[{"article_processing_charge":"No","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"status":"public","date_updated":"2025-09-23T08:30:43Z","oa_version":"Published Version","title":"Root traits computed by DynamicRoots for the maize root shown in fig 2","related_material":{"record":[{"relation":"used_in_publication","status":"public","id":"1793"}]},"citation":{"apa":"Symonova, O., Topp, C., &#38; Edelsbrunner, H. (2015). Root traits computed by DynamicRoots for the maize root shown in fig 2. Public Library of Science. <a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">https://doi.org/10.1371/journal.pone.0127657.s001</a>","mla":"Symonova, Olga, et al. <i>Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2</i>. Public Library of Science, 2015, doi:<a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">10.1371/journal.pone.0127657.s001</a>.","chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2.” Public Library of Science, 2015. <a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">https://doi.org/10.1371/journal.pone.0127657.s001</a>.","short":"O. Symonova, C. Topp, H. Edelsbrunner, (2015).","ama":"Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for the maize root shown in fig 2. 2015. doi:<a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">10.1371/journal.pone.0127657.s001</a>","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots for the maize root shown in fig 2.” Public Library of Science, 2015.","ista":"Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots for the maize root shown in fig 2, Public Library of Science, <a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">10.1371/journal.pone.0127657.s001</a>."},"date_published":"2015-06-01T00:00:00Z","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","day":"01","publisher":"Public Library of Science","date_created":"2021-07-28T06:20:13Z","author":[{"first_name":"Olga","orcid":"0000-0003-2012-9947","last_name":"Symonova","full_name":"Symonova, Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Christopher","last_name":"Topp","full_name":"Topp, Christopher"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"}],"doi":"10.1371/journal.pone.0127657.s001","month":"06","_id":"9737","type":"research_data_reference","year":"2015"},{"abstract":[{"lang":"eng","text":"Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology."}],"oa_version":"None","title":"A Koksma-Hlawka inequality for general discrepancy systems","publication_status":"published","page":"773 - 797","quality_controlled":"1","acknowledgement":"F.P. is supported by the Graduate School of IST Austria, A.M.S is supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum Foundation.","intvolume":"        31","volume":31,"scopus_import":"1","_id":"1792","author":[{"last_name":"Pausinger","orcid":"0000-0002-8379-3768","first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","full_name":"Pausinger, Florian"},{"full_name":"Svane, Anne","last_name":"Svane","first_name":"Anne"}],"doi":"10.1016/j.jco.2015.06.002","date_created":"2018-12-11T11:54:02Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” <i>Journal of Complexity</i>. Academic Press, 2015. <a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">https://doi.org/10.1016/j.jco.2015.06.002</a>.","mla":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” <i>Journal of Complexity</i>, vol. 31, no. 6, Academic Press, 2015, pp. 773–97, doi:<a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">10.1016/j.jco.2015.06.002</a>.","short":"F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.","ama":"Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems. <i>Journal of Complexity</i>. 2015;31(6):773-797. doi:<a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">10.1016/j.jco.2015.06.002</a>","apa":"Pausinger, F., &#38; Svane, A. (2015). A Koksma-Hlawka inequality for general discrepancy systems. <i>Journal of Complexity</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">https://doi.org/10.1016/j.jco.2015.06.002</a>","ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","ieee":"F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” <i>Journal of Complexity</i>, vol. 31, no. 6. Academic Press, pp. 773–797, 2015."},"date_published":"2015-12-01T00:00:00Z","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"1399"}]},"date_updated":"2026-04-09T14:26:05Z","status":"public","external_id":{"isi":["000362926900001"]},"isi":1,"department":[{"_id":"HeEd"}],"publication":"Journal of Complexity","article_processing_charge":"No","year":"2015","type":"journal_article","month":"12","corr_author":"1","publisher":"Academic Press","issue":"6","day":"01","publist_id":"5320"},{"abstract":[{"lang":"eng","text":"This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold."}],"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"part_of_dissertation","id":"1662","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"1792"},{"id":"2255","status":"public","relation":"part_of_dissertation"}]},"oa_version":"None","title":"On the approximation of intrinsic volumes","publication_status":"published","date_updated":"2026-04-16T10:09:04Z","status":"public","page":"144","department":[{"_id":"HeEd"}],"article_processing_charge":"No","alternative_title":["ISTA Thesis"],"year":"2015","publication_identifier":{"issn":["2663-337X"]},"type":"dissertation","OA_place":"publisher","month":"06","_id":"1399","corr_author":"1","publisher":"Institute of Science and Technology Austria","date_created":"2018-12-11T11:51:48Z","author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","last_name":"Pausinger","first_name":"Florian"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","day":"01","publist_id":"5808","citation":{"chicago":"Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015.","short":"F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science and Technology Austria, 2015.","mla":"Pausinger, Florian. <i>On the Approximation of Intrinsic Volumes</i>. Institute of Science and Technology Austria, 2015.","ama":"Pausinger F. On the approximation of intrinsic volumes. 2015.","apa":"Pausinger, F. (2015). <i>On the approximation of intrinsic volumes</i>. Institute of Science and Technology Austria.","ista":"Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","ieee":"F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015."},"supervisor":[{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"date_published":"2015-06-01T00:00:00Z","degree_awarded":"PhD"},{"day":"01","publist_id":"3842","month":"01","corr_author":"1","publisher":"European Mathematical Society","conference":{"end_date":"2012-07-07","start_date":"2012-07-02","name":"ECM: European Congress of Mathematics","location":"Kraków, Poland"},"year":"2014","pubrep_id":"544","type":"conference","department":[{"_id":"HeEd"}],"has_accepted_license":"1","article_processing_charge":"No","status":"public","date_updated":"2025-06-03T11:46:59Z","ddc":["000"],"file":[{"content_type":"application/pdf","date_updated":"2020-07-14T12:45:52Z","file_size":435320,"access_level":"open_access","creator":"system","checksum":"1d4a046f1af945c407c5c4d411d4c5e4","file_id":"5232","file_name":"IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf","date_created":"2018-12-12T10:16:43Z","relation":"main_file"}],"language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice. ECM: European Congress of Mathematics, 31–50.","ieee":"H. Edelsbrunner and D. Morozovy, “Persistent homology: Theory and practice,” presented at the ECM: European Congress of Mathematics, Kraków, Poland, 2014, pp. 31–50.","ama":"Edelsbrunner H, Morozovy D. Persistent homology: Theory and practice. In: European Mathematical Society; 2014:31-50. doi:<a href=\"https://doi.org/10.4171/120-1/3\">10.4171/120-1/3</a>","chicago":"Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory and Practice,” 31–50. European Mathematical Society, 2014. <a href=\"https://doi.org/10.4171/120-1/3\">https://doi.org/10.4171/120-1/3</a>.","mla":"Edelsbrunner, Herbert, and