[{"intvolume":"        67","year":"2012","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2012-10-01T00:00:00Z","title":"On the configuration space for the shortest networks","date_created":"2018-12-11T12:00:18Z","oa_version":"None","language":[{"iso":"eng"}],"_id":"2912","type":"journal_article","publist_id":"3831","publication_status":"published","quality_controlled":"1","day":"01","citation":{"chicago":"Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space for the Shortest Networks.” <i>Russian Mathematical Surveys</i>. Russian Academy of Sciences, 2012. <a href=\"https://doi.org/10.4213/rm9503\">https://doi.org/10.4213/rm9503</a>.","ama":"Edelsbrunner H, Strelkova N. On the configuration space for the shortest networks. <i>Russian Mathematical Surveys</i>. 2012;67(6):1167–1168. doi:<a href=\"https://doi.org/10.4213/rm9503\">10.4213/rm9503</a>","ista":"Edelsbrunner H, Strelkova N. 2012. On the configuration space for the shortest networks. Russian Mathematical Surveys. 67(6), 1167–1168.","apa":"Edelsbrunner, H., &#38; Strelkova, N. (2012). On the configuration space for the shortest networks. <i>Russian Mathematical Surveys</i>. Russian Academy of Sciences. <a href=\"https://doi.org/10.4213/rm9503\">https://doi.org/10.4213/rm9503</a>","mla":"Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space for the Shortest Networks.” <i>Russian Mathematical Surveys</i>, vol. 67, no. 6, Russian Academy of Sciences, 2012, pp. 1167–1168, doi:<a href=\"https://doi.org/10.4213/rm9503\">10.4213/rm9503</a>.","ieee":"H. Edelsbrunner and N. Strelkova, “On the configuration space for the shortest networks,” <i>Russian Mathematical Surveys</i>, vol. 67, no. 6. Russian Academy of Sciences, pp. 1167–1168, 2012.","short":"H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168."},"article_processing_charge":"No","publisher":"Russian Academy of Sciences","status":"public","page":"1167–1168","issue":"6","doi":"10.4213/rm9503","publication":"Russian Mathematical Surveys","date_updated":"2023-10-17T11:40:39Z","volume":67,"author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Strelkova","full_name":"Strelkova, Nataliya","first_name":"Nataliya"}],"month":"10","department":[{"_id":"HeEd"}]},{"intvolume":"        67","year":"2012","ddc":["510"],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2012-11-01T00:00:00Z","_id":"2941","language":[{"iso":"eng"}],"external_id":{"isi":["000310789000005"]},"type":"journal_article","quality_controlled":"1","has_accepted_license":"1","day":"01","citation":{"ama":"Dolbilin N, Edelsbrunner H, Musin O. On the optimality of functionals over triangulations of Delaunay sets. <i>Russian Mathematical Surveys</i>. 2012;67(4):781-783. doi:<a href=\"https://doi.org/10.1070/RM2012v067n04ABEH004807\">10.1070/RM2012v067n04ABEH004807</a>","ista":"Dolbilin N, Edelsbrunner H, Musin O. 2012. On the optimality of functionals over triangulations of Delaunay sets. Russian Mathematical Surveys. 67(4), 781–783.","chicago":"Dolbilin, Nikolai, Herbert Edelsbrunner, and Oleg Musin. “On the Optimality of Functionals over Triangulations of Delaunay Sets.” <i>Russian Mathematical Surveys</i>. IOP Publishing, 2012. <a href=\"https://doi.org/10.1070/RM2012v067n04ABEH004807\">https://doi.org/10.1070/RM2012v067n04ABEH004807</a>.","mla":"Dolbilin, Nikolai, et al. “On the Optimality of Functionals over Triangulations of Delaunay Sets.” <i>Russian Mathematical Surveys</i>, vol. 67, no. 4, IOP Publishing, 2012, pp. 781–83, doi:<a href=\"https://doi.org/10.1070/RM2012v067n04ABEH004807\">10.1070/RM2012v067n04ABEH004807</a>.","short":"N. Dolbilin, H. Edelsbrunner, O. Musin, Russian Mathematical Surveys 67 (2012) 781–783.","ieee":"N. Dolbilin, H. Edelsbrunner, and O. Musin, “On the optimality of functionals over triangulations of Delaunay sets,” <i>Russian Mathematical Surveys</i>, vol. 67, no. 4. IOP Publishing, pp. 781–783, 2012.","apa":"Dolbilin, N., Edelsbrunner, H., &#38; Musin, O. (2012). On the optimality of functionals over triangulations of Delaunay sets. <i>Russian Mathematical Surveys</i>. IOP Publishing. <a href=\"https://doi.org/10.1070/RM2012v067n04ABEH004807\">https://doi.org/10.1070/RM2012v067n04ABEH004807</a>"},"page":"781 - 783","status":"public","issue":"4","scopus_import":"1","file_date_updated":"2020-07-14T12:45:55Z","publication":"Russian Mathematical Surveys","date_updated":"2025-09-30T08:13:48Z","isi":1,"title":"On the optimality of functionals over triangulations of Delaunay sets","date_created":"2018-12-11T12:00:28Z","oa_version":"Submitted Version","publist_id":"3792","publication_status":"published","file":[{"date_created":"2018-12-12T10:16:49Z","file_size":253816,"content_type":"application/pdf","access_level":"open_access","creator":"system","date_updated":"2020-07-14T12:45:55Z","file_id":"5239","relation":"main_file","file_name":"IST-2013-132-v1+1_2012-J-04-Functional-E.pdf","checksum":"389a5ae53d6347de36c3468034f2821d"}],"article_processing_charge":"No","publisher":"IOP Publishing","oa":1,"doi":"10.1070/RM2012v067n04ABEH004807","pubrep_id":"132","volume":67,"author":[{"first_name":"Nikolai","full_name":"Dolbilin, Nikolai","last_name":"Dolbilin"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Musin, Oleg","last_name":"Musin","first_name":"Oleg"}],"month":"11","department":[{"_id":"HeEd"}]},{"intvolume":"      7476","year":"2012","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2012-08-01T00:00:00Z","abstract":[{"text":"We study the task of interactive semantic labeling of a segmentation hierarchy. To this end we propose a framework interleaving two components: an automatic labeling step, based on a Conditional Random Field whose dependencies are defined by the inclusion tree of the segmentation hierarchy, and an interaction step that integrates incremental input from a human user. Evaluated on two distinct datasets, the proposed interactive approach efficiently integrates human interventions and illustrates the advantages of structured prediction in an interactive framework. ","lang":"eng"}],"_id":"2971","language":[{"iso":"eng"}],"type":"conference","quality_controlled":"1","citation":{"ama":"Zankl G, Haxhimusa Y, Ion A. Interactive labeling of image segmentation hierarchies. In: <i>34th DAGM and 36th OAGM Symposium</i>. Vol 7476. Springer; 2012:11-20. doi:<a href=\"https://doi.org/10.1007/978-3-642-32717-9_2\">10.1007/978-3-642-32717-9_2</a>","ista":"Zankl G, Haxhimusa Y, Ion A. 2012. Interactive labeling of image segmentation hierarchies. 34th DAGM and 36th OAGM Symposium. Pattern Recognition, LNCS, vol. 7476, 11–20.","chicago":"Zankl, Georg, Yll Haxhimusa, and Adrian Ion. “Interactive Labeling of Image Segmentation Hierarchies.” In <i>34th DAGM and 36th OAGM Symposium</i>, 7476:11–20. Springer, 2012. <a href=\"https://doi.org/10.1007/978-3-642-32717-9_2\">https://doi.org/10.1007/978-3-642-32717-9_2</a>.","mla":"Zankl, Georg, et al. “Interactive Labeling of Image Segmentation Hierarchies.” <i>34th DAGM and 36th OAGM Symposium</i>, vol. 7476, Springer, 2012, pp. 11–20, doi:<a href=\"https://doi.org/10.1007/978-3-642-32717-9_2\">10.1007/978-3-642-32717-9_2</a>.","short":"G. Zankl, Y. Haxhimusa, A. Ion, in:, 34th DAGM and 36th OAGM Symposium, Springer, 2012, pp. 11–20.","ieee":"G. Zankl, Y. Haxhimusa, and A. Ion, “Interactive labeling of image segmentation hierarchies,” in <i>34th DAGM and 36th OAGM Symposium</i>, Graz, Austria, 2012, vol. 7476, pp. 11–20.","apa":"Zankl, G., Haxhimusa, Y., &#38; Ion, A. (2012). Interactive labeling of image segmentation hierarchies. In <i>34th DAGM and 36th OAGM Symposium</i> (Vol. 7476, pp. 11–20). Graz, Austria: Springer. <a href=\"https://doi.org/10.1007/978-3-642-32717-9_2\">https://doi.org/10.1007/978-3-642-32717-9_2</a>"},"day":"01","page":"11 - 20","status":"public","scopus_import":"1","publication":"34th DAGM and 36th OAGM Symposium","date_updated":"2025-05-20T07:21:42Z","publication_identifier":{"eisbn":["9783642327179"],"eissn":["1611-3349"]},"date_created":"2018-12-11T12:00:37Z","alternative_title":["LNCS"],"title":"Interactive labeling of image segmentation hierarchies","oa_version":"None","OA_type":"closed access","publist_id":"3737","conference":{"name":"Pattern