":"4896","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"IST-2016-538-v1+1_2011-B-02-ApparentContour.pdf","date_created":"2018-12-12T10:11:40Z","file_size":210710,"date_updated":"2020-07-14T12:46:16Z","creator":"system"}],"alternative_title":["Mathematics and Visualization"],"scopus_import":1,"month":"12","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."}],"oa_version":"Submitted Version","publist_id":"2428","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Dmitriy","last_name":"Morozov","full_name":"Morozov, Dmitriy"},{"first_name":"Amit","id":"34A254A0-F248-11E8-B48F-1D18A9856A87","last_name":"Patel","full_name":"Patel, Amit"}],"title":"The stability of the apparent contour of an orientable 2-manifold","citation":{"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.","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","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","short":"H. Edelsbrunner, D. Morozov, A. Patel, in:, Topological Data Analysis and Visualization: Theory, Algorithms and Applications, Springer, 2010, pp. 27–42.","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.","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.","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."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","page":"27 - 42","date_created":"2018-12-11T12:05:13Z","date_published":"2010-12-22T00:00:00Z","doi":"10.1007/978-3-642-15014-2_3","year":"2010","has_accepted_license":"1","publication":"Topological Data Analysis and Visualization: Theory, Algorithms and Applications","day":"22","oa":1,"publisher":"Springer","quality_controlled":"1","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."},{"_id":"3848","status":"public","conference":{"name":"ESA: European Symposium on Algorithms","start_date":"2010-09-06","end_date":"2010-09-08","location":"Liverpool, UK"},"type":"conference","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","short":"P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, in:, Springer, 2010, pp. 1–10.","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.","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."},"date_updated":"2021-01-12T07:52:38Z","title":"The robustness of level sets","department":[{"_id":"HeEd"}],"author":[{"full_name":"Bendich, Paul","last_name":"Bendich","first_name":"Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"first_name":"Dmitriy","full_name":"Morozov, Dmitriy","last_name":"Morozov"},{"full_name":"Patel, Amit","last_name":"Patel","first_name":"Amit","id":"34A254A0-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"2336","oa_version":"None","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."}],"intvolume":" 6346","month":"09","quality_controlled":"1","alternative_title":["LNCS"],"publisher":"Springer","scopus_import":1,"language":[{"iso":"eng"}],"day":"01","publication_status":"published","year":"2010","date_created":"2018-12-11T12:05:30Z","volume":6346,"date_published":"2010-09-01T00:00:00Z","doi":"10.1007/978-3-642-15775-2_1","page":"1 - 10"},{"file":[{"date_created":"2018-12-12T10:15:41Z","file_name":"IST-2012-62-v1+1_Mean-payoff_automaton_expressions.pdf","creator":"system","date_updated":"2020-07-14T12:46:17Z","file_size":233260,"file_id":"5163","checksum":"4f753ae99d076553fb8733e2c8b390e2","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":6269,"ec_funded":1,"oa_version":"Submitted Version","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."}],"month":"11","intvolume":" 6269","scopus_import":1,"alternative_title":["LNCS"],"ddc":["000","005"],"date_updated":"2021-01-12T07:52:40Z","file_date_updated":"2020-07-14T12:46:17Z","department":[{"_id":"KrCh"},{"_id":"HeEd"},{"_id":"ToHe"}],"_id":"3853","status":"public","pubrep_id":"62","type":"conference","conference":{"name":"CONCUR: Concurrency Theory","end_date":"2010-09-03","location":"Paris, France","start_date":"2010-08-31"},"day":"18","has_accepted_license":"1","year":"2010","doi":"10.1007/978-3-642-15375-4_19","date_published":"2010-11-18T00:00:00Z","date_created":"2018-12-11T12:05:31Z","page":"269 - 283","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","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","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.","short":"K. Chatterjee, L. Doyen, H. Edelsbrunner, T.A. Henzinger, P. Rannou, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2010, pp. 269–283.","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.","ista":"Chatterjee K, Doyen L, Edelsbrunner H, Henzinger TA, Rannou P. 2010. Mean-payoff automaton expressions. CONCUR: Concurrency Theory, LNCS, vol. 6269, 269–283."},"title":"Mean-payoff automaton expressions","author":[{"first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"first_name":"Laurent","full_name":"Doyen, Laurent","last_name":"Doyen"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Henzinger","full_name":"Henzinger, Thomas A","orcid":"0000−0002−2985−7724","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A"},{"last_name":"Rannou","full_name":"Rannou, Philippe","first_name":"Philippe"}],"publist_id":"2328","project":[{"_id":"25EFB36C-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"COMponent-Based Embedded Systems design Techniques","grant_number":"215543"},{"name":"Design for Embedded Systems","grant_number":"214373","call_identifier":"FP7","_id":"25F1337C-B435-11E9-9278-68D0E5697425"}]},{"volume":6281,"language":[{"iso":"eng"}],"file":[{"date_updated":"2020-07-14T12:46:17Z","file_size":142357,"creator":"system","date_created":"2018-12-12T10:13:13Z","file_name":"IST-2016-537-v1+1_2010-P-05-NonuniformError.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"4994","checksum":"af61e1c2bb42f3d556179d4692caeb1b"}],"publication_status":"published","intvolume":" 6281","month":"08","alternative_title":["LNCS"],"scopus_import":1,"oa_version":"Submitted Version","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."