Dmitriy Morozovy. <i>Persistent Homology: Theory and Practice</i>. European Mathematical Society, 2014, pp. 31–50, doi:<a href=\"https://doi.org/10.4171/120-1/3\">10.4171/120-1/3</a>.","short":"H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society, 2014, pp. 31–50.","apa":"Edelsbrunner, H., &#38; Morozovy, D. (2014). Persistent homology: Theory and practice (pp. 31–50). Presented at the ECM: European Congress of Mathematics, Kraków, Poland: European Mathematical Society. <a href=\"https://doi.org/10.4171/120-1/3\">https://doi.org/10.4171/120-1/3</a>"},"date_published":"2014-01-01T00:00:00Z","oa":1,"_id":"2905","doi":"10.4171/120-1/3","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dmitriy","last_name":"Morozovy","full_name":"Morozovy, Dmitriy"}],"date_created":"2018-12-11T12:00:16Z","acknowledgement":"This research is partially supported by NSF under grant DBI-0820624, by ESF under the Research Networking Programme, and by the Russian Government Project 11.G34.31.0053.","file_date_updated":"2020-07-14T12:45:52Z","quality_controlled":"1","page":"31 - 50","oa_version":"Submitted Version","title":"Persistent homology: Theory and practice","publication_status":"published","abstract":[{"lang":"eng","text":"Persistent homology is a recent grandchild of homology that has found use in\r\nscience and engineering as well as in mathematics. This paper surveys the method as well\r\nas the applications, neglecting completeness in favor of highlighting ideas and directions."}]},{"language":[{"iso":"eng"}],"date_updated":"2024-10-09T20:55:54Z","file":[{"relation":"main_file","file_name":"IST-2016-443-v1+1_S0218195914500034.pdf","file_id":"4704","date_created":"2018-12-12T10:08:43Z","checksum":"be45c133ab4d43351260e21beaa8f4b1","creator":"system","access_level":"open_access","date_updated":"2020-07-14T12:45:17Z","file_size":991734,"content_type":"application/pdf"}],"ddc":["000"],"status":"public","department":[{"_id":"HeEd"}],"has_accepted_license":"1","publication":"International Journal of Computational Geometry and Applications","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"year":"2014","pubrep_id":"443","type":"journal_article","month":"03","corr_author":"1","publisher":"World Scientific Publishing","license":"https://creativecommons.org/licenses/by/4.0/","day":"16","publist_id":"5290","issue":"1","abstract":[{"text":"Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques.","lang":"eng"}],"title":"Topology-preserving watermarking of vector graphics","oa_version":"Published Version","publication_status":"published","page":"61 - 86","file_date_updated":"2020-07-14T12:45:17Z","quality_controlled":"1","acknowledgement":"Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.","intvolume":"        24","volume":24,"scopus_import":1,"_id":"1816","date_created":"2018-12-11T11:54:10Z","doi":"10.1142/S0218195914500034","author":[{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber","first_name":"Stefan"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"last_name":"Meerwald","first_name":"Peter","full_name":"Meerwald, Peter"},{"first_name":"Roland","last_name":"Kwitt","full_name":"Kwitt, Roland"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Huber, S., Held, M., Meerwald, P., &#38; Kwitt, R. (2014). Topology-preserving watermarking of vector graphics. <i>International Journal of Computational Geometry and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218195914500034\">https://doi.org/10.1142/S0218195914500034</a>","ama":"Huber S, Held M, Meerwald P, Kwitt R. Topology-preserving watermarking of vector graphics. <i>International Journal of Computational Geometry and Applications</i>. 2014;24(1):61-86. doi:<a href=\"https://doi.org/10.1142/S0218195914500034\">10.1142/S0218195914500034</a>","short":"S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 61–86.","mla":"Huber, Stefan, et al. “Topology-Preserving Watermarking of Vector Graphics.” <i>International Journal of Computational Geometry and Applications</i>, vol. 24, no. 1, World Scientific Publishing, 2014, pp. 61–86, doi:<a href=\"https://doi.org/10.1142/S0218195914500034\">10.1142/S0218195914500034</a>.","chicago":"Huber, Stefan, Martin Held, Peter Meerwald, and Roland Kwitt. “Topology-Preserving Watermarking of Vector Graphics.” <i>International Journal of Computational Geometry and Applications</i>. World Scientific Publishing, 2014. <a href=\"https://doi.org/10.1142/S0218195914500034\">https://doi.org/10.1142/S0218195914500034</a>.","ieee":"S. Huber, M. Held, P. Meerwald, and R. Kwitt, “Topology-preserving watermarking of vector graphics,” <i>International Journal of Computational Geometry and Applications</i>, vol. 24, no. 1. World Scientific Publishing, pp. 61–86, 2014.","ista":"Huber S, Held M, Meerwald P, Kwitt R. 2014. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 24(1), 61–86."},"oa":1,"date_published":"2014-03-16T00:00:00Z"},{"issue":"1","publist_id":"5260","day":"14","month":"11","publisher":"Springer","year":"2014","type":"journal_article","isi":1,"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publication":"Discrete & Computational Geometry","article_processing_charge":"No","status":"public","external_id":{"isi":["000346774600005"],"arxiv":["1310.7004"]},"date_updated":"2025-09-29T13:11:56Z","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","arxiv":1,"citation":{"mla":"Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.” <i>Discrete &#38; Computational Geometry</i>, vol. 53, no. 1, Springer, 2014, pp. 64–79, doi:<a href=\"https://doi.org/10.1007/s00454-014-9646-x\">10.1007/s00454-014-9646-x</a>.","short":"J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete &#38; Computational Geometry 53 (2014) 64–79.","chicago":"Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On the Geometric Ramsey Number of Outerplanar Graphs.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s00454-014-9646-x\">https://doi.org/10.1007/s00454-014-9646-x</a>.","ama":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number of outerplanar graphs. <i>Discrete &#38; Computational Geometry</i>. 2014;53(1):64-79. doi:<a href=\"https://doi.org/10.1007/s00454-014-9646-x\">10.1007/s00454-014-9646-x</a>","apa":"Cibulka, J., Gao, P., Krcál, M., Valla, T., &#38; Valtr, P. (2014). On the geometric ramsey number of outerplanar graphs. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-014-9646-x\">https://doi.org/10.1007/s00454-014-9646-x</a>","ista":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey number of outerplanar graphs. Discrete &#38; Computational Geometry. 53(1), 64–79.","ieee":"J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey number of outerplanar graphs,” <i>Discrete &#38; Computational Geometry</i>, vol. 53, no. 1. Springer, pp. 64–79, 2014."},"oa":1,"date_published":"2014-11-14T00:00:00Z","scopus_import":"1","_id":"1842","author":[{"first_name":"Josef","last_name":"Cibulka","full_name":"Cibulka, Josef"},{"full_name":"Gao, Pu","first_name":"Pu","last_name":"Gao"},{"full_name":"Krcál, Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","last_name":"Krcál"},{"full_name":"Valla, Tomáš","last_name":"Valla","first_name":"Tomáš"},{"full_name":"Valtr, Pavel","last_name":"Valtr","first_name":"Pavel"}],"doi":"10.1007/s00454-014-9646-x","date_created":"2018-12-11T11:54:18Z","volume":53,"acknowledgement":"Marek Krčál was supported by the ERC Advanced Grant No. 267165.","intvolume":"        53","main_file_link":[{"url":"http://arxiv.org/abs/1310.7004","open_access":"1"}],"page":"64 - 79","oa_version":"Submitted Version","title":"On the geometric ramsey number of outerplanar graphs","publication_status":"published","abstract":[{"lang":"eng","text":"We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by O(n3) and O(n10), in the convex and general case, respectively. We then apply similar methods to prove an (Formula presented.) upper bound on the Ramsey number of a path with n ordered vertices."