Recognition","start_date":"2012-08-28","end_date":"2012-08-31","location":"Graz, Austria"},"publication_status":"published","article_processing_charge":"No","publisher":"Springer","doi":"10.1007/978-3-642-32717-9_2","volume":7476,"author":[{"last_name":"Zankl","full_name":"Zankl, Georg","first_name":"Georg"},{"first_name":"Yll","full_name":"Haxhimusa, Yll","last_name":"Haxhimusa"},{"last_name":"Ion","full_name":"Ion, Adrian","id":"29F89302-F248-11E8-B48F-1D18A9856A87","first_name":"Adrian"}],"month":"08","department":[{"_id":"HeEd"}]},{"arxiv":1,"date_created":"2018-12-11T12:01:28Z","title":"Deconstructing approximate offsets","oa_version":"Preprint","publist_id":"3584","publication_status":"published","corr_author":"1","article_processing_charge":"No","publisher":"Springer","related_material":{"record":[{"id":"3329","status":"public","relation":"earlier_version"}]},"acknowledgement":"We thank Eyal Flato (Plataine Ltd.) for raising the offset-deconstruction problem in connection with wood cutting. We also thank Tim Bretl (UIUC) for suggesting the digital-pen offset-deconstruction problem. This work has been supported in part by the Israel Science Foundation (grant no. 1102/11), by the German–Israeli Foundation (grant no. 969/07), by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University, and by the EU Project under Contract No. 255827 (CGL—Computational Geometry Learning).\r\n","oa":1,"doi":"10.1007/s00454-012-9441-5","volume":48,"author":[{"first_name":"Eric","last_name":"Berberich","full_name":"Berberich, Eric"},{"last_name":"Halperin","full_name":"Halperin, Dan","first_name":"Dan"},{"full_name":"Kerber, Michael","last_name":"Kerber","orcid":"0000-0002-8030-9299","first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Roza","last_name":"Pogalnikova","full_name":"Pogalnikova, Roza"}],"department":[{"_id":"HeEd"}],"month":"12","intvolume":"        48","year":"2012","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2012-12-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1109.2158"}],"abstract":[{"lang":"eng","text":"We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(nlogn)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. A variant of the algorithm, which we have implemented using the cgal library, is based on rational arithmetic and answers the same deconstruction problem up to an uncertainty parameter δ its running time additionally depends on δ. If the input shape is found to be approximable, this algorithm also computes an approximate solution for the problem. It also allows us to solve parameter-optimization problems induced by the offset-deconstruction problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution P with at most one more vertex than a vertex-minimal one."}],"_id":"3115","language":[{"iso":"eng"}],"external_id":{"isi":["000311503200006"],"arxiv":["1109.2158"]},"type":"journal_article","quality_controlled":"1","citation":{"apa":"Berberich, E., Halperin, D., Kerber, M., &#38; Pogalnikova, R. (2012). Deconstructing approximate offsets. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-012-9441-5\">https://doi.org/10.1007/s00454-012-9441-5</a>","mla":"Berberich, Eric, et al. “Deconstructing Approximate Offsets.” <i>Discrete &#38; Computational Geometry</i>, vol. 48, no. 4, Springer, 2012, pp. 964–89, doi:<a href=\"https://doi.org/10.1007/s00454-012-9441-5\">10.1007/s00454-012-9441-5</a>.","short":"E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, Discrete &#38; Computational Geometry 48 (2012) 964–989.","ieee":"E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing approximate offsets,” <i>Discrete &#38; Computational Geometry</i>, vol. 48, no. 4. Springer, pp. 964–989, 2012.","chicago":"Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing Approximate Offsets.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s00454-012-9441-5\">https://doi.org/10.1007/s00454-012-9441-5</a>.","ama":"Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate offsets. <i>Discrete &#38; Computational Geometry</i>. 2012;48(4):964-989. doi:<a href=\"https://doi.org/10.1007/s00454-012-9441-5\">10.1007/s00454-012-9441-5</a>","ista":"Berberich E, Halperin D, Kerber M, Pogalnikova R. 2012. Deconstructing approximate offsets. Discrete &#38; Computational Geometry. 48(4), 964–989."},"day":"01","page":"964 - 989","status":"public","issue":"4","scopus_import":"1","date_updated":"2025-09-30T08:01:36Z","publication":"Discrete & Computational Geometry","isi":1},{"issue":"4","scopus_import":"1","page":"1171 - 1194","status":"public","date_updated":"2025-09-30T07:59:55Z","publication":"Compositio Mathematica","isi":1,"date_published":"2012-07-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1009.4313"}],"intvolume":"       148","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2012","day":"01","citation":{"short":"G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 1171–1194.","ieee":"G. Brown, M. Kerber, and M. Reid, “Fano 3 folds in codimension 4 Tom and Jerry Part I,” <i>Compositio Mathematica</i>, vol. 148, no. 4. Cambridge University Press, pp. 1171–1194, 2012.","mla":"Brown, Gavin, et al. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” <i>Compositio Mathematica</i>, vol. 148, no. 4, Cambridge University Press, 2012, pp. 1171–94, doi:<a href=\"https://doi.org/10.1112/S0010437X11007226\">10.1112/S0010437X11007226</a>.","apa":"Brown, G., Kerber, M., &#38; Reid, M. (2012). Fano 3 folds in codimension 4 Tom and Jerry Part I. <i>Compositio Mathematica</i>. Cambridge University Press. <a href=\"https://doi.org/10.1112/S0010437X11007226\">https://doi.org/10.1112/S0010437X11007226</a>","ista":"Brown G, Kerber M, Reid M. 2012. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 148(4), 1171–1194.","ama":"Brown G, Kerber M, Reid M. Fano 3 folds in codimension 4 Tom and Jerry Part I. <i>Compositio Mathematica</i>. 2012;148(4):1171-1194. doi:<a href=\"https://doi.org/10.1112/S0010437X11007226\">10.1112/S0010437X11007226</a>","chicago":"Brown, Gavin, Michael Kerber, and Miles Reid. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” <i>Compositio Mathematica</i>. Cambridge University Press, 2012. <a href=\"https://doi.org/10.1112/S0010437X11007226\">https://doi.org/10.1112/S0010437X11007226</a>."},"external_id":{"arxiv":["1009.4313"],"isi":["000307176400007"]},"abstract":[{"text":"We introduce a strategy based on Kustin-Miller unprojection that allows us to construct many hundreds of Gorenstein codimension 4 ideals with 9 × 16 resolutions (that is, nine equations and sixteen first syzygies). Our two basic games are called Tom and Jerry; the main application is the biregular construction of most of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type I projection. In every case, at least one Tom and one Jerry construction works, providing at least two deformation families of quasismooth Fano 3-folds having the same numerics but different topology. © 2012 Copyright Foundation Compositio Mathematica.","lang":"eng"}],"_id":"3120","language":[{"iso":"eng"}],"quality_controlled":"1","type":"journal_article","article_processing_charge":"No","publisher":"Cambridge University Press","author":[{"last_name":"Brown","full_name":"Brown, Gavin","first_name":"Gavin"},{"last_name":"Kerber","full_name":"Kerber, Michael","first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299"},{"full_name":"Reid, Miles","last_name":"Reid","first_name":"Miles"}],"volume":148,"department":[{"_id":"HeEd"}],"month":"07","oa":1,"doi":"10.1112/S0010437X11007226","acknowledgement":"This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0.","title":"Fano 3 folds in codimension 4 Tom and Jerry Part I","date_created":"2018-12-11T12:01:30Z","oa_version":"Preprint","arxiv":1,"publication_status":"published","publist_id":"3579"},{"page":"211-218","status":"public","publisher":"ML Research Press","article_processing_charge":"No","scopus_import":"1","oa":1,"month":"06","department":[{"_id":"ChLa"},{"_id":"HeEd"}],"author":[{"first_name":"Novi","last_name":"Quadrianto","full_name":"Quadrianto, Novi"},{"full_name":"Lampert, Christoph","last_name":"Lampert","orcid":"0000-0001-8622-7887","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","first_name":"Christoph"},{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao","last_name":"Chen","full_name":"Chen, Chao"}],"date_updated":"2025-06-11T08:09:42Z","publication":"Proceedings of the 29th International Conference on Machine Learning","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"year":"2012","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1206.4652"}],"oa_version":"Preprint","title":"The most persistent soft-clique in a set of sampled graphs","date_created":"2018-12-11T12:01:33Z","date_published":"2012-06-01T00:00:00Z","quality_controlled":"1","conference":{"end_date":"2012-07-01","location":"Edinburgh, United Kingdom","name":"ICML: International Conference on Machine Learning","start_date":"2012-06-26"},"publication_status":"published","publist_id":"3572","type":"conference","external_id":{"arxiv":["1206.4652"]},"language":[{"iso":"eng"}],"_id":"3127","abstract":[{"lang":"eng","text":"When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques.\r\n    We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data, we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations."}],"citation":{"chicago":"Quadrianto, Novi, Christoph Lampert, and Chao Chen. “The Most Persistent Soft-Clique in a Set of Sampled Graphs.” In <i>Proceedings of the 29th International Conference on Machine Learning</i>, 211–18. ML Research Press, 2012.","ama":"Quadrianto N, Lampert C, Chen C. The most persistent soft-clique in a set of sampled graphs. In: <i>Proceedings of the 29th International Conference on Machine Learning</i>. ML Research Press; 2012:211-218.","ista":"Quadrianto N, Lampert C, Chen C. 2012. The most persistent soft-clique in a set of sampled graphs. Proceedings of the 29th International Conference on Machine Learning. ICML: International Conference on Machine Learning, 211–218.","apa":"Quadrianto, N., Lampert, C., &#38; Chen, C. (2012). The most persistent soft-clique in a set of sampled graphs. In <i>Proceedings of the 29th International Conference on Machine Learning</i> (pp. 211–218). Edinburgh, United Kingdom: ML Research Press.","mla":"Quadrianto, Novi, et al. “The Most Persistent Soft-Clique in a Set of Sampled Graphs.” <i>Proceedings of the 29th International Conference on Machine Learning</i>, ML Research Press, 2012, pp. 211–18.","short":"N. Quadrianto, C. Lampert, C. Chen, in:, Proceedings of the 29th International Conference on Machine Learning, ML Research Press, 2012, pp. 211–218.","ieee":"N. Quadrianto, C. Lampert, and C. Chen, “The most persistent soft-clique in a set of sampled graphs,” in <i>Proceedings of the 29th International Conference on Machine Learning</i>, Edinburgh, United Kingdom, 2012, pp. 211–218."},"day":"01"},{"arxiv":1,"date_created":"2018-12-11T12:01:33Z","alternative_title":["LNCS"],"title":"Annotating simplices with a homology basis and its applications","oa_version":"Preprint","publist_id":"3569","publication_status":"published","conference":{"start_date":"2012-07-04","name":"SWAT: Symposium and Workshops on Algorithm Theory","location":"Helsinki, Finland","end_date":"2012-07-06"},"article_processing_charge":"No","publisher":"Springer","acknowledgement":"Research was partially supported by the Slovenian Research Agency, program P1-0297 and NSF grant CCF 1064416.","oa":1,"doi":"10.1007/978-3-642-31155-0_17","volume":7357,"author":[{"full_name":"Busaryev, Oleksiy","last_name":"Busaryev","first_name":"Oleksiy"},{"full_name":"Cabello, Sergio","last_name":"Cabello","first_name":"Sergio"},{"id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao","last_name":"Chen","full_name":"Chen, Chao"},{"first_name":"Tamal","last_name":"Dey","full_name":"Dey, Tamal"},{"first_name":"Yusu","last_name":"Wang","full_name":"Wang, Yusu"}],"month":"06","department":[{"_id":"HeEd"}],"intvolume":"      7357","year":"2012","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2012-06-19T00:00:00Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1107.3793"}],"abstract":[{"lang":"eng","text":"Let K be a simplicial complex and g the rank of its p-th homology group Hp(K) defined with ℤ2 coefficients. We show that we can compute a basis H of Hp(K) and annotate each p-simplex of K with a binary vector of length g with the following property: the annotations, summed over all p-simplices in any p-cycle z, provide the coordinate vector of the homology class [z] in the basis H. The basis and the annotations for all simplices can be computed in O(n ω ) time, where n is the size of K and ω &lt; 2.376 is a quantity so that two n×n matrices can be multiplied in O(n ω ) time. The precomputed annotations permit answering queries about the independence or the triviality of p-cycles efficiently.\r\n\r\nUsing annotations of edges in 2-complexes, we derive better algorithms for computing optimal basis and optimal homologous cycles in 1 - dimensional homology. Specifically, for computing an optimal basis of H1(K) , we improve the previously known time complexity from O(n 4) to O(n ω  + n 2 g ω − 1). Here n denotes the size of the 2-skeleton of K and g the rank of H1(K) . Computing an optimal cycle homologous to a given 1-cycle is NP-hard even for surfaces and an algorithm taking 2 O(g) nlogn time is known for surfaces. We extend this algorithm to work with arbitrary 2-complexes in O(n ω ) + 2 O(g) n 2logn time using annotations.\r\n"}],"_id":"3129","language":[{"iso":"eng"}],"external_id":{"arxiv":["1107.3793"]},"type":"conference","quality_controlled":"1","citation":{"chicago":"Busaryev, Oleksiy, Sergio Cabello, Chao Chen, Tamal Dey, and Yusu Wang. “Annotating Simplices with a Homology Basis and Its Applications,” 7357:189–200. Springer, 2012. <a href=\"https://doi.org/10.1007/978-3-642-31155-0_17\">https://doi.org/10.1007/978-3-642-31155-0_17</a>.","ama":"Busaryev O, Cabello S, Chen C, Dey T, Wang Y. Annotating simplices with a homology basis and its applications. In: Vol 7357. Springer; 2012:189-200. doi:<a href=\"https://doi.org/10.1007/978-3-642-31155-0_17\">10.1007/978-3-642-31155-0_17</a>","ista":"Busaryev O, Cabello S, Chen C, Dey T, Wang Y. 2012. Annotating simplices with a homology basis and its applications. SWAT: Symposium and Workshops on Algorithm Theory, LNCS, vol. 7357, 189–200.","apa":"Busaryev, O., Cabello, S., Chen, C., Dey, T., &#38; Wang, Y. (2012). Annotating simplices with a homology basis and its applications (Vol. 7357, pp. 189–200). Presented at the SWAT: Symposium and Workshops on Algorithm Theory, Helsinki, Finland: Springer. <a href=\"https://doi.org/10.1007/978-3-642-31155-0_17\">https://doi.org/10.1007/978-3-642-31155-0_17</a>","mla":"Busaryev, Oleksiy, et al. <i>Annotating Simplices with a Homology Basis and Its Applications</i>. Vol. 7357, Springer, 2012, pp. 189–200, doi:<a href=\"https://doi.org/10.1007/978-3-642-31155-0_17\">10.1007/978-3-642-31155-0_17</a>.","short":"O. Busaryev, S. Cabello, C. Chen, T. Dey, Y. Wang, in:, Springer, 2012, pp. 189–200.","ieee":"O. Busaryev, S. Cabello, C. Chen, T. Dey, and Y. Wang, “Annotating simplices with a homology basis and its applications,” presented at the SWAT: Symposium and Workshops on Algorithm Theory, Helsinki, Finland, 2012, vol. 7357, pp. 189–200."},"day":"19","status":"public","page":"189 - 200","scopus_import":"1","date_updated":"2025-06-26T08:59:21Z"},{"publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","date_updated":"2025-06-11T08:10:04Z","scopus_import":"1","status":"public","page":"249 - 258","day":"20","citation":{"apa":"Edelsbrunner, H., &#38; Kerber, M. (2012). Alexander duality for functions: The persistent behavior of land and water and shore. In <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i> (pp. 249–258). Chapel Hill, NC, USA: ACM. <a href=\"https://doi.org/10.1145/2261250.2261287\">https://doi.org/10.1145/2261250.2261287</a>","mla":"Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>, ACM, 2012, pp. 249–58, doi:<a href=\"https://doi.org/10.1145/2261250.2261287\">10.1145/2261250.2261287</a>.","ieee":"H. Edelsbrunner and M. Kerber, “Alexander duality for functions: The persistent behavior of land and water and shore,” in <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i>, Chapel Hill, NC, USA, 2012, pp. 249–258.","short":"H. Edelsbrunner, M. Kerber, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–258.","chicago":"Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” In <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>, 249–58. ACM, 2012. <a href=\"https://doi.org/10.1145/2261250.2261287\">https://doi.org/10.1145/2261250.2261287</a>.","ama":"Edelsbrunner H, Kerber M. Alexander duality for functions: The persistent behavior of land and water and shore. In: <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>. ACM; 2012:249-258. doi:<a href=\"https://doi.org/10.1145/2261250.2261287\">10.1145/2261250.2261287</a>","ista":"Edelsbrunner H, Kerber M. 2012. Alexander duality for functions: The persistent behavior of land and water and shore. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 249–258."},"external_id":{"arxiv":["1109.5052"]},"abstract":[{"lang":"eng","text":"This note contributes to the point calculus of persistent homology by extending Alexander duality from spaces to real-valued functions. Given a perfect Morse function f: S n+1 →[0, 1 and a decomposition S n+1 = U ∪ V into two (n + 1)-manifolds with common boundary M, we prove elementary relationships between the persistence diagrams of f restricted to U, to V, and to M. "}],"_id":"3133","language":[{"iso":"eng"}],"quality_controlled":"1","type":"conference","date_published":"2012-06-20T00:00:00Z","main_file_link":[{"url":"http://arxiv.org/abs/1109.5052","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2012","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"orcid":"0000-0002-8030-9299","first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael","last_name":"Kerber"}],"month":"06","department":[{"_id":"HeEd"}],"oa":1,"doi":"10.1145/2261250.2261287","acknowledgement":"his research is partially supported by the National Science Foundation (NSF) under grant DBI-0820624, the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.\r\nThe authors thank an anonymous referee for suggesting the simplified proof of the Contravariant PE Theorem given in this paper. They also thank Frederick Cohen, Yuriy Mileyko and Amit Patel for helpful discussions.","article_processing_charge":"No","corr_author":"1","publisher":"ACM","publication_status":"published","conference":{"location":"Chapel Hill, NC, USA","end_date":"2012-06-20","start_date":"2012-06-17","name":"SCG: Symposium on Computational Geometry"},"publist_id":"3564","date_created":"2018-12-11T12:01:35Z","title":"Alexander duality for functions: The persistent behavior of land and water and shore","oa_version":"Preprint","arxiv":1},{"type":"conference","publist_id":"3563","conference":{"start_date":"2012-06-17","name":"SCG: Symposium on Computational Geometry","location":"Chapel Hill, NC, USA","end_date":"2012-06-20"},"publication_status":"published","quality_controlled":"1","abstract":[{"text":"It has been an open question whether the sum of finitely many isotropic Gaussian kernels in n ≥ 2 dimensions can have more modes than kernels, until in 2003 Carreira-Perpiñán and Williams exhibited n +1 isotropic Gaussian kernels in ℝ n with n + 2 modes. We give a detailed analysis of this example, showing that it has exponentially many critical points and that the resilience of the extra mode grows like √n. In addition, we exhibit finite configurations of isotropic Gaussian kernels with superlinearly many modes. ","lang":"eng"}],"_id":"3134","language":[{"iso":"eng"}],"citation":{"apa":"Edelsbrunner, H., Fasy, B., &#38; Rote, G. (2012). Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i> (pp. 91–100). Chapel Hill, NC, USA: ACM. <a href=\"https://doi.org/10.1145/2261250.2261265\">https://doi.org/10.1145/2261250.2261265</a>","mla":"Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>, ACM, 2012, pp. 91–100, doi:<a href=\"https://doi.org/10.1145/2261250.2261265\">10.1145/2261250.2261265</a>.","ieee":"H. Edelsbrunner, B. Fasy, and G. Rote, “Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions,” in <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i>, Chapel Hill, NC, USA, 2012, pp. 91–100.","short":"H. Edelsbrunner, B. Fasy, G. Rote, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100.","chicago":"Edelsbrunner, Herbert, Brittany Fasy, and Günter Rote. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” In <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>, 91–100. ACM, 2012. <a href=\"https://doi.org/10.1145/2261250.2261265\">https://doi.org/10.1145/2261250.2261265</a>.","ama":"Edelsbrunner H, Fasy B, Rote G. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In: <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>. ACM; 2012:91-100. doi:<a href=\"https://doi.org/10.1145/2261250.2261265\">10.1145/2261250.2261265</a>","ista":"Edelsbrunner H, Fasy B, Rote G. 2012. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 91–100."},"day":"20","year":"2012","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"None","date_published":"2012-06-20T00:00:00Z","title":"Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions","date_created":"2018-12-11T12:01:35Z","acknowledgement":"This research is partially supported by the National Science Foun- dation (NSF) under grant DBI-0820624, by the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.","doi":"10.1145/2261250.2261265","department":[{"_id":"HeEd"}],"month":"06","publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","date_updated":"2025-09-29T14:02:00Z","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"first_name":"Brittany","last_name":"Fasy","full_name":"Fasy, Brittany"},{"first_name":"Günter","full_name":"Rote, Günter","last_name":"Rote"}],"publisher":"ACM","page":"91 - 100","status":"public","scopus_import":1,"related_material":{"record":[{"relation":"later_version","id":"2815","status":"public"}]}},{"status":"public","issue":"6","scopus_import":"1","file_date_updated":"2020-07-14T12:46:01Z","date_updated":"2025-09-30T07:53:26Z","publication":"PLoS One","isi":1,"intvolume":"         7","article_number":"e36715","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","ddc":["510"],"year":"2012","date_published":"2012-06-06T00:00:00Z","external_id":{"isi":["000305348400006"]},"language":[{"iso":"eng"}],"_id":"3159","abstract":[{"text":"The structure of hierarchical networks in biological and physical systems has long been characterized using the Horton-Strahler ordering scheme. The scheme assigns an integer order to each edge in the network based on the topology of branching such that the order increases from distal parts of the network (e.g., mountain streams or capillaries) to the &quot;root&quot; of the network (e.g., the river outlet or the aorta). However, Horton-Strahler ordering cannot be applied to networks with loops because they they create a contradiction in the edge ordering in terms of which edge precedes another in the hierarchy. Here, we present a generalization of the Horton-Strahler order to weighted planar reticular networks, where weights are assumed to correlate with the importance of network edges, e.g., weights estimated from edge widths may correlate to flow capacity. Our method assigns hierarchical levels not only to edges of the network, but also to its loops, and classifies the edges into reticular edges, which are responsible for loop formation, and tree edges. In addition, we perform a detailed and rigorous theoretical analysis of the sensitivity of the hierarchical levels to weight perturbations. In doing so, we show that the ordering of the reticular edges is more robust to noise in weight estimation than is the ordering of the tree edges. We discuss applications of this generalized Horton-Strahler ordering to the study of leaf venation and other biological networks.","lang":"eng"}],"quality_controlled":"1","type":"journal_article","citation":{"ama":"Mileyko Y, Edelsbrunner H, Price C, Weitz J. Hierarchical ordering of reticular networks. <i>PLoS One</i>. 