}],"file_date_updated":"2020-07-14T12:46:17Z","department":[{"_id":"HeEd"}],"ddc":["000"],"date_updated":"2021-01-12T07:52:38Z","pubrep_id":"537","status":"public","conference":{"start_date":"2010-08-23","location":"Brno, Czech Republic","end_date":"2010-08-27","name":"MFCS: Mathematical Foundations of Computer Science"},"type":"conference","_id":"3849","date_created":"2018-12-11T12:05:30Z","doi":"10.1007/978-3-642-15155-2_2","date_published":"2010-08-10T00:00:00Z","page":"12 - 23","day":"10","year":"2010","has_accepted_license":"1","oa":1,"quality_controlled":"1","publisher":"Springer","title":"Persistent homology under non-uniform error","author":[{"first_name":"Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","full_name":"Bendich, Paul","last_name":"Bendich"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87"},{"id":"34A254A0-F248-11E8-B48F-1D18A9856A87","first_name":"Amit","full_name":"Patel, Amit","last_name":"Patel"}],"publist_id":"2333","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"short":"P. Bendich, H. Edelsbrunner, M. Kerber, A. Patel, in:, Springer, 2010, pp. 12–23.","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.","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","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","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.","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.","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."}},{"_id":"3850","conference":{"name":"EuroCG: European Workshop on Computational Geometry","start_date":"2010-03-22","location":"Dortmund, Germany","end_date":"2010-03-24"},"type":"conference","status":"public","citation":{"short":"E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, in:, TU Dortmund, 2010, pp. 12–23.","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.","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.","ama":"Berberich E, Halperin D, Kerber M, Pogalnikova R. Polygonal reconstruction from approximate offsets. In: TU Dortmund; 2010:12-23.","mla":"Berberich, Eric, et al. Polygonal Reconstruction from Approximate Offsets. TU Dortmund, 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.","chicago":"Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Polygonal Reconstruction from Approximate Offsets,” 12–23. TU Dortmund, 2010."},"date_updated":"2021-01-12T07:52:39Z","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","publist_id":"2334","author":[{"first_name":"Eric","full_name":"Berberich, Eric","last_name":"Berberich"},{"last_name":"Halperin","full_name":"Halperin, Dan","first_name":"Dan"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299"},{"full_name":"Pogalnikova, Roza","last_name":"Pogalnikova","first_name":"Roza"}],"department":[{"_id":"HeEd"}],"title":"Polygonal reconstruction from approximate offsets","abstract":[{"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.","lang":"eng"}],"oa_version":"None","quality_controlled":"1","publisher":"TU Dortmund","month":"01","publication_status":"published","year":"2010","language":[{"iso":"eng"}],"day":"01","page":"12 - 23","date_created":"2018-12-11T12:05:30Z","date_published":"2010-01-01T00:00:00Z"},{"quality_controlled":"1","publisher":"IEEE","oa":1,"day":"28","publication":"IEEE Transactions of Visualization and Computer Graphics","has_accepted_license":"1","year":"2010","doi":"10.1109/TVCG.2010.139","date_published":"2010-10-28T00:00:00Z","date_created":"2018-12-11T12:05:47Z","page":"1251 - 1260","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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.","short":"P. Bendich, H. Edelsbrunner, M. Kerber, IEEE Transactions of Visualization and Computer Graphics 16 (2010) 1251–1260."},"title":"Computing robustness and persistence for images","publist_id":"2253","author":[{"first_name":"Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","full_name":"Bendich, Paul","last_name":"Bendich"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber"}],"oa_version":"Submitted Version","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."}],"month":"10","intvolume":" 16","scopus_import":1,"file":[{"creator":"system","file_size":721994,"date_updated":"2020-07-14T12:46:21Z","file_name":"IST-2016-536-v1+1_2010-J-02-PersistenceforImages.pdf","date_created":"2018-12-12T10:17:10Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"5262","checksum":"f6d813c04f4b46023cec6b9a17f15472"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":16,"issue":"6","_id":"3901","status":"public","pubrep_id":"536","type":"journal_article","ddc":["000"],"date_updated":"2021-01-12T07:53:04Z","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:46:21Z"},{"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","short":"H. Edelsbrunner, J. Harer, in:, Springer, 2009, pp. 36–50.","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.","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.","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"John","full_name":"Harer, John","last_name":"Harer"}],"publist_id":"2160","title":"The persistent Morse complex segmentation of a 3-manifold","has_accepted_license":"1","year":"2009","day":"17","page":"36 - 50","doi":"10.1007/978-3-642-10470-1_4","date_published":"2009-11-17T00:00:00Z","date_created":"2018-12-11T12:06:10Z","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.","quality_controlled":"1","publisher":"Springer","oa":1,"date_updated":"2021-01-12T07:53:32Z","ddc":["000"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:46:21Z","_id":"3968","type":"conference","conference":{"start_date":"2009-11-29","end_date":"2009-12-02","location":"Zermatt, Switzerland","name":"3DPH: Modelling the Physiological Human"},"status":"public","pubrep_id":"535","publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"4694","checksum":"11fc85bcc19bab1f020e706a4b8a4660","file_size":165090,"date_updated":"2020-07-14T12:46:21Z","creator":"system","file_name":"IST-2016-535-v1+1_2009-P-04-3ManifoldSegmentation.pdf","date_created":"2018-12-12T10:08:33Z"}],"language":[{"iso":"eng"}],"volume":5903,"abstract":[{"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.","lang":"eng"}],"oa_version":"Submitted Version","alternative_title":["LNCS"],"scopus_import":1,"month":"11","intvolume":" 5903"}]