}]},{"abstract":[{"text":"The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of overlap with other balls. We study two natural choices of overlap measures and obtain the optimal lattice packings in a parameterized family of lattices which contains the FCC, BCC, and integer lattice.","lang":"eng"}],"title":"Sphere packing with limited overlap","oa_version":"Preprint","publication_status":"published","main_file_link":[{"url":"http://cccg.ca/proceedings/2014/papers/paper23.pdf","open_access":"1"}],"page":"155-161","quality_controlled":"1","acknowledgement":"We thank Herbert Edelsbrunner for his valuable discussions and ideas on the topic of this paper.  The second author has been supported by the Max Planck Center for Visual Computing and Communication","scopus_import":"1","OA_place":"repository","_id":"2012","date_created":"2018-12-11T11:55:12Z","author":[{"full_name":"Iglesias Ham, Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel","last_name":"Iglesias Ham"},{"first_name":"Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber","full_name":"Kerber, Michael"},{"full_name":"Uhler, Caroline","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","first_name":"Caroline","orcid":"0000-0002-7008-0216","last_name":"Uhler"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"citation":{"ieee":"M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,” in <i>26th Canadian Conference on Computational Geometry</i>, Halifax, Canada, 2014, pp. 155–161.","ista":"Iglesias Ham M, Kerber M, Uhler C. 2014. Sphere packing with limited overlap. 26th Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry, 155–161.","apa":"Iglesias Ham, M., Kerber, M., &#38; Uhler, C. (2014). Sphere packing with limited overlap. In <i>26th Canadian Conference on Computational Geometry</i> (pp. 155–161). Halifax, Canada: Canadian Conference on Computational Geometry.","ama":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. In: <i>26th Canadian Conference on Computational Geometry</i>. Canadian Conference on Computational Geometry; 2014:155-161.","mla":"Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” <i>26th Canadian Conference on Computational Geometry</i>, Canadian Conference on Computational Geometry, 2014, pp. 155–61.","short":"M. Iglesias Ham, M. Kerber, C. Uhler, in:, 26th Canadian Conference on Computational Geometry, Canadian Conference on Computational Geometry, 2014, pp. 155–161.","chicago":"Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing with Limited Overlap.” In <i>26th Canadian Conference on Computational Geometry</i>, 155–61. Canadian Conference on Computational Geometry, 2014."},"oa":1,"date_published":"2014-09-01T00:00:00Z","language":[{"iso":"eng"}],"date_updated":"2025-01-20T13:57:24Z","status":"public","external_id":{"arxiv":["1401.0468"]},"department":[{"_id":"HeEd"},{"_id":"CaUh"}],"publication":"26th Canadian Conference on Computational Geometry","article_processing_charge":"No","year":"2014","type":"conference","month":"09","corr_author":"1","publisher":"Canadian Conference on Computational Geometry","conference":{"location":"Halifax, Canada","name":"CCCG: Canadian Conference on Computational Geometry","start_date":"2014-08-11","end_date":"2014-08-13"},"OA_type":"green","publist_id":"5064","day":"01"},{"date_created":"2018-12-11T11:55:23Z","doi":"10.1137/1.9781611973198.4","author":[{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","full_name":"Bauer, Ulrich","last_name":"Bauer","orcid":"0000-0002-9683-0724","first_name":"Ulrich"},{"full_name":"Kerber, Michael","last_name":"Kerber","orcid":"0000-0002-8030-9299","first_name":"Michael"},{"full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus"}],"scopus_import":"1","_id":"2043","arxiv":1,"citation":{"ista":"Bauer U, Kerber M, Reininghaus J. 2014. Distributed computation of persistent homology. Proceedings of the Workshop on Algorithm Engineering and Experiments. ALENEX: Algorithm Engineering and Experiments, 31–38.","ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent homology,” in <i>Proceedings of the Workshop on Algorithm Engineering and Experiments</i>, Portland, USA, 2014, pp. 31–38.","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Distributed Computation of Persistent Homology.” In <i>Proceedings of the Workshop on Algorithm Engineering and Experiments</i>, edited by Catherine  McGeoch and Ulrich Meyer, 31–38. Society for Industrial and Applied Mathematics, 2014. <a href=\"https://doi.org/10.1137/1.9781611973198.4\">https://doi.org/10.1137/1.9781611973198.4</a>.","short":"U. Bauer, M. Kerber, J. Reininghaus, in:, C.  McGeoch, U. Meyer (Eds.), Proceedings of the Workshop on Algorithm Engineering and Experiments, Society for Industrial and Applied Mathematics, 2014, pp. 31–38.","mla":"Bauer, Ulrich, et al. “Distributed Computation of Persistent Homology.” <i>Proceedings of the Workshop on Algorithm Engineering and Experiments</i>, edited by Catherine  McGeoch and Ulrich Meyer, Society for Industrial and Applied Mathematics, 2014, pp. 31–38, doi:<a href=\"https://doi.org/10.1137/1.9781611973198.4\">10.1137/1.9781611973198.4</a>.","ama":"Bauer U, Kerber M, Reininghaus J. Distributed computation of persistent homology. In:  McGeoch C, Meyer U, eds. <i>Proceedings of the Workshop on Algorithm Engineering and Experiments</i>. Society for Industrial and Applied Mathematics; 2014:31-38. doi:<a href=\"https://doi.org/10.1137/1.9781611973198.4\">10.1137/1.9781611973198.4</a>","apa":"Bauer, U., Kerber, M., &#38; Reininghaus, J. (2014). Distributed computation of persistent homology. In C.  McGeoch &#38; U. Meyer (Eds.), <i>Proceedings of the Workshop on Algorithm Engineering and Experiments</i> (pp. 31–38). Portland, USA: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611973198.4\">https://doi.org/10.1137/1.9781611973198.4</a>"},"oa":1,"date_published":"2014-01-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"31 - 38","main_file_link":[{"url":"http://arxiv.org/abs/1310.0710","open_access":"1"}],"quality_controlled":"1","abstract":[{"text":"Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically – as long as the algorithm does not exhaust the available memory. Following up on a recently presented parallel method for persistence computation on shared memory systems [1], we demonstrate that a simple adaption of the standard reduction algorithm leads to a variant for distributed systems. Our algorithmic design ensures that the data is distributed over the nodes without redundancy; this permits the computation of much larger instances than on a single machine. Moreover, we observe that the parallelism at least compensates for the overhead caused by communication between nodes, and often even speeds up the computation compared to sequential and even parallel shared memory algorithms. In our experiments, we were able to compute the persistent homology of filtrations with more than a billion (109) elements within seconds on a cluster with 32 nodes using less than 6GB of memory per node.","lang":"eng"}],"publication_status":"published","oa_version":"Submitted Version","title":"Distributed computation of persistent homology","publisher":"Society for Industrial and Applied Mathematics","conference":{"location":"Portland, USA","end_date":"2014-01-05","name":"ALENEX: Algorithm Engineering and Experiments","start_date":"2014-01-05"},"month":"01","publist_id":"5008","day":"01","ec_funded":1,"type":"conference","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"year":"2014","external_id":{"arxiv":["1310.0710"]},"status":"public","article_processing_charge":"No","department":[{"_id":"HeEd"}],"publication":"Proceedings of the Workshop on Algorithm Engineering and Experiments","language":[{"iso":"eng"}],"date_updated":"2025-06-11T08:03:07Z","editor":[{"full_name":" McGeoch, Catherine","first_name":"Catherine","last_name":" McGeoch"},{"first_name":"Ulrich","last_name":"Meyer","full_name":"Meyer, Ulrich"}]},{"citation":{"ista":"Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent Homology in Chunks. In: Topological Methods in Data Analysis and Visualization III. , 103–117.","ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent Homology in Chunks,” in <i>Topological Methods in Data Analysis and Visualization III</i>, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014, pp. 103–117.","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress: Computing Persistent Homology in Chunks.” In <i>Topological Methods in Data Analysis and Visualization III</i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">https://doi.org/10.1007/978-3-319-04099-8_7</a>.","mla":"Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in Chunks.” <i>Topological Methods in Data Analysis and Visualization III</i>, edited by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">10.1007/978-3-319-04099-8_7</a>.","short":"U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III, Springer, 2014, pp. 103–117.","ama":"Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. <i>Topological Methods in Data Analysis and Visualization III</i>. Mathematics and Visualization. Springer; 2014:103-117. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">10.1007/978-3-319-04099-8_7</a>","apa":"Bauer, U., Kerber, M., &#38; Reininghaus, J. (2014). Clear and Compress: Computing Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III</i> (pp. 103–117). Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">https://doi.org/10.1007/978-3-319-04099-8_7</a>"},"arxiv":1,"date_published":"2014-03-19T00:00:00Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:55:23Z","author":[{"full_name":"Bauer, Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich","orcid":"0000-0002-9683-0724","last_name":"Bauer"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber","orcid":"0000-0002-8030-9299"},{"full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus"}],"doi":"10.1007/978-3-319-04099-8_7","scopus_import":"1","_id":"2044","publication_status":"published","title":"Clear and Compress: Computing Persistent Homology in Chunks","oa_version":"Submitted Version","abstract":[{"text":"We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation.","lang":"eng"}],"quality_controlled":"1","page":"103 - 117","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1303.0477"}],"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"type":"book_chapter","year":"2014","ec_funded":1,"publist_id":"5007","day":"19","publisher":"Springer","month":"03","corr_author":"1","date_updated":"2025-06-11T07:56:57Z","series_title":"Mathematics and Visualization","editor":[{"first_name":"Peer-Timo","last_name":"Bremer","full_name":"Bremer, Peer-Timo"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"},{"first_name":"Valerio","last_name":"Pascucci","full_name":"Pascucci, Valerio"},{"last_name":"Peikert","first_name":"Ronald","full_name":"Peikert, Ronald"}],"language":[{"iso":"eng"}],"article_processing_charge":"No","department":[{"_id":"HeEd"}],"publication":"Topological Methods in Data Analysis and Visualization III","external_id":{"arxiv":["1303.0477"]},"status":"public"},{"year":"2014","type":"journal_article","issue":"3","publist_id":"5220","day":"01","month":"07","publisher":"Independent University of Moscow","date_updated":"2025-07-10T11:51:26Z","language":[{"iso":"eng"}],"department":[{"_id":"HeEd"}],"publication":"Moscow Mathematical Journal","article_processing_charge":"No","status":"public","external_id":{"arxiv":["1211.7053"]},"article_type":"original","publication_identifier":{"issn":["1609-3321"]},"volume":14,"intvolume":"        14","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"citation":{"ama":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. Functionals on triangulations of delaunay sets. <i>Moscow Mathematical Journal</i>. 2014;14(3):491-504. doi:<a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">10.17323/1609-4514-2014-14-3-491-504</a>","chicago":"Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin. “Functionals on Triangulations of Delaunay Sets.” <i>Moscow Mathematical Journal</i>. Independent University of Moscow, 2014. <a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">https://doi.org/10.17323/1609-4514-2014-14-3-491-504</a>.","mla":"Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.” <i>Moscow Mathematical Journal</i>, vol. 14, no. 3, Independent University of Moscow, 2014, pp. 491–504, doi:<a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">10.17323/1609-4514-2014-14-3-491-504</a>.","short":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical Journal 14 (2014) 491–504.","apa":"Dolbilin, N., Edelsbrunner, H., Glazyrin, A., &#38; Musin, O. (2014). Functionals on triangulations of delaunay sets. <i>Moscow Mathematical Journal</i>. Independent University of Moscow. <a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">https://doi.org/10.17323/1609-4514-2014-14-3-491-504</a>","ista":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504.","ieee":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, and O. Musin, “Functionals on triangulations of delaunay sets,” <i>Moscow Mathematical Journal</i>, vol. 14, no. 3. Independent University of Moscow, pp. 491–504, 2014."},"date_published":"2014-07-01T00:00:00Z","oa":1,"scopus_import":"1","_id":"1876","date_created":"2018-12-11T11:54:29Z","doi":"10.17323/1609-4514-2014-14-3-491-504","author":[{"first_name":"Nikolai","last_name":"Dolbilin","full_name":"Dolbilin, Nikolai"},{"first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Glazyrin, Alexey","last_name":"Glazyrin","first_name":"Alexey"},{"full_name":"Musin, Oleg","last_name":"Musin","first_name":"Oleg"}],"title":"Functionals on triangulations of delaunay sets","oa_version":"Submitted Version","publication_status":"published","abstract":[{"lang":"eng","text":"We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets."}],"quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1211.7053","open_access":"1"}],"page":"491 - 504"},{"quality_controlled":"1","page":"754 - 760","publication_status":"published","title":"An algorithm for cartographic generalization that preserves global topology","oa_version":"None","abstract":[{"text":"We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales.","lang":"eng"}],"date_published":"2014-11-16T00:00:00Z","citation":{"apa":"Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y., Edelsbrunner, H., &#38; Yakimova, O. (2014). An algorithm for cartographic generalization that preserves global topology. <i>Journal of Mathematical Sciences</i>. Springer. <a href=\"https://doi.org/10.1007/s10958-014-2165-8\">https://doi.org/10.1007/s10958-014-2165-8</a>","ama":"Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H, Yakimova O. An algorithm for cartographic generalization that preserves global topology. <i>Journal of Mathematical Sciences</i>. 2014;203(6):754-760. doi:<a href=\"https://doi.org/10.1007/s10958-014-2165-8\">10.1007/s10958-014-2165-8</a>","short":"V.V. Alexeev, V.G. Bogaevskaya, M.M. Preobrazhenskaya, A.Y. Ukhalov, H. Edelsbrunner, O. Yakimova, Journal of Mathematical Sciences 203 (2014) 754–760.","mla":"Alexeev, V. V., et al. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” <i>Journal of Mathematical Sciences</i>, vol. 203, no. 6, Springer, 2014, pp. 754–60, doi:<a href=\"https://doi.org/10.1007/s10958-014-2165-8\">10.1007/s10958-014-2165-8</a>.","chicago":"Alexeev, V V, V G Bogaevskaya, M M Preobrazhenskaya, A Y Ukhalov, Herbert Edelsbrunner, and Olga Yakimova. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” <i>Journal of Mathematical Sciences</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s10958-014-2165-8\">https://doi.org/10.1007/s10958-014-2165-8</a>.","ieee":"V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H. Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that preserves global topology,” <i>Journal of Mathematical Sciences</i>, vol. 203, no. 6. Springer, pp. 754–760, 2014.","ista":"Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H, Yakimova O. 2014. An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. 203(6), 754–760."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s10958-014-2165-8","date_created":"2018-12-11T11:54:46Z","author":[{"first_name":"V V","last_name":"Alexeev","full_name":"Alexeev, V V"},{"full_name":"Bogaevskaya, V G","first_name":"V G","last_name":"Bogaevskaya"},{"first_name":"M M","last_name":"Preobrazhenskaya","full_name":"Preobrazhenskaya, M M"},{"last_name":"Ukhalov","first_name":"A Y","full_name":"Ukhalov, A Y"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"last_name":"Yakimova","first_name":"Olga","full_name":"Yakimova, Olga"}],"_id":"1929","scopus_import":"1","publication_identifier":{"issn":["1072-3374"],"eissn":["1573-8795"]},"volume":203,"article_type":"original","intvolume":"       203","acknowledgement":"We would like to offer our special thanks to students of the Department of Mathematics of Demidov Yaroslavl State University A. A. Gorokhov and V. N. Knyazev for participation in developing the program and assistance in preparation of test data. This work was supported by grant 11.G34.31.0053 from the government of the Russian Federation.","article_processing_charge":"No","publication":"Journal of Mathematical Sciences","department":[{"_id":"HeEd"}],"status":"public","date_updated":"2022-05-24T10:39:06Z","language":[{"iso":"eng"}],"issue":"6","day":"16","publist_id":"5165","publisher":"Springer","month":"11","type":"journal_article","year":"2014"},{"date_created":"2018-12-11T11:54:46Z","doi":"10.1109/TVCG.2014.2346432","author":[{"first_name":"David","last_name":"Günther","full_name":"Günther, David"},{"last_name":"Jacobson","first_name":"Alec","full_name":"Jacobson, Alec"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan"},{"full_name":"Seidel, Hans","first_name":"Hans","last_name":"Seidel"},{"first_name":"Olga","last_name":"Sorkine Hornung","full_name":"Sorkine Hornung, Olga"},{"first_name":"Tino","last_name":"Weinkauf","full_name":"Weinkauf, Tino"}],"_id":"1930","scopus_import":"1","date_published":"2014-12-31T00:00:00Z","citation":{"ista":"Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. 2014. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. 20(12), 2585–2594.","ieee":"D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, and T. Weinkauf, “Fast and memory-efficient topological denoising of 2D and 3D scalar fields,” <i>IEEE Transactions on Visualization and Computer Graphics</i>, vol. 20, no. 12. IEEE, pp. 2585–2594, 2014.","ama":"Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. <i>IEEE Transactions on Visualization and Computer Graphics</i>. 2014;20(12):2585-2594. doi:<a href=\"https://doi.org/10.1109/TVCG.2014.2346432\">10.1109/TVCG.2014.2346432</a>","chicago":"Günther, David, Alec Jacobson, Jan Reininghaus, Hans Seidel, Olga Sorkine Hornung, and Tino Weinkauf. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” <i>IEEE Transactions on Visualization and Computer Graphics</i>. IEEE, 2014. <a href=\"https://doi.org/10.1109/TVCG.2014.2346432\">https://doi.org/10.1109/TVCG.2014.2346432</a>.","short":"D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, T. Weinkauf, IEEE Transactions on Visualization and Computer Graphics 20 (2014) 2585–2594.","mla":"Günther, David, et al. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” <i>IEEE Transactions on Visualization and Computer Graphics</i>, vol. 20, no. 12, IEEE, 2014, pp. 2585–94, doi:<a href=\"https://doi.org/10.1109/TVCG.2014.2346432\">10.1109/TVCG.2014.2346432</a>.","apa":"Günther, D., Jacobson, A., Reininghaus, J., Seidel, H., Sorkine Hornung, O., &#38; Weinkauf, T. (2014). Fast and memory-efficient topological denoising of 2D and 3D scalar fields. <i>IEEE Transactions on Visualization and Computer Graphics</i>. IEEE. <a href=\"https://doi.org/10.1109/TVCG.2014.2346432\">https://doi.org/10.1109/TVCG.2014.2346432</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":"        20","acknowledgement":"RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship; MPC-VCC","volume":20,"page":"2585 - 2594","quality_controlled":"1","abstract":[{"lang":"eng","text":"(Figure Presented) Data acquisition, numerical inaccuracies, and sampling often introduce noise in measurements and simulations. Removing this noise is often necessary for efficient analysis and visualization of this data, yet many denoising techniques change the minima and maxima of a scalar field. For example, the extrema can appear or disappear, spatially move, and change their value. This can lead to wrong interpretations of the data, e.g., when the maximum temperature over an area is falsely reported being a few degrees cooler because the denoising method is unaware of these features. Recently, a topological denoising technique based on a global energy optimization was proposed, which allows the topology-controlled denoising of 2D scalar fields. While this method preserves the minima and maxima, it is constrained by the size of the data. We extend this work to large 2D data and medium-sized 3D data by introducing a novel domain decomposition approach. It allows processing small patches of the domain independently while still avoiding the introduction of new critical points. Furthermore, we propose an iterative refinement of the solution, which decreases the optimization energy compared to the previous approach and therefore gives smoother results that are closer to the input. We illustrate our technique on synthetic and real-world 2D and 3D data sets that highlight potential applications."}],"publication_status":"published","oa_version":"None","title":"Fast and memory-efficient topological denoising of 2D and 3D scalar fields","publisher":"IEEE","month":"12","issue":"12","publist_id":"5164","day":"31","type":"journal_article","year":"2014","external_id":{"isi":["000344991700104"]},"status":"public","article_processing_charge":"No","publication":"IEEE Transactions on Visualization and Computer Graphics","department":[{"_id":"HeEd"}],"isi":1,"language":[{"iso":"eng"}],"date_updated":"2025-09-29T12:11:45Z"},{"editor":[{"first_name":"Peer-Timo","last_name":"Bremer","full_name":"Bremer, Peer-Timo"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"},{"first_name":"Valerio","last_name":"Pascucci","full_name":"Pascucci, Valerio"},{"full_name":"Peikert, Ronald","last_name":"Peikert","first_name":"Ronald"}],"place":"Cham","date_updated":"2025-04-15T08:37:54Z","series_title":"Mathematics and Visualization","language":[{"iso":"eng"}],"publication":"Topological Methods in Data Analysis and Visualization III.","department":[{"_id":"HeEd"}],"article_processing_charge":"No","status":"public","year":"2014","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"type":"book_chapter","ec_funded":1,"day":"19","month":"03","publisher":"Springer Nature","title":"Notes on the simplification of the Morse-Smale complex","oa_version":"None","publication_status":"published","abstract":[{"lang":"eng","text":"The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption."}],"quality_controlled":"1","page":"135-150","publication_identifier":{"isbn":["9783319040981"],"issn":["1612-3786"],"eisbn":["9783319040998"],"eissn":["2197-666X"]},"acknowledgement":"This research is supported and funded by the Digiteo unTopoVis project, the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_published":"2014-03-19T00:00:00Z","citation":{"ieee":"D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the simplification of the Morse-Smale complex,” in <i>Topological Methods in Data Analysis and Visualization III.</i>, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150.","ista":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. 2014.Notes on the simplification of the Morse-Smale complex. In: Topological Methods in Data Analysis and Visualization III. , 135–150.","apa":"Günther, D., Reininghaus, J., Seidel, H.