2012;7(6). doi:<a href=\"https://doi.org/10.1371/journal.pone.0036715\">10.1371/journal.pone.0036715</a>","ista":"Mileyko Y, Edelsbrunner H, Price C, Weitz J. 2012. Hierarchical ordering of reticular networks. PLoS One. 7(6), e36715.","chicago":"Mileyko, Yuriy, Herbert Edelsbrunner, Charles Price, and Joshua Weitz. “Hierarchical Ordering of Reticular Networks.” <i>PLoS One</i>. Public Library of Science, 2012. <a href=\"https://doi.org/10.1371/journal.pone.0036715\">https://doi.org/10.1371/journal.pone.0036715</a>.","mla":"Mileyko, Yuriy, et al. “Hierarchical Ordering of Reticular Networks.” <i>PLoS One</i>, vol. 7, no. 6, e36715, Public Library of Science, 2012, doi:<a href=\"https://doi.org/10.1371/journal.pone.0036715\">10.1371/journal.pone.0036715</a>.","ieee":"Y. Mileyko, H. Edelsbrunner, C. Price, and J. Weitz, “Hierarchical ordering of reticular networks,” <i>PLoS One</i>, vol. 7, no. 6. Public Library of Science, 2012.","short":"Y. Mileyko, H. Edelsbrunner, C. Price, J. Weitz, PLoS One 7 (2012).","apa":"Mileyko, Y., Edelsbrunner, H., Price, C., &#38; Weitz, J. (2012). Hierarchical ordering of reticular networks. <i>PLoS One</i>. Public Library of Science. <a href=\"https://doi.org/10.1371/journal.pone.0036715\">https://doi.org/10.1371/journal.pone.0036715</a>"},"day":"06","has_accepted_license":"1","article_processing_charge":"No","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publisher":"Public Library of Science","oa":1,"doi":"10.1371/journal.pone.0036715","acknowledgement":"his work was supported by the National Science Foundation Plant Genome Research Program (grant 0820624 to H.E. and J.S.W.), the Defense Advanced Projects Research Agency (grant HR0011-09-1-0055 to H.E. and J.S.W.), and the European Science Foundation (under the Research Networking Programme on “Applied and Computational Algebraic Topology” run by H.E.). Joshua S. Weitz, Ph.D., holds a Career Award at the Scientific Interface from the Burroughs Wellcome Fund.\r\n\r\n\r\n\r\nDuring preparation of this manuscript the authors became aware of a related work by Katifori and Magnasco (arXiv:1110.1412v1), concurrently submitted and accepted for publication in PLoS ONE.","pubrep_id":"385","author":[{"first_name":"Yuriy","last_name":"Mileyko","full_name":"Mileyko, Yuriy"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Price, Charles","last_name":"Price","first_name":"Charles"},{"first_name":"Joshua","last_name":"Weitz","full_name":"Weitz, Joshua"}],"volume":7,"month":"06","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T12:01:44Z","title":"Hierarchical ordering of reticular networks","oa_version":"Published Version","publication_status":"published","publist_id":"3530","file":[{"date_created":"2019-02-05T12:38:43Z","file_size":541583,"content_type":"application/pdf","access_level":"open_access","file_id":"5922","creator":"kschuh","relation":"main_file","date_updated":"2020-07-14T12:46:01Z","file_name":"2012_PLoS_Mileyko.PDF","checksum":"515a98ad72e470752f03f13663dcaff8"}]},{"file_date_updated":"2020-07-14T12:46:05Z","isi":1,"date_updated":"2025-09-30T07:43:46Z","publication":"Discrete & Computational Geometry","page":"393 - 414","status":"public","scopus_import":"1","issue":"2","quality_controlled":"1","type":"journal_article","external_id":{"isi":["000299057200010"]},"abstract":[{"text":"We use a distortion to define the dual complex of a cubical subdivision of ℝ n as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated by the topological analysis of high-dimensional digital image data, we consider such subdivisions defined by generalizations of quad- and oct-trees to n dimensions. Assuming the subdivision is balanced, we show that mapping each vertex to the center of the corresponding n-cube gives a geometric realization of the dual complex in ℝ n.","lang":"eng"}],"_id":"3256","language":[{"iso":"eng"}],"citation":{"chicago":"Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s00454-011-9382-4\">https://doi.org/10.1007/s00454-011-9382-4</a>.","ama":"Edelsbrunner H, Kerber M. Dual complexes of cubical subdivisions of ℝn. <i>Discrete &#38; Computational Geometry</i>. 2012;47(2):393-414. doi:<a href=\"https://doi.org/10.1007/s00454-011-9382-4\">10.1007/s00454-011-9382-4</a>","ista":"Edelsbrunner H, Kerber M. 2012. Dual complexes of cubical subdivisions of ℝn. Discrete &#38; Computational Geometry. 47(2), 393–414.","apa":"Edelsbrunner, H., &#38; Kerber, M. (2012). Dual complexes of cubical subdivisions of ℝn. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-011-9382-4\">https://doi.org/10.1007/s00454-011-9382-4</a>","mla":"Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” <i>Discrete &#38; Computational Geometry</i>, vol. 47, no. 2, Springer, 2012, pp. 393–414, doi:<a href=\"https://doi.org/10.1007/s00454-011-9382-4\">10.1007/s00454-011-9382-4</a>.","short":"H. Edelsbrunner, M. Kerber, Discrete &#38; Computational Geometry 47 (2012) 393–414.","ieee":"H. Edelsbrunner and M. Kerber, “Dual complexes of cubical subdivisions of ℝn,” <i>Discrete &#38; Computational Geometry</i>, vol. 47, no. 2. Springer, pp. 393–414, 2012."},"day":"01","has_accepted_license":"1","ddc":["000"],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2012","intvolume":"        47","date_published":"2012-03-01T00:00:00Z","pubrep_id":"543","oa":1,"doi":"10.1007/s00454-011-9382-4","acknowledgement":"This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0057 and HR0011-09-0065 as well as the National Science Foundation (NSF) under grant DBI-0820624.","department":[{"_id":"HeEd"}],"month":"03","volume":47,"author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"orcid":"0000-0002-8030-9299","first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael","last_name":"Kerber"}],"publisher":"Springer","article_processing_charge":"No","corr_author":"1","publication_status":"published","publist_id":"3398","file":[{"access_level":"open_access","content_type":"application/pdf","file_size":203636,"date_created":"2018-12-12T10:08:15Z","checksum":"76486f3b2c9e7fd81342f3832ca387e7","file_name":"IST-2016-543-v1+1_2012-J-08-HierarchyCubeComplex.pdf","date_updated":"2020-07-14T12:46:05Z","file_id":"4675","creator":"system","relation":"main_file"}],"oa_version":"Submitted Version","title":"Dual complexes of cubical subdivisions of ℝn","date_created":"2018-12-11T12:02:17Z"},{"publisher":"IEEE","status":"public","doi":"10.1109/ICCV.2011.6126486","month":"01","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T07:42:15Z","author":[{"first_name":"Adrian","id":"29F89302-F248-11E8-B48F-1D18A9856A87","last_name":"Ion","full_name":"Ion, Adrian"},{"last_name":"Carreira","full_name":"Carreira, Joao","first_name":"Joao"},{"first_name":"Cristian","full_name":"Sminchisescu, Cristian","last_name":"Sminchisescu"}],"year":"2012","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","article_number":"6126486","oa_version":"None","date_published":"2012-01-12T00:00:00Z","date_created":"2018-12-11T12:02:21Z","title":"Image segmentation by figure-ground composition into maximal cliques","publist_id":"3382","type":"conference","quality_controlled":"1","publication_status":"published","conference":{"end_date":"2011-11-13","location":"Barcelona, Spain","name":"ICCV: International Conference on Computer Vision","start_date":"2011-11-06"},"language":[{"iso":"eng"}],"_id":"3265","abstract":[{"lang":"eng","text":"We propose a mid-level statistical model for image segmentation that composes multiple figure-ground hypotheses (FG) obtained by applying constraints at different locations and scales, into larger interpretations (tilings) of the entire image. Inference is cast as optimization over sets of maximal cliques sampled from a graph connecting all non-overlapping figure-ground segment hypotheses. Potential functions over cliques combine unary, Gestalt-based figure qualities, and pairwise compatibilities among spatially neighboring segments, constrained by T-junctions and the boundary interface statistics of real scenes. Learning the model parameters is based on maximum likelihood, alternating between sampling image tilings and optimizing their potential function parameters. State of the art results are reported on the Berkeley and Stanford segmentation datasets, as well as VOC2009, where a 28% improvement was achieved."}],"citation":{"ama":"Ion A, Carreira J, Sminchisescu C. Image segmentation by figure-ground composition into maximal cliques. In: IEEE; 2012. doi:<a href=\"https://doi.org/10.1109/ICCV.2011.6126486\">10.1109/ICCV.2011.6126486</a>","ista":"Ion A, Carreira J, Sminchisescu C. 2012. Image segmentation by figure-ground composition into maximal cliques. ICCV: International Conference on Computer Vision, 6126486.","chicago":"Ion, Adrian, Joao Carreira, and Cristian Sminchisescu. “Image Segmentation by Figure-Ground Composition into Maximal Cliques.” IEEE, 2012. <a href=\"https://doi.org/10.1109/ICCV.2011.6126486\">https://doi.org/10.1109/ICCV.2011.6126486</a>.","mla":"Ion, Adrian, et al. <i>Image Segmentation by Figure-Ground Composition into Maximal Cliques</i>. 