[{"oa":1,"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"type":"journal_article","date_published":"2023-01-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"date_updated":"2023-02-02T11:01:10Z","file_name":"2023_DiscreteCompGeometry_Boissonnat.pdf","content_type":"application/pdf","date_created":"2023-02-02T11:01:10Z","checksum":"46352e0ee71e460848f88685ca852681","file_size":582850,"file_id":"12488","creator":"dernst","access_level":"open_access","success":1,"relation":"main_file"}],"month":"01","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073","name":"Learning and triangulating manifolds via collapses"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Discrete & Computational Geometry","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"language":[{"iso":"eng"}],"abstract":[{"text":"We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use.","lang":"eng"}],"day":"01","doi":"10.1007/s00454-022-00431-7","external_id":{"isi":["000862193600001"]},"isi":1,"year":"2023","citation":{"ista":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete &#38; Computational Geometry. 69, 156–191.","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete &#38; Computational Geometry 69 (2023) 156–191.","mla":"Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.” <i>Discrete &#38; Computational Geometry</i>, vol. 69, Springer Nature, 2023, pp. 156–91, doi:<a href=\"https://doi.org/10.1007/s00454-022-00431-7\">10.1007/s00454-022-00431-7</a>.","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for triangulating general manifolds,” <i>Discrete &#38; Computational Geometry</i>, vol. 69. Springer Nature, pp. 156–191, 2023.","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken. “Local Criteria for Triangulating General Manifolds.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-022-00431-7\">https://doi.org/10.1007/s00454-022-00431-7</a>.","ama":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating general manifolds. <i>Discrete &#38; Computational Geometry</i>. 2023;69:156-191. doi:<a href=\"https://doi.org/10.1007/s00454-022-00431-7\">10.1007/s00454-022-00431-7</a>","apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., &#38; Wintraecken, M. (2023). Local criteria for triangulating general manifolds. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00431-7\">https://doi.org/10.1007/s00454-022-00431-7</a>"},"date_updated":"2023-08-01T12:47:32Z","ddc":["510"],"volume":69,"acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). Arijit Ghosh is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015). Part of this work was done when Arijit Ghosh was a Researcher at Max-Planck-Institute for Informatics, Germany, supported by the IndoGerman Max Planck Center for Computer Science (IMPECS). Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Austrian Science Fund (FWF): M-3073. A part of the results described in this paper were presented at SoCG 2018 and in [3]. \r\nOpen access funding provided by the Austrian Science Fund (FWF).","intvolume":"        69","title":"Local criteria for triangulating general manifolds","article_processing_charge":"No","date_created":"2023-01-16T10:04:06Z","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel","last_name":"Boissonnat"},{"full_name":"Dyer, Ramsay","first_name":"Ramsay","last_name":"Dyer"},{"last_name":"Ghosh","first_name":"Arijit","full_name":"Ghosh, Arijit"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken","first_name":"Mathijs"}],"scopus_import":"1","_id":"12287","article_type":"original","publisher":"Springer Nature","file_date_updated":"2023-02-02T11:01:10Z","quality_controlled":"1","ec_funded":1,"page":"156-191"},{"type":"journal_article","date_published":"2023-09-01T00:00:00Z","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"oa":1,"main_file_link":[{"url":"https://inserm.hal.science/INRIA-SACLAY/hal-04083524v1","open_access":"1"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Journal of Applied and Computational Topology","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"oa_version":"Submitted Version","month":"09","language":[{"iso":"eng"}],"citation":{"ista":"Boissonnat JD, Wintraecken M. 2023. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 7, 619–641.","short":"J.D. Boissonnat, M. Wintraecken, Journal of Applied and Computational Topology 7 (2023) 619–641.","mla":"Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” <i>Journal of Applied and Computational Topology</i>, vol. 7, Springer Nature, 2023, pp. 619–41, doi:<a href=\"https://doi.org/10.1007/s41468-023-00116-x\">10.1007/s41468-023-00116-x</a>.","chicago":"Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s41468-023-00116-x\">https://doi.org/10.1007/s41468-023-00116-x</a>.","ieee":"J. D. Boissonnat and M. Wintraecken, “The reach of subsets of manifolds,” <i>Journal of Applied and Computational Topology</i>, vol. 7. Springer Nature, pp. 619–641, 2023.","ama":"Boissonnat JD, Wintraecken M. The reach of subsets of manifolds. <i>Journal of Applied and Computational Topology</i>. 2023;7:619-641. doi:<a href=\"https://doi.org/10.1007/s41468-023-00116-x\">10.1007/s41468-023-00116-x</a>","apa":"Boissonnat, J. D., &#38; Wintraecken, M. (2023). The reach of subsets of manifolds. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-023-00116-x\">https://doi.org/10.1007/s41468-023-00116-x</a>"},"year":"2023","date_updated":"2023-10-04T12:07:18Z","day":"01","doi":"10.1007/s41468-023-00116-x","abstract":[{"lang":"eng","text":"Kleinjohann (Archiv der Mathematik 35(1):574–582, 1980; Mathematische Zeitschrift 176(3), 327–344, 1981) and Bangert (Archiv der Mathematik 38(1):54–57, 1982) extended the reach rch(S) from subsets S of Euclidean space to the reach rchM(S) of subsets S of Riemannian manifolds M, where M is smooth (we’ll assume at least C3). Bangert showed that sets of positive reach in Euclidean space and Riemannian manifolds are very similar. In this paper we introduce a slight variant of Kleinjohann’s and Bangert’s extension and quantify the similarity between sets of positive reach in Euclidean space and Riemannian manifolds in a new way: Given p∈M and q∈S, we bound the local feature size (a local version of the reach) of its lifting to the tangent space via the inverse exponential map (exp−1p(S)) at q, assuming that rchM(S) and the geodesic distance dM(p,q) are bounded. These bounds are motivated by the importance of the reach and local feature size to manifold learning, topological inference, and triangulating manifolds and the fact that intrinsic approaches circumvent the curse of dimensionality."}],"volume":7,"acknowledgement":"We thank Eddie Aamari, David Cohen-Steiner, Isa Costantini, Fred Chazal, Ramsay Dyer, André Lieutier, and Alef Sterk for discussion and Pierre Pansu for encouragement. We further acknowledge the anonymous reviewers whose comments helped improve the exposition.\r\nThe research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions). The first author is further supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002. The second author is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Austrian science fund (FWF) M-3073.","scopus_import":"1","_id":"12763","author":[{"full_name":"Boissonnat, Jean Daniel","first_name":"Jean Daniel","last_name":"Boissonnat"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","date_created":"2023-03-26T22:01:08Z","department":[{"_id":"HeEd"}],"publication_status":"published","intvolume":"         7","title":"The reach of subsets of manifolds","ec_funded":1,"quality_controlled":"1","page":"619-641","publisher":"Springer Nature","article_type":"original"},{"main_file_link":[{"url":"https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9441"}]},"publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"oa":1,"date_published":"2023-04-30T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"oa_version":"Submitted Version","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"month":"04","publication":"SIAM Journal on Computing","acknowledgement":"The authors have received funding from the European Research Council under the European Union's ERC grant greement 339025 GUDHI (Algorithmic Foundations of Geometric Un-derstanding  in  Higher  Dimensions).   The  first  author  was  supported  by  the  French  government,through the 3IA C\\^ote d'Azur Investments in the Future project managed by the National ResearchAgency (ANR) with the reference ANR-19-P3IA-0002.  The third author was supported by the Eu-ropean Union's Horizon 2020 research and innovation programme under the Marie Sk\\lodowska-Curiegrant agreement 754411 and the FWF (Austrian Science Fund) grant M 3073.","volume":52,"doi":"10.1137/21M1412918","day":"30","abstract":[{"text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e., submanifolds of Rd defined as the zero set of some multivariate multivalued smooth function f:Rd→Rd−n, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M=f−1(0) is to consider its piecewise linear (PL) approximation M^\r\n based on a triangulation T of the ambient space Rd. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ=1/D (and unavoidably exponential in n). Since it is known that for δ=Ω(d2.5), M^ is O(D2)-close and isotopic to M\r\n, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M^ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. ","lang":"eng"}],"date_updated":"2023-10-10T07:34:35Z","citation":{"chicago":"Boissonnat, Jean Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” <i>SIAM Journal on Computing</i>. Society for Industrial and Applied Mathematics, 2023. <a href=\"https://doi.org/10.1137/21M1412918\">https://doi.org/10.1137/21M1412918</a>.","ieee":"J. D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations,” <i>SIAM Journal on Computing</i>, vol. 52, no. 2. Society for Industrial and Applied Mathematics, pp. 452–486, 2023.","ama":"Boissonnat JD, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. <i>SIAM Journal on Computing</i>. 2023;52(2):452-486. doi:<a href=\"https://doi.org/10.1137/21M1412918\">10.1137/21M1412918</a>","apa":"Boissonnat, J. D., Kachanovich, S., &#38; Wintraecken, M. (2023). Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. <i>SIAM Journal on Computing</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21M1412918\">https://doi.org/10.1137/21M1412918</a>","ista":"Boissonnat JD, Kachanovich S, Wintraecken M. 2023. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. 