-P., &#38; Weinkauf, T. (2014). Notes on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III.</i> (pp. 135–150). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">https://doi.org/10.1007/978-3-319-04099-8_9</a>","mla":"Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.” <i>Topological Methods in Data Analysis and Visualization III.</i>, edited by Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">10.1007/978-3-319-04099-8_9</a>.","chicago":"Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf. “Notes on the Simplification of the Morse-Smale Complex.” In <i>Topological Methods in Data Analysis and Visualization III.</i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization. Cham: Springer Nature, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">https://doi.org/10.1007/978-3-319-04099-8_9</a>.","short":"D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III., Springer Nature, Cham, 2014, pp. 135–150.","ama":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. Notes on the simplification of the Morse-Smale complex. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. <i>Topological Methods in Data Analysis and Visualization III.</i> Mathematics and Visualization. Cham: Springer Nature; 2014:135-150. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">10.1007/978-3-319-04099-8_9</a>"},"_id":"10817","scopus_import":"1","doi":"10.1007/978-3-319-04099-8_9","date_created":"2022-03-04T08:33:57Z","author":[{"full_name":"Günther, David","last_name":"Günther","first_name":"David"},{"full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus"},{"full_name":"Seidel, Hans-Peter","last_name":"Seidel","first_name":"Hans-Peter"},{"full_name":"Weinkauf, Tino","last_name":"Weinkauf","first_name":"Tino"}]},{"abstract":[{"text":"We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply the definition of the HKS. The resulting scalar quantity is used for the visualization of tensor fields. The HKS is closely related to the Gaussian curvature of the Riemannian manifold and the time parameter of the heat kernel allows a multiscale analysis in a natural way. In this way, the HKS represents field related scale space properties, enabling a level of detail analysis of tensor fields. This makes the HKS an interesting new scalar quantity for tensor fields, which differs significantly from usual tensor invariants like the trace or the determinant. A method for visualization and a numerical realization of the HKS for tensor fields is proposed in this chapter. To validate the approach we apply it to some illustrating simple examples as isolated critical points and to a medical diffusion tensor data set.","lang":"eng"}],"language":[{"iso":"eng"}],"oa_version":"None","title":"Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature","publication_status":"published","date_updated":"2023-09-05T14:13:16Z","status":"public","page":"249-262","quality_controlled":"1","department":[{"_id":"HeEd"}],"publication":"Topological Methods in Data Analysis and Visualization III ","article_processing_charge":"No","acknowledgement":"This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.","alternative_title":["Mathematics and Visualization"],"year":"2014","publication_identifier":{"isbn":["9783319040981"],"issn":["1612-3786"],"eissn":["2197-666X"],"eisbn":["9783319040998"]},"type":"conference","scopus_import":"1","month":"03","_id":"10886","publisher":"Springer","date_created":"2022-03-18T13:05:39Z","author":[{"first_name":"Valentin","last_name":"Zobel","full_name":"Zobel, Valentin"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"}],"doi":"10.1007/978-3-319-04099-8_16","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","day":"19","citation":{"apa":"Zobel, V., Reininghaus, J., &#38; Hotz, I. (2014). Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In <i>Topological Methods in Data Analysis and Visualization III </i> (pp. 249–262). Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">https://doi.org/10.1007/978-3-319-04099-8_16</a>","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In <i>Topological Methods in Data Analysis and Visualization III </i>, 249–62. Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">https://doi.org/10.1007/978-3-319-04099-8_16</a>.","mla":"Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” <i>Topological Methods in Data Analysis and Visualization III </i>, Springer, 2014, pp. 249–62, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">10.1007/978-3-319-04099-8_16</a>.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–262.","ama":"Zobel V, Reininghaus J, Hotz I. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In: <i>Topological Methods in Data Analysis and Visualization III </i>. Springer; 2014:249-262. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">10.1007/978-3-319-04099-8_16</a>","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature,” in <i>Topological Methods in Data Analysis and Visualization III </i>, 2014, pp. 249–262.","ista":"Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. Topological Methods in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262."},"date_published":"2014-03-19T00:00:00Z"},{"date_updated":"2025-09-29T13:22:55Z","related_material":{"record":[{"relation":"later_version","id":"481","status":"public"}]},"language":[{"iso":"eng"}],"publication":"25th International Symposium, ISAAC 2014","isi":1,"department":[{"_id":"HeEd"}],"article_processing_charge":"No","status":"public","external_id":{"isi":["000354865900010"]},"year":"2014","type":"conference","day":"08","corr_author":"1","month":"11","conference":{"start_date":"2014-12-15","name":"ISAAC: International Symposium on Algorithms and Computation","end_date":"2014-12-17","location":"Jeonju, Korea"},"publisher":"Springer Nature","oa_version":"None","title":"Planar matchings for weighted straight skeletons","publication_status":"published","abstract":[{"lang":"eng","text":"In this paper, we introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist.\r\nUsing our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings."}],"quality_controlled":"1","page":"117-127","volume":8889,"publication_identifier":{"eisbn":["9783319130750"],"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["9783319130743"]},"alternative_title":["LNCS"],"intvolume":"      8889","acknowledgement":"T. Biedl was supported by NSERC and the Ross and Muriel Cheriton Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2014-11-08T00:00:00Z","citation":{"apa":"Biedl, T., Huber, S., &#38; Palfrader, P. (2014). Planar matchings for weighted straight skeletons. In <i>25th International Symposium, ISAAC 2014</i> (Vol. 8889, pp. 117–127). Jeonju, Korea: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">https://doi.org/10.1007/978-3-319-13075-0_10</a>","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. In: <i>25th International Symposium, ISAAC 2014</i>. Vol 8889. Springer Nature; 2014:117-127. doi:<a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">10.1007/978-3-319-13075-0_10</a>","chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” In <i>25th International Symposium, ISAAC 2014</i>, 8889:117–27. Springer Nature, 2014. <a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">https://doi.org/10.1007/978-3-319-13075-0_10</a>.","mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” <i>25th International Symposium, ISAAC 2014</i>, vol. 8889, Springer Nature, 2014, pp. 117–27, doi:<a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">10.1007/978-3-319-13075-0_10</a>.","short":"T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC 2014, Springer Nature, 2014, pp. 117–127.","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” in <i>25th International Symposium, ISAAC 2014</i>, Jeonju, Korea, 2014, vol. 8889, pp. 117–127.","ista":"Biedl T, Huber S, Palfrader P. 2014. Planar matchings for weighted straight skeletons. 