6126486, IEEE, 2012, doi:<a href=\"https://doi.org/10.1109/ICCV.2011.6126486\">10.1109/ICCV.2011.6126486</a>.","short":"A. Ion, J. Carreira, C. Sminchisescu, in:, IEEE, 2012.","ieee":"A. Ion, J. Carreira, and C. Sminchisescu, “Image segmentation by figure-ground composition into maximal cliques,” presented at the ICCV: International Conference on Computer Vision, Barcelona, Spain, 2012.","apa":"Ion, A., Carreira, J., &#38; Sminchisescu, C. (2012). Image segmentation by figure-ground composition into maximal cliques. Presented at the ICCV: International Conference on Computer Vision, Barcelona, Spain: IEEE. <a href=\"https://doi.org/10.1109/ICCV.2011.6126486\">https://doi.org/10.1109/ICCV.2011.6126486</a>"},"day":"12"},{"publication_status":"published","publist_id":"3330","file":[{"file_id":"5116","relation":"main_file","date_updated":"2020-07-14T12:46:06Z","creator":"system","checksum":"d65f79775b51258a604ca5ec741297cc","file_name":"IST-2016-542-v1+1_2012-J-01-Poinculus.pdf","content_type":"application/pdf","file_size":280280,"date_created":"2018-12-12T10:15:00Z","access_level":"open_access"}],"title":"A point calculus for interlevel set homology","date_created":"2018-12-11T12:02:36Z","oa_version":"Submitted Version","oa":1,"doi":"10.1016/j.patrec.2011.10.007","acknowledgement":"Research by the third author is partially supported by the National Science Foundation (NSF) under grant DBI-0820624.","pubrep_id":"542","volume":33,"author":[{"last_name":"Bendich","full_name":"Bendich, Paul","first_name":"Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Sergio","last_name":"Cabello","full_name":"Cabello, Sergio"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833"}],"department":[{"_id":"HeEd"}],"month":"08","article_processing_charge":"No","publisher":"Elsevier","external_id":{"isi":["000307204300002"]},"abstract":[{"text":"The theory of persistent homology opens up the possibility to reason about topological features of a space or a function quantitatively and in combinatorial terms. We refer to this new angle at a classical subject within algebraic topology as a point calculus, which we present for the family of interlevel sets of a real-valued function. Our account of the subject is expository, devoid of proofs, and written for non-experts in algebraic topology.","lang":"eng"}],"_id":"3310","language":[{"iso":"eng"}],"quality_controlled":"1","type":"journal_article","day":"01","citation":{"apa":"Bendich, P., Cabello, S., &#38; Edelsbrunner, H. (2012). A point calculus for interlevel set homology. <i>Pattern Recognition Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.patrec.2011.10.007\">https://doi.org/10.1016/j.patrec.2011.10.007</a>","mla":"Bendich, Paul, et al. “A Point Calculus for Interlevel Set Homology.” <i>Pattern Recognition Letters</i>, vol. 33, no. 11, Elsevier, 2012, pp. 1436–44, doi:<a href=\"https://doi.org/10.1016/j.patrec.2011.10.007\">10.1016/j.patrec.2011.10.007</a>.","ieee":"P. Bendich, S. Cabello, and H. Edelsbrunner, “A point calculus for interlevel set homology,” <i>Pattern Recognition Letters</i>, vol. 33, no. 11. Elsevier, pp. 1436–1444, 2012.","short":"P. Bendich, S. Cabello, H. Edelsbrunner, Pattern Recognition Letters 33 (2012) 1436–1444.","chicago":"Bendich, Paul, Sergio Cabello, and Herbert Edelsbrunner. “A Point Calculus for Interlevel Set Homology.” <i>Pattern Recognition Letters</i>. Elsevier, 2012. <a href=\"https://doi.org/10.1016/j.patrec.2011.10.007\">https://doi.org/10.1016/j.patrec.2011.10.007</a>.","ama":"Bendich P, Cabello S, Edelsbrunner H. A point calculus for interlevel set homology. <i>Pattern Recognition Letters</i>. 2012;33(11):1436-1444. doi:<a href=\"https://doi.org/10.1016/j.patrec.2011.10.007\">10.1016/j.patrec.2011.10.007</a>","ista":"Bendich P, Cabello S, Edelsbrunner H. 2012. A point calculus for interlevel set homology. Pattern Recognition Letters. 33(11), 1436–1444."},"has_accepted_license":"1","intvolume":"        33","ddc":["000"],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2012","date_published":"2012-08-01T00:00:00Z","file_date_updated":"2020-07-14T12:46:06Z","publication":"Pattern Recognition Letters","date_updated":"2025-09-30T07:39:47Z","isi":1,"status":"public","page":"1436 - 1444","issue":"11","scopus_import":"1"},{"publist_id":"3303","publication_status":"published","title":"A worst case bound for topology computation of algebraic curves","date_created":"2018-12-11T12:02:43Z","oa_version":"Preprint","arxiv":1,"author":[{"orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"},{"first_name":"Michael","last_name":"Sagraloff","full_name":"Sagraloff, Michael"}],"volume":47,"month":"03","department":[{"_id":"HeEd"}],"oa":1,"doi":"10.1016/j.jsc.2011.11.001","corr_author":"1","article_processing_charge":"No","publisher":"Elsevier","citation":{"apa":"Kerber, M., &#38; Sagraloff, M. (2012). A worst case bound for topology computation of algebraic curves. <i> Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jsc.2011.11.001\">https://doi.org/10.1016/j.jsc.2011.11.001</a>","short":"M. Kerber, M. Sagraloff,  Journal of Symbolic Computation 47 (2012) 239–258.","ieee":"M. Kerber and M. Sagraloff, “A worst case bound for topology computation of algebraic curves,” <i> Journal of Symbolic Computation</i>, vol. 47, no. 3. Elsevier, pp. 239–258, 2012.","mla":"Kerber, Michael, and Michael Sagraloff. “A Worst Case Bound for Topology Computation of Algebraic Curves.” <i> Journal of Symbolic Computation</i>, vol. 47, no. 3, Elsevier, 2012, pp. 239–58, doi:<a href=\"https://doi.org/10.1016/j.jsc.2011.11.001\">10.1016/j.jsc.2011.11.001</a>.","chicago":"Kerber, Michael, and Michael Sagraloff. “A Worst Case Bound for Topology Computation of Algebraic Curves.” <i> Journal of Symbolic Computation</i>. Elsevier, 2012. <a href=\"https://doi.org/10.1016/j.jsc.2011.11.001\">https://doi.org/10.1016/j.jsc.2011.11.001</a>.","ista":"Kerber M, Sagraloff M. 2012. A worst case bound for topology computation of algebraic curves.  Journal of Symbolic Computation. 47(3), 239–258.","ama":"Kerber M, Sagraloff M. A worst case bound for topology computation of algebraic curves. <i> Journal of Symbolic Computation</i>. 2012;47(3):239-258. doi:<a href=\"https://doi.org/10.1016/j.jsc.2011.11.001\">10.1016/j.jsc.2011.11.001</a>"},"day":"01","_id":"3331","abstract":[{"text":"Computing the topology of an algebraic plane curve C means computing a combinatorial graph that is isotopic to C and thus represents its topology in R2. We prove that, for a polynomial of degree n with integer coefficients bounded by 2ρ, the topology of the induced curve can be computed with  bit operations ( indicates that we omit logarithmic factors). Our analysis improves the previous best known complexity bounds by a factor of n2. The improvement is based on new techniques to compute and refine isolating intervals for the real roots of polynomials, and on the consequent amortized analysis of the critical fibers of the algebraic curve.","lang":"eng"}],"language":[{"iso":"eng"}],"external_id":{"arxiv":["1104.1510"],"isi":["000300115300002"]},"type":"journal_article","quality_controlled":"1","date_published":"2012-03-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1104.1510"}],"intvolume":"        47","year":"2012","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_updated":"2025-09-30T07:33:48Z","publication":" Journal of Symbolic Computation","isi":1,"issue":"3","scopus_import":"1","status":"public","page":"239 - 258"},{"publisher":"B. Verkin Institute for Low Temperature Physics and Engineering","corr_author":"1","article_processing_charge":"No","article_type":"original","department":[{"_id":"HeEd"}],"month":"01","author":[{"orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","first_name":"Florian","full_name":"Pausinger, Florian","last_name":"Pausinger"}],"volume":8,"acknowledgement":"This work is supported by the Austrian Science Fund (FWF), Project P22025-N18.