52(2), 452–486.","mla":"Boissonnat, Jean Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” <i>SIAM Journal on Computing</i>, vol. 52, no. 2, Society for Industrial and Applied Mathematics, 2023, pp. 452–86, doi:<a href=\"https://doi.org/10.1137/21M1412918\">10.1137/21M1412918</a>.","short":"J.D. Boissonnat, S. Kachanovich, M. Wintraecken, SIAM Journal on Computing 52 (2023) 452–486."},"year":"2023","isi":1,"external_id":{"isi":["001013183000012"]},"publisher":"Society for Industrial and Applied Mathematics","article_type":"original","page":"452-486","quality_controlled":"1","ec_funded":1,"publication_status":"published","date_created":"2023-05-14T22:01:00Z","article_processing_charge":"No","department":[{"_id":"HeEd"}],"title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations","intvolume":"        52","_id":"12960","scopus_import":"1","author":[{"first_name":"Jean Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean Daniel"},{"first_name":"Siargey","last_name":"Kachanovich","full_name":"Kachanovich, Siargey"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"issue":"2"},{"date_published":"2023-06-02T00:00:00Z","type":"conference","publication_identifier":{"isbn":["9781450399135"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2303.04014"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Proceedings of the 55th Annual ACM Symposium on Theory of Computing","oa_version":"Preprint","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"month":"06","language":[{"iso":"eng"}],"conference":{"end_date":"2023-06-23","location":"Orlando, FL, United States","name":"STOC: Symposium on Theory of Computing","start_date":"2023-06-20"},"date_updated":"2023-05-22T08:15:19Z","year":"2023","citation":{"ama":"Lieutier A, Wintraecken M. Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. In: <i>Proceedings of the 55th Annual ACM Symposium on Theory of Computing</i>. Association for Computing Machinery; 2023:1768-1776. doi:<a href=\"https://doi.org/10.1145/3564246.3585113\">10.1145/3564246.3585113</a>","apa":"Lieutier, A., &#38; Wintraecken, M. (2023). Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. In <i>Proceedings of the 55th Annual ACM Symposium on Theory of Computing</i> (pp. 1768–1776). Orlando, FL, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3564246.3585113\">https://doi.org/10.1145/3564246.3585113</a>","chicago":"Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis.” In <i>Proceedings of the 55th Annual ACM Symposium on Theory of Computing</i>, 1768–76. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3564246.3585113\">https://doi.org/10.1145/3564246.3585113</a>.","ieee":"A. Lieutier and M. Wintraecken, “Hausdorff and Gromov-Hausdorff stable subsets of the medial axis,” in <i>Proceedings of the 55th Annual ACM Symposium on Theory of Computing</i>, Orlando, FL, United States, 2023, pp. 1768–1776.","mla":"Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis.” <i>Proceedings of the 55th Annual ACM Symposium on Theory of Computing</i>, Association for Computing Machinery, 2023, pp. 1768–76, doi:<a href=\"https://doi.org/10.1145/3564246.3585113\">10.1145/3564246.3585113</a>.","short":"A. Lieutier, M. Wintraecken, in:, Proceedings of the 55th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–1776.","ista":"Lieutier A, Wintraecken M. 2023. Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. Proceedings of the 55th Annual ACM Symposium on Theory of Computing. STOC: Symposium on Theory of Computing, 1768–1776."},"external_id":{"arxiv":["2303.04014"]},"arxiv":1,"doi":"10.1145/3564246.3585113","day":"02","abstract":[{"lang":"eng","text":"In this paper we introduce a pruning of the medial axis called the (λ,α)-medial axis (axλα). We prove that the (λ,α)-medial axis of a set K is stable in a Gromov-Hausdorff sense under weak assumptions. More formally we prove that if K and K′ are close in the Hausdorff (dH) sense then the (λ,α)-medial axes of K and K′ are close as metric spaces, that is the Gromov-Hausdorff distance (dGH) between the two is 1/4-Hölder in the sense that dGH (axλα(K),axλα(K′)) ≲ dH(K,K′)1/4. The Hausdorff distance between the two medial axes is also bounded, by dH (axλα(K),λα(K′)) ≲ dH(K,K′)1/2. These quantified stability results provide guarantees for practical computations of medial axes from approximations. Moreover, they provide key ingredients for studying the computability of the medial axis in the context of computable analysis."}],"acknowledgement":"We are greatly indebted to Erin Chambers for posing a number of questions that eventually led to this paper. We would also like to thank the other organizers of the workshop on ‘Algorithms\r\nfor the medial axis’. We are also indebted to Tatiana Ezubova for helping with the search for and translation of Russian literature. The second author thanks all members of the Edelsbrunner and Datashape groups for the atmosphere in which the research was conducted.\r\nThe research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions). Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411. The Austrian science fund (FWF) M-3073.","_id":"13048","author":[{"full_name":"Lieutier, André","first_name":"André","last_name":"Lieutier"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","article_processing_charge":"No","department":[{"_id":"HeEd"}],"date_created":"2023-05-22T08:02:02Z","title":"Hausdorff and Gromov-Hausdorff stable subsets of the medial axis","page":"1768-1776","quality_controlled":"1","ec_funded":1,"publisher":"Association for Computing Machinery"},{"volume":224,"acknowledgement":"Partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics” and the European Research Council (ERC), grant no. 788183, “Alpha Shape Theory Extended”. Erin Chambers: Supported in part by the National Science Foundation through grants DBI-1759807, CCF-1907612, and CCF-2106672. Mathijs Wintraecken: Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411. The Austrian science fund (FWF) M-3073 Acknowledgements We thank André Lieutier, David Letscher, Ellen Gasparovic, Kathryn Leonard, and Tao Ju for early discussions on this work. We also thank Lu Liu, Yajie Yan and Tao Ju for sharing code to generate the examples.","ddc":["510"],"date_updated":"2023-02-21T09:50:52Z","citation":{"short":"E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc, M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9.","mla":"Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” <i>38th International Symposium on Computational Geometry</i>, edited by Xavier Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">10.4230/LIPIcs.SoCG.2022.66</a>.","ista":"Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. 2022. A cautionary tale: Burning the medial axis is unstable. 38th International Symposium on Computational Geometry. SoCG: Symposium on Computational GeometryLIPIcs vol. 224, 66:1-66:9.","apa":"Chambers, E., Fillmore, C. D., Stephenson, E. R., &#38; Wintraecken, M. (2022). A cautionary tale: Burning the medial axis is unstable. In X. Goaoc &#38; M. Kerber (Eds.), <i>38th International Symposium on Computational Geometry</i> (Vol. 224, p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">https://doi.org/10.4230/LIPIcs.SoCG.2022.66</a>","ama":"Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale: Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. <i>38th International Symposium on Computational Geometry</i>. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022:66:1-66:9. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">10.4230/LIPIcs.SoCG.2022.66</a>","ieee":"E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary tale: Burning the medial axis is unstable,” in <i>38th International Symposium on Computational Geometry</i>, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.","chicago":"Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In <i>38th International Symposium on Computational Geometry</i>, edited by Xavier Goaoc and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">https://doi.org/10.4230/LIPIcs.SoCG.2022.66</a>."},"year":"2022","doi":"10.4230/LIPIcs.SoCG.2022.66","day":"01","abstract":[{"lang":"eng","text":"The medial axis of a set consists of the points in the ambient space without a unique closest point on the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a topologically equivalent skeleton. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities various prunings of the medial axis have been proposed. Here, we examine one type of pruning, called burning. Because of the good experimental results, it was hoped that the burning method of simplifying the medial axis would be stable. In this work we show a simple example that dashes such hopes based on Bing’s house with two rooms, demonstrating an isotopy of a shape where the medial axis goes from collapsible to non-collapsible."}],"page":"66:1-66:9","ec_funded":1,"series_title":"LIPIcs","quality_controlled":"1","file_date_updated":"2022-06-07T07:58:30Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","editor":[{"last_name":"Goaoc","first_name":"Xavier","full_name":"Goaoc, Xavier"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber"}],"_id":"11428","scopus_import":"1","author":[{"first_name":"Erin","last_name":"Chambers","full_name":"Chambers, Erin"},{"first_name":"Christopher D","last_name":"Fillmore","full_name":"Fillmore, Christopher D","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425"},{"full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X","last_name":"Stephenson","first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","article_processing_charge":"No","date_created":"2022-06-01T14:18:04Z","department":[{"_id":"HeEd"}],"title":"A cautionary tale: Burning the medial axis is unstable","intvolume":"       224","file":[{"content_type":"application/pdf","file_name":"2022_LIPICs_Chambers.pdf","date_updated":"2022-06-07T07:58:30Z","checksum":"b25ce40fade4ebc0bcaae176db4f5f1f","file_size":17580705,"date_created":"2022-06-07T07:58:30Z","creator":"dernst","file_id":"11437","access_level":"open_access","success":1,"relation":"main_file"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2022-06-01T00:00:00Z","type":"conference","publication_identifier":{"isbn":["978-3-95977-227-3"],"issn":["1868-8969"]},"oa":1,"language":[{"iso":"eng"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","start_date":"2022-06-07","end_date":"2022-06-10","location":"Berlin, Germany"},"publication":"38th International Symposium on Computational Geometry","has_accepted_license":"1","oa_version":"Published Version","project":[{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses","grant_number":"M03073"},{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"month":"06"}]