25th International Symposium, ISAAC 2014. ISAAC: International Symposium on Algorithms and Computation, LNCS, vol. 8889, 117–127."},"_id":"10892","scopus_import":"1","date_created":"2022-03-21T07:09:03Z","doi":"10.1007/978-3-319-13075-0_10","author":[{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber"},{"last_name":"Palfrader","first_name":"Peter","full_name":"Palfrader, Peter"}]},{"publisher":"Springer","month":"03","day":"19","ec_funded":1,"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"type":"book_chapter","year":"2014","status":"public","article_processing_charge":"No","department":[{"_id":"HeEd"}],"publication":"Topological Methods in Data Analysis and Visualization III ","language":[{"iso":"eng"}],"series_title":"Mathematics and Visualization","date_updated":"2025-04-15T08:37:54Z","place":"Cham","editor":[{"last_name":"Bremer","first_name":"Peer-Timo","full_name":"Bremer, Peer-Timo"},{"full_name":"Hotz, Ingrid","last_name":"Hotz","first_name":"Ingrid"},{"first_name":"Valerio","last_name":"Pascucci","full_name":"Pascucci, Valerio"},{"first_name":"Ronald","last_name":"Peikert","full_name":"Peikert, Ronald"}],"doi":"10.1007/978-3-319-04099-8_4","date_created":"2022-03-21T07:11:23Z","author":[{"full_name":"Kasten, Jens","last_name":"Kasten","first_name":"Jens"},{"last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan"},{"full_name":"Reich, Wieland","last_name":"Reich","first_name":"Wieland"},{"first_name":"Gerik","last_name":"Scheuermann","full_name":"Scheuermann, Gerik"}],"scopus_import":"1","_id":"10893","citation":{"ista":"Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization III . vol. 1, 55–69.","ieee":"J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction of saddle periodic orbits,” in <i>Topological Methods in Data Analysis and Visualization III </i>, vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer, 2014, pp. 55–69.","short":"J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III , Springer, Cham, 2014, pp. 55–69.","mla":"Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” <i>Topological Methods in Data Analysis and Visualization III </i>, edited by Peer-Timo Bremer et al., vol. 1, Springer, 2014, pp. 55–69, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">10.1007/978-3-319-04099-8_4</a>.","chicago":"Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward the Extraction of Saddle Periodic Orbits.” In <i>Topological Methods in Data Analysis and Visualization III </i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">https://doi.org/10.1007/978-3-319-04099-8_4</a>.","ama":"Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. <i>Topological Methods in Data Analysis and Visualization III </i>. Vol 1. Mathematics and Visualization. Cham: Springer; 2014:55-69. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">10.1007/978-3-319-04099-8_4</a>","apa":"Kasten, J., Reininghaus, J., Reich, W., &#38; Scheuermann, G. (2014). Toward the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III </i> (Vol. 1, pp. 55–69). Cham: Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">https://doi.org/10.1007/978-3-319-04099-8_4</a>"},"date_published":"2014-03-19T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"First, we thank the reviewers of this paper for their ideas and critical comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions. This research is supported by the European Commission under the TOPOSYS project FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the European Science Foundation under the ACAT Research Network Program.","intvolume":"         1","publication_identifier":{"issn":["1612-3786"],"eissn":["2197-666X"],"eisbn":["9783319040998"],"isbn":["9783319040981"]},"volume":1,"page":"55-69","quality_controlled":"1","abstract":[{"lang":"eng","text":"Saddle periodic orbits are an essential and stable part of the topological skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm to robustly extract these features. In this chapter, we present a novel technique to extract saddle periodic orbits. Exploiting the analytic properties of such an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent (FTLE) that indicates its presence. Using persistent homology, we can then extract the robust cycles of this field. These cycles thereby represent the saddle periodic orbits of the given vector field. We discuss the different existing FTLE approximation schemes regarding their applicability to this specific problem and propose an adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate our method using simple analytic vector field data."}],"publication_status":"published","title":"Toward the extraction of saddle periodic orbits","oa_version":"None"},{"year":"2014","type":"conference","day":"01","month":"09","publisher":"Springer Berlin Heidelberg","conference":{"location":"Seoul, South Korea","end_date":"2014-08-09","name":"ICMS: International Congress on Mathematical Software","start_date":"2014-08-05"},"date_updated":"2025-10-01T07:39:50Z","series_title":"LNCS","place":"Berlin, Heidelberg","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"later_version","id":"1433","status":"public"}]},"department":[{"_id":"HeEd"}],"publication":"ICMS 2014: International Congress on Mathematical Software","article_processing_charge":"No","status":"public","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"eisbn":["9783662441992"],"isbn":["9783662441985"]},"volume":8592,"intvolume":"      8592","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2014. PHAT – Persistent Homology Algorithms Toolbox. ICMS 2014: International Congress on Mathematical Software. ICMS: International Congress on Mathematical SoftwareLNCS vol. 8592, 137–143.","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology Algorithms Toolbox,” in <i>ICMS 2014: International Congress on Mathematical Software</i>, Seoul, South Korea, 2014, vol. 8592, pp. 137–143.","mla":"Bauer, Ulrich, et al. “PHAT – Persistent Homology Algorithms Toolbox.” <i>ICMS 2014: International Congress on Mathematical Software</i>, vol. 8592, Springer Berlin Heidelberg, 2014, pp. 137–43, doi:<a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">10.1007/978-3-662-44199-2_24</a>.","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “PHAT – Persistent Homology Algorithms Toolbox.” In <i>ICMS 2014: International Congress on Mathematical Software</i>, 8592:137–43. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. <a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">https://doi.org/10.1007/978-3-662-44199-2_24</a>.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, in:, ICMS 2014: International Congress on Mathematical Software, Springer Berlin Heidelberg, Berlin, Heidelberg, 2014, pp. 137–143.","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms Toolbox. In: <i>ICMS 2014: International Congress on Mathematical Software</i>. Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143. doi:<a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">10.1007/978-3-662-44199-2_24</a>","apa":"Bauer, U., Kerber, M., Reininghaus, J., &#38; Wagner, H. (2014). PHAT – Persistent Homology Algorithms Toolbox. In <i>ICMS 2014: International Congress on Mathematical Software</i> (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">https://doi.org/10.1007/978-3-662-44199-2_24</a>"},"date_published":"2014-09-01T00:00:00Z","scopus_import":"1","_id":"10894","doi":"10.1007/978-3-662-44199-2_24","date_created":"2022-03-21T07:12:16Z","author":[{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","full_name":"Bauer, Ulrich","last_name":"Bauer","orcid":"0000-0002-9683-0724","first_name":"Ulrich"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert"}],"oa_version":"None","title":"PHAT – Persistent Homology Algorithms Toolbox","publication_status":"published","abstract":[{"text":"PHAT is a C++ library for the computation of persistent homology by matrix reduction. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. This makes PHAT a versatile platform for experimenting with algorithmic ideas and comparing them to state of the art implementations.","lang":"eng"}],"quality_controlled":"1","page":"137-143"},{"abstract":[{"lang":"eng","text":"We define a simple, explicit map sending a morphism f : M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f . As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence modules induces a δ-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. Copyright is held by the owner/author(s)."}],"title":"Induced matchings of barcodes and the algebraic stability of persistence","oa_version":"Submitted Version","publication_status":"published","main_file_link":[{"url":"http://arxiv.org/abs/1311.3681","open_access":"1"}],"page":"355 - 364","quality_controlled":"1","scopus_import":"1","_id":"2153","date_created":"2018-12-11T11:56:01Z","author":[{"last_name":"Bauer","orcid":"0000-0002-9683-0724","first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","full_name":"Bauer, Ulrich"},{"full_name":"Lesnick, Michael","last_name":"Lesnick","first_name":"Michael"}],"doi":"10.1145/2582112.2582168","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Bauer, U., &#38; Lesnick, M. (2014). Induced matchings of barcodes and the algebraic stability of persistence. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 355–364). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582168\">https://doi.org/10.1145/2582112.2582168</a>","ama":"Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability of persistence. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:355-364. doi:<a href=\"https://doi.org/10.1145/2582112.2582168\">10.1145/2582112.2582168</a>","chicago":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 355–64. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582168\">https://doi.org/10.1145/2582112.2582168</a>.","mla":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 355–64, doi:<a href=\"https://doi.org/10.1145/2582112.2582168\">10.1145/2582112.2582168</a>.","short":"U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–364.","ieee":"U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic stability of persistence,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 355–364.","ista":"Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic stability of persistence. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 355–364."},"arxiv":1,"oa":1,"date_published":"2014-06-01T00:00:00Z","language":[{"iso":"eng"}],"date_updated":"2025-06-11T07:57:54Z","status":"public","external_id":{"arxiv":["1311.3681"]},"department":[{"_id":"HeEd"}],"publication":"Proceedings of the Annual Symposium on Computational Geometry","article_processing_charge":"No","ec_funded":1,"year":"2014","type":"conference","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"}],"month":"06","publisher":"ACM","conference":{"end_date":"2014-06-11","name":"SoCG: Symposium on Computational Geometry","start_date":"2014-06-08","location":"Kyoto, Japan"},"day":"01","publist_id":"4853"},{"ec_funded":1,"year":"2014","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"type":"conference","corr_author":"1","month":"06","conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2014-06-08","end_date":"2014-06-11","location":"Kyoto, Japan"},"publisher":"ACM","day":"01","publist_id":"4851","language":[{"iso":"eng"}],"date_updated":"2025-06-11T07:58:27Z","status":"public","external_id":{"arxiv":["1312.1231"]},"publication":"Proceedings of the Annual Symposium on Computational Geometry","department":[{"_id":"HeEd"}],"article_processing_charge":"No","acknowledgement":"This research is partially supported by ESF under the ACAT Research Network Programme, and by the Russian Government under mega project 11.G34.31.0053","_id":"2155","scopus_import":"1","author":[{"orcid":"0000-0002-9683-0724","last_name":"Bauer","first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","full_name":"Bauer, Ulrich"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"}],"date_created":"2018-12-11T11:56:01Z","doi":"10.1145/2582112.2582167","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"date_published":"2014-06-01T00:00:00Z","arxiv":1,"citation":{"ama":"Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:484-490. doi:<a href=\"https://doi.org/10.1145/2582112.2582167\">10.1145/2582112.2582167</a>","mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 484–90, doi:<a href=\"https://doi.org/10.1145/2582112.2582167\">10.1145/2582112.2582167</a>.","chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 484–90. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582167\">https://doi.org/10.1145/2582112.2582167</a>.","short":"U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–490.","apa":"Bauer, U., &#38; Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay filtrations. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 484–490). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582167\">https://doi.org/10.1145/2582112.2582167</a>","ista":"Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 484–490.","ieee":"U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 484–490."},"abstract":[{"text":"Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s).","lang":"eng"}],"title":"The morse theory of Čech and Delaunay filtrations","oa_version":"Submitted Version","publication_status":"published","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1312.1231"}],"page":"484 - 490","quality_controlled":"1"},{"month":"06","publisher":"ACM","conference":{"location":"Kyoto, Japan","end_date":"2014-06-11","start_date":"2014-06-08","name":"SoCG: Symposium on Computational Geometry"},"day":"01","publist_id":"4850","ec_funded":1,"year":"2014","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"type":"conference","status":"public","external_id":{"arxiv":["1307.2839"]},"department":[{"_id":"HeEd"}],"publication":"Proceedings of the Annual Symposium on Computational Geometry","article_processing_charge":"No","language":[{"iso":"eng"}],"date_updated":"2025-06-11T07:58:42Z","scopus_import":"1","_id":"2156","doi":"10.1145/2582112.2582169","date_created":"2018-12-11T11:56:02Z","author":[{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","full_name":"Bauer, Ulrich","last_name":"Bauer","orcid":"0000-0002-9683-0724","first_name":"Ulrich"},{"full_name":"Ge, Xiaoyin","last_name":"Ge","first_name":"Xiaoyin"},{"full_name":"Wang, Yusu","last_name":"Wang","first_name":"Yusu"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"citation":{"ama":"Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:464-473. doi:<a href=\"https://doi.org/10.1145/2582112.2582169\">10.1145/2582112.2582169</a>","short":"U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–473.","mla":"Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 464–73, doi:<a href=\"https://doi.org/10.1145/2582112.2582169\">10.1145/2582112.2582169</a>.","chicago":"Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb Graphs.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 464–73. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582169\">https://doi.org/10.1145/2582112.2582169</a>.","apa":"Bauer, U., Ge, X., &#38; Wang, Y. (2014). Measuring distance between Reeb graphs. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 464–473). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582169\">https://doi.org/10.1145/2582112.2582169</a>","ista":"Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 464–473.","ieee":"U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 464–473."},"date_published":"2014-06-01T00:00:00Z","oa":1,"acknowledgement":"National Science Foundation under grants CCF-1319406, CCF-1116258.","main_file_link":[{"url":"http://arxiv.org/abs/1307.2839","open_access":"1"}],"page":"464 - 473","quality_controlled":"1","abstract":[{"text":"We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).","lang":"eng"}],"oa_version":"Submitted Version","title":"Measuring distance between Reeb graphs","publication_status":"published"}]