\r\n","oa":1,"oa_version":"Published Version","date_created":"2019-06-27T08:16:56Z","title":"Elementary solutions of the Bernstein problem on two intervals","publication_identifier":{"issn":["1812-9471"]},"publication_status":"published","scopus_import":"1","issue":"1","status":"public","page":"63-78","isi":1,"publication":"Journal of Mathematical Physics, Analysis, Geometry","date_updated":"2025-06-26T12:10:42Z","main_file_link":[{"url":"https://www.mathnet.ru/eng/jmag525","open_access":"1"}],"date_published":"2012-01-01T00:00:00Z","OA_place":"publisher","year":"2012","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"         8","citation":{"ama":"Pausinger F. Elementary solutions of the Bernstein problem on two intervals. <i>Journal of Mathematical Physics, Analysis, Geometry</i>. 2012;8(1):63-78.","ista":"Pausinger F. 2012. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 8(1), 63–78.","chicago":"Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.” <i>Journal of Mathematical Physics, Analysis, Geometry</i>. B. Verkin Institute for Low Temperature Physics and Engineering, 2012.","mla":"Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.” <i>Journal of Mathematical Physics, Analysis, Geometry</i>, vol. 8, no. 1, B. Verkin Institute for Low Temperature Physics and Engineering, 2012, pp. 63–78.","short":"F. Pausinger, Journal of Mathematical Physics, Analysis, Geometry 8 (2012) 63–78.","ieee":"F. Pausinger, “Elementary solutions of the Bernstein problem on two intervals,” <i>Journal of Mathematical Physics, Analysis, Geometry</i>, vol. 8, no. 1. B. Verkin Institute for Low Temperature Physics and Engineering, pp. 63–78, 2012.","apa":"Pausinger, F. (2012). Elementary solutions of the Bernstein problem on two intervals. <i>Journal of Mathematical Physics, Analysis, Geometry</i>. B. Verkin Institute for Low Temperature Physics and Engineering."},"day":"01","type":"journal_article","quality_controlled":"1","language":[{"iso":"eng"}],"_id":"6588","abstract":[{"lang":"eng","text":"First we note that the best polynomial approximation to vertical bar x vertical bar on the set, which consists of an interval on the positive half-axis and a point on the negative half-axis, can be given by means of the classical Chebyshev polynomials. Then we explore the cases when a solution of the related problem on two intervals can be given in elementary functions."}],"external_id":{"isi":["000301173600004"]}},{"date_updated":"2021-01-12T07:42:15Z","publication":"NIPS Proceedings","volume":24,"author":[{"full_name":"Ion, Adrian","last_name":"Ion","id":"29F89302-F248-11E8-B48F-1D18A9856A87","first_name":"Adrian"},{"last_name":"Carreira","full_name":"Carreira, Joao","first_name":"Joao"},{"first_name":"Cristian","full_name":"Sminchisescu, Cristian","last_name":"Sminchisescu"}],"department":[{"_id":"HeEd"}],"month":"12","publisher":"Neural Information Processing Systems Foundation","status":"public","page":"1827 - 1835","scopus_import":1,"_id":"3266","abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"type":"conference","publist_id":"3381","quality_controlled":"1","publication_status":"published","conference":{"start_date":"2011-12-12","name":"NIPS: Neural Information Processing Systems","location":"Granada, Spain","end_date":"2011-12-14"},"day":"01","citation":{"short":"A. Ion, J. Carreira, C. Sminchisescu, in:, NIPS Proceedings, Neural Information Processing Systems Foundation, 2011, pp. 1827–1835.","ieee":"A. Ion, J. Carreira, and C. Sminchisescu, “Probabilistic joint image segmentation and labeling,” in <i>NIPS Proceedings</i>, Granada, Spain, 2011, vol. 24, pp. 1827–1835.","mla":"Ion, Adrian, et al. “Probabilistic Joint Image Segmentation and Labeling.” <i>NIPS Proceedings</i>, vol. 24, Neural Information Processing Systems Foundation, 2011, pp. 1827–35.","apa":"Ion, A., Carreira, J., &#38; Sminchisescu, C. (2011). Probabilistic joint image segmentation and labeling. In <i>NIPS Proceedings</i> (Vol. 24, pp. 1827–1835). Granada, Spain: Neural Information Processing Systems Foundation.","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.","ama":"Ion A, Carreira J, Sminchisescu C. Probabilistic joint image segmentation and labeling. In: <i>NIPS Proceedings</i>. Vol 24. Neural Information Processing Systems Foundation; 2011:1827-1835.","chicago":"Ion, Adrian, Joao Carreira, and Cristian Sminchisescu. “Probabilistic Joint Image Segmentation and Labeling.” In <i>NIPS Proceedings</i>, 24:1827–35. Neural Information Processing Systems Foundation, 2011."},"intvolume":"        24","year":"2011","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2011-12-01T00:00:00Z","date_created":"2018-12-11T12:02:21Z","title":"Probabilistic joint image segmentation and labeling","oa_version":"None"},{"publication_status":"published","publist_id":"3379","oa_version":"None","title":"Hardness results for homology localization","date_created":"2018-12-11T12:02:21Z","month":"01","department":[{"_id":"HeEd"}],"volume":45,"author":[{"first_name":"Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","last_name":"Chen","full_name":"Chen, Chao"},{"first_name":"Daniel","full_name":"Freedman, Daniel","last_name":"Freedman"}],"doi":"10.1007/s00454-010-9322-8","related_material":{"record":[{"status":"public","id":"10909","relation":"earlier_version"}]},"publisher":"Springer","article_processing_charge":"No","corr_author":"1","day":"14","citation":{"ama":"Chen C, Freedman D. Hardness results for homology localization. <i>Discrete &#38; Computational Geometry</i>. 2011;45(3):425-448. doi:<a href=\"https://doi.org/10.1007/s00454-010-9322-8\">10.1007/s00454-010-9322-8</a>","ista":"Chen C, Freedman D. 2011. Hardness results for homology localization. Discrete &#38; Computational Geometry. 45(3), 425–448.","chicago":"Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2011. <a href=\"https://doi.org/10.1007/s00454-010-9322-8\">https://doi.org/10.1007/s00454-010-9322-8</a>.","mla":"Chen, Chao, and Daniel Freedman. “Hardness Results for Homology Localization.” <i>Discrete &#38; Computational Geometry</i>, vol. 45, no. 3, Springer, 2011, pp. 425–48, doi:<a href=\"https://doi.org/10.1007/s00454-010-9322-8\">10.1007/s00454-010-9322-8</a>.","short":"C. Chen, D. Freedman, Discrete &#38; Computational Geometry 45 (2011) 425–448.","ieee":"C. Chen and D. Freedman, “Hardness results for homology localization,” <i>Discrete &#38; Computational Geometry</i>, vol. 45, no. 3. Springer, pp. 425–448, 2011.","apa":"Chen, C., &#38; Freedman, D. (2011). Hardness results for homology localization. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-010-9322-8\">https://doi.org/10.1007/s00454-010-9322-8</a>"},"quality_controlled":"1","type":"journal_article","external_id":{"isi":["000287146600005"]},"abstract":[{"lang":"eng","text":"We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We study the problem with different measures: volume, diameter and radius. For volume, that is, the 1-norm of a cycle, two main results are presented. First, we prove that the problem is NP-hard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NP-hard to approximate even when the Betti number is O(1). The latter result leads to the inapproximability of the problem of computing the nonbounding cycle with the smallest volume and computing cycles representing a homology basis with the minimal total volume. As for the other two measures defined by pairwise geodesic distance, diameter and radius, we show that the localization problem is NP-hard for diameter but is polynomial for radius. Our work is restricted to homology over the ℤ2 field."}],"_id":"3267","language":[{"iso":"eng"}],"date_published":"2011-01-14T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2011","intvolume":"        45","isi":1,"publication":"Discrete & Computational Geometry","date_updated":"2025-09-30T09:22:32Z","scopus_import":"1","issue":"3","page":"425 - 448","status":"public"},{"citation":{"mla":"Sheng, Yu, et al. “Perceptual Global Illumination Cancellation in Complex Projection Environments.” <i>Computer Graphics Forum</i>, vol. 30, no. 4, Wiley-Blackwell, 2011, pp. 1261–68, doi:<a href=\"https://doi.org/10.1111/j.1467-8659.2011.01985.x\">10.1111/j.1467-8659.2011.01985.x</a>.","ieee":"Y. Sheng, B. Cutler, C. Chen, and J. Nasman, “Perceptual global illumination cancellation in complex projection environments,” <i>Computer Graphics Forum</i>, vol. 30, no. 4. Wiley-Blackwell, pp. 1261–1268, 2011.","short":"Y. Sheng, B. Cutler, C. Chen, J. Nasman, Computer Graphics Forum 30 (2011) 1261–1268.","apa":"Sheng, Y., Cutler, B., Chen, C., &#38; Nasman, J. (2011). Perceptual global illumination cancellation in complex projection environments. <i>Computer Graphics Forum</i>. Wiley-Blackwell. <a href=\"https://doi.org/10.1111/j.1467-8659.2011.01985.x\">https://doi.org/10.1111/j.1467-8659.2011.01985.x</a>","ama":"Sheng Y, Cutler B, Chen C, Nasman J. Perceptual global illumination cancellation in complex projection environments. <i>Computer Graphics Forum</i>. 2011;30(4):1261-1268. doi:<a href=\"https://doi.org/10.1111/j.1467-8659.2011.01985.x\">10.1111/j.1467-8659.2011.01985.x</a>","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.” <i>Computer Graphics Forum</i>. Wiley-Blackwell, 2011. <a href=\"https://doi.org/10.1111/j.1467-8659.2011.01985.x\">https://doi.org/10.1111/j.1467-8659.2011.01985.x</a>."},"day":"19","language":[{"iso":"eng"}],"_id":"3269","abstract":[{"lang":"eng","text":"The unintentional scattering of light between neighboring surfaces in complex projection environments increases the brightness and decreases the contrast, disrupting the appearance of the desired imagery. To achieve satisfactory projection results, the inverse problem of global illumination must be solved to cancel this secondary scattering. In this paper, we propose a global illumination cancellation method that minimizes the perceptual difference between the desired imagery and the actual total illumination in the resulting physical environment. Using Gauss-Newton and active set methods, we design a fast solver for the bound constrained nonlinear least squares problem raised by the perceptual error metrics. Our solver is further accelerated with a CUDA implementation and multi-resolution method to achieve 1–2 fps for problems with approximately 3000 variables. We demonstrate the global illumination cancellation algorithm with our multi-projector system. Results show that our method preserves the color fidelity of the desired imagery significantly better than previous methods."}],"external_id":{"isi":["000292884700011"]},"type":"journal_article","quality_controlled":"1","date_published":"2011-07-19T00:00:00Z","main_file_link":[{"url":"http://www.cs.cmu.edu/%7Eshengyu/download/egsr2011_paper.pdf","open_access":"1"}],"intvolume":"        30","year":"2011","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_updated":"2025-09-30T09:22:04Z","publication":"Computer Graphics Forum","isi":1,"issue":"4","scopus_import":"1","page":"1261 - 1268","status":"public","publist_id":"3377","publication_status":"published","date_created":"2018-12-11T12:02:22Z","title":"Perceptual global illumination cancellation in complex projection environments","oa_version":"Published Version","author":[{"first_name":"Yu","full_name":"Sheng, Yu","last_name":"Sheng"},{"first_name":"Barbara","last_name":"Cutler","full_name":"Cutler, Barbara"},{"full_name":"Chen, Chao","last_name":"Chen","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","first_name":"Chao"},{"full_name":"Nasman, Joshua","last_name":"Nasman","first_name":"Joshua"}],"volume":30,"article_type":"original","month":"07","department":[{"_id":"HeEd"}],"doi":"10.1111/j.1467-8659.2011.01985.x","oa":1,"article_processing_charge":"No","publisher":"Wiley-Blackwell"},{"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","year":"2011","title":"Persistent homology computation with a twist","date_created":"2018-12-11T12:02:22Z","date_published":"2011-01-01T00:00:00Z","oa_version":"None","language":[{"iso":"eng"}],"_id":"3270","abstract":[{"lang":"eng","text":"The persistence diagram of a filtered simplicial com- plex is usually computed by reducing the boundary matrix of the complex. We introduce a simple op- timization technique: by processing the simplices of the complex in decreasing dimension, we can “kill” columns (i.e., set them to zero) without reducing them. This technique completely avoids reduction on roughly half of the columns. We demonstrate that this idea significantly improves the running time of the reduction algorithm in practice. We also give an output-sensitive complexity analysis for the new al- gorithm which yields to sub-cubic asymptotic bounds under certain assumptions."}],"conference":{"start_date":"2011-03-28","name":"EuroCG: European Workshop on Computational Geometry","location":"Morschach, Switzerland","end_date":"2011-03-30"},"publication_status":"published","quality_controlled":"1","type":"conference","publist_id":"3376","citation":{"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.","ama":"Chen C, Kerber M. Persistent homology computation with a twist. In: TU Dortmund; 2011:197-200.","apa":"Chen, C., &#38; 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.","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.","mla":"Chen, Chao, and Michael Kerber. <i>Persistent Homology Computation with a Twist</i>. TU Dortmund, 2011, pp. 197–200."},"day":"01","corr_author":"1","page":"197 - 200","status":"public","publisher":"TU Dortmund","author":[{"first_name":"Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87","last_name":"Chen","full_name":"Chen, Chao"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber","full_name":"Kerber, Michael"}],"date_updated":"2024-10-09T20:54:35Z","department":[{"_id":"HeEd"}],"month":"01"},{"date_published":"2011-11-14T00:00:00Z","alternative_title":["Theory, Algorithms, and Applications"],"title":"Efficient computation of persistent homology for cubical data","date_created":"2018-12-11T12:02:23Z","oa_version":"None","year":"2011","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","day":"14","citation":{"mla":"Wagner, Hubert, et al. “Efficient Computation of Persistent Homology for Cubical Data.” <i>Topological Methods in Data Analysis and Visualization II</i>, edited by Ronald Peikert et al., Springer, 2011, pp. 91–106, doi:<a href=\"https://doi.org/10.1007/978-3-642-23175-9_7\">10.1007/978-3-642-23175-9_7</a>.","ieee":"H. Wagner, C. Chen, and E. Vuçini, “Efficient computation of persistent homology for cubical data,” in <i>Topological Methods in Data Analysis and Visualization II</i>, 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.","apa":"Wagner, H., Chen, C., &#38; Vuçini, E. (2011). Efficient computation of persistent homology for cubical data. In R. Peikert, H. Hauser, H. Carr, &#38; R. Fuchs (Eds.), <i>Topological Methods in Data Analysis and Visualization II</i> (pp. 91–106). Springer. <a href=\"https://doi.org/10.1007/978-3-642-23175-9_7\">https://doi.org/10.1007/978-3-642-23175-9_7</a>","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. <i>Topological Methods in Data Analysis and Visualization II</i>. Springer; 2011:91-106. doi:<a href=\"https://doi.org/10.1007/978-3-642-23175-9_7\">10.1007/978-3-642-23175-9_7</a>","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.","chicago":"Wagner, Hubert, Chao Chen, and Erald Vuçini. “Efficient Computation of Persistent Homology for Cubical Data.” In <i>Topological Methods in Data Analysis and Visualization II</i>, edited by Ronald Peikert, Helwig Hauser, Hamish Carr, and Raphael Fuchs, 91–106. Springer, 2011. <a href=\"https://doi.org/10.1007/978-3-642-23175-9_7\">https://doi.org/10.1007/978-3-642-23175-9_7</a>."},"_id":"3271","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"}],"language":[{"iso":"eng"}],"type":"book_chapter","publist_id":"3375","publication_status":"published","quality_controlled":"1","scopus_import":1,"editor":[{"first_name":"Ronald","full_name":"Peikert, Ronald","last_name":"Peikert"},{"full_name":"Hauser, Helwig","last_name":"Hauser","first_name":"Helwig"},{"last_name":"Carr","full_name":"Carr, Hamish","first_name":"Hamish"},{"last_name":"Fuchs","full_name":"Fuchs, Raphael","first_name":"Raphael"}],"publisher":"Springer","page":"91 - 106","status":"public","publication":"Topological Methods in Data Analysis and Visualization II","date_updated":"2021-01-12T07:42:18Z","author":[{"first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert"},{"full_name":"Chen, Chao","last_name":"Chen","first_name":"Chao","id":"3E92416E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Vuçini, Erald","last_name":"Vuçini","first_name":"Erald"}],"month":"11","department":[{"_id":"HeEd"}],"doi":"10.1007/978-3-642-23175-9_7"}]