[{"isi":1,"department":[{"_id":"HeEd"}],"publist_id":"5885","intvolume":"       144","page":"4501 - 4513","arxiv":1,"date_published":"2016-10-01T00:00:00Z","type":"journal_article","year":"2016","issue":"10","language":[{"iso":"eng"}],"publication":"Proceedings of the American Mathematical Society","title":"Elementary approach to closed billiard trajectories in asymmetric normed spaces","date_created":"2018-12-11T11:51:34Z","scopus_import":"1","quality_controlled":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2016. <a href=\"https://doi.org/10.1090/proc/13062\">https://doi.org/10.1090/proc/13062</a>.","apa":"Akopyan, A., Balitskiy, A., Karasev, R., &#38; Sharipova, A. (2016). Elementary approach to closed billiard trajectories in asymmetric normed spaces. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/13062\">https://doi.org/10.1090/proc/13062</a>","ieee":"A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016.","mla":"Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:<a href=\"https://doi.org/10.1090/proc/13062\">10.1090/proc/13062</a>.","ama":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces. <i>Proceedings of the American Mathematical Society</i>. 2016;144(10):4501-4513. doi:<a href=\"https://doi.org/10.1090/proc/13062\">10.1090/proc/13062</a>","short":"A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513.","ista":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 144(10), 4501–4513."},"status":"public","volume":144,"oa":1,"oa_version":"Preprint","date_updated":"2025-09-22T07:44:59Z","month":"10","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1401.0442"}],"acknowledgement":"The first and third authors were supported by the Dynasty Foundation. The first, second and third authors were supported by the Russian Foundation for Basic Re- search grant 15-31-20403 (mol a ved).","ec_funded":1,"external_id":{"isi":["000383054200034"],"arxiv":["1401.0442"]},"_id":"1360","author":[{"last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Balitskiy","first_name":"Alexey","full_name":"Balitskiy, Alexey"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"},{"last_name":"Sharipova","full_name":"Sharipova, Anastasia","first_name":"Anastasia"}],"publication_status":"published","publisher":"American Mathematical Society","project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"day":"01","doi":"10.1090/proc/13062","article_processing_charge":"No","abstract":[{"text":"We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results. ","lang":"eng"}]},{"isi":1,"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"license":"https://creativecommons.org/licenses/by/4.0/","intvolume":"        56","publist_id":"5799","date_published":"2016-07-01T00:00:00Z","page":"126 - 164","year":"2016","type":"journal_article","issue":"1","publication":"Discrete & Computational Geometry","corr_author":"1","title":"On computability and triviality of well groups","file":[{"date_created":"2018-12-12T10:10:55Z","date_updated":"2020-07-14T12:44:53Z","content_type":"application/pdf","relation":"main_file","file_size":905303,"file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","checksum":"e0da023abf6b72abd8c6a8c76740d53c","creator":"system","file_id":"4846","access_level":"open_access"}],"language":[{"iso":"eng"}],"quality_controlled":"1","scopus_import":"1","related_material":{"record":[{"id":"1510","status":"public","relation":"earlier_version"}]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_created":"2018-12-11T11:51:51Z","status":"public","volume":56,"citation":{"chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00454-016-9794-2\">https://doi.org/10.1007/s00454-016-9794-2</a>.","apa":"Franek, P., &#38; Krcál, M. (2016). On computability and triviality of well groups. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-016-9794-2\">https://doi.org/10.1007/s00454-016-9794-2</a>","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” <i>Discrete &#38; Computational Geometry</i>, vol. 56, no. 1. Springer, pp. 126–164, 2016.","mla":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” <i>Discrete &#38; Computational Geometry</i>, vol. 56, no. 1, Springer, 2016, pp. 126–64, doi:<a href=\"https://doi.org/10.1007/s00454-016-9794-2\">10.1007/s00454-016-9794-2</a>.","ama":"Franek P, Krcál M. On computability and triviality of well groups. <i>Discrete &#38; Computational Geometry</i>. 2016;56(1):126-164. doi:<a href=\"https://doi.org/10.1007/s00454-016-9794-2\">10.1007/s00454-016-9794-2</a>","short":"P. Franek, M. Krcál, Discrete &#38; Computational Geometry 56 (2016) 126–164.","ista":"Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete &#38; Computational Geometry. 56(1), 126–164."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"pubrep_id":"614","oa_version":"Published Version","file_date_updated":"2020-07-14T12:44:53Z","month":"07","has_accepted_license":"1","date_updated":"2025-09-18T14:30:52Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","ddc":["510"],"ec_funded":1,"project":[{"call_identifier":"FWF","grant_number":"M01980","name":"Robust Invariants of Nonlinear Systems","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"day":"01","_id":"1408","publication_status":"published","external_id":{"isi":["000377722100005"]},"publisher":"Springer","author":[{"first_name":"Peter","full_name":"Franek, Peter","orcid":"0000-0001-8878-8397","id":"473294AE-F248-11E8-B48F-1D18A9856A87","last_name":"Franek"},{"full_name":"Krcál, Marek","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál"}],"doi":"10.1007/s00454-016-9794-2","abstract":[{"text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map (Formula presented.) on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within (Formula presented.) distance r from f for a given (Formula presented.). The main drawback of the approach is that the computability of well groups was shown only when (Formula presented.) or (Formula presented.). Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of (Formula presented.) by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and (Formula presented.), our approximation of the (Formula presented.)th well group is exact. For the second part, we find examples of maps (Formula presented.) with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status.","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)"},{"day":"01","_id":"1617","author":[{"first_name":"Florian","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Stefan","full_name":"Steinerberger, Stefan","last_name":"Steinerberger"}],"publication_status":"published","publisher":"Academic Press","external_id":{"isi":["000370090400011"],"arxiv":["1510.00251"]},"abstract":[{"text":"We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of equal measure and placing a random point inside each of the N=md cubes. We prove that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d, where the upper bound with an unspecified constant Cd was proven earlier by Beck. Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality and a suitably taylored Bernstein inequality; we have reasons to believe that the upper bound has the sharp scaling in N. Additional heuristics suggest that jittered sampling should be able to improve known bounds on the inverse of the star-discrepancy in the regime N≳dd. We also prove a partition principle showing that every partition of [0,1]d combined with a jittered sampling construction gives rise to a set whose expected squared L2-discrepancy is smaller than that of purely random points.","lang":"eng"}],"article_processing_charge":"No","doi":"10.1016/j.jco.2015.11.003","month":"04","date_updated":"2025-09-18T10:57:52Z","acknowledgement":"We are grateful to the referee whose suggestions greatly improved the quality and clarity of the exposition.","main_file_link":[{"url":"http://arxiv.org/abs/1510.00251","open_access":"1"}],"oa":1,"oa_version":"Submitted Version","scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:53:03Z","volume":33,"status":"public","citation":{"ama":"Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. <i>Journal of Complexity</i>. 2016;33:199-216. doi:<a href=\"https://doi.org/10.1016/j.jco.2015.11.003\">10.1016/j.jco.2015.11.003</a>","mla":"Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” <i>Journal of Complexity</i>, vol. 33, Academic Press, 2016, pp. 199–216, doi:<a href=\"https://doi.org/10.1016/j.jco.2015.11.003\">10.1016/j.jco.2015.11.003</a>.","ista":"Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling. Journal of Complexity. 33, 199–216.","short":"F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.","chicago":"Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” <i>Journal of Complexity</i>. Academic Press, 2016. <a href=\"https://doi.org/10.1016/j.jco.2015.11.003\">https://doi.org/10.1016/j.jco.2015.11.003</a>.","ieee":"F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,” <i>Journal of Complexity</i>, vol. 33. Academic Press, pp. 199–216, 2016.","apa":"Pausinger, F., &#38; Steinerberger, S. (2016). On the discrepancy of jittered sampling. <i>Journal of Complexity</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jco.2015.11.003\">https://doi.org/10.1016/j.jco.2015.11.003</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","year":"2016","title":"On the discrepancy of jittered sampling","publication":"Journal of Complexity","language":[{"iso":"eng"}],"intvolume":"        33","publist_id":"5549","date_published":"2016-04-01T00:00:00Z","page":"199 - 216","arxiv":1,"department":[{"_id":"HeEd"}],"isi":1},{"doi":"10.1016/j.aim.2015.10.004","abstract":[{"text":"We introduce a modification of the classic notion of intrinsic volume using persistence moments of height functions. Evaluating the modified first intrinsic volume on digital approximations of a compact body with smoothly embedded boundary in Rn, we prove convergence to the first intrinsic volume of the body as the resolution of the approximation improves. We have weaker results for the other modified intrinsic volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional unit ball.","lang":"eng"}],"article_processing_charge":"No","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7"}],"day":"10","_id":"1662","author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger"}],"external_id":{"isi":["000375634100016"]},"publisher":"Academic Press","publication_status":"published","ec_funded":1,"ddc":["004"],"acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne Marie Svane for her comments on an early version of this paper. The second author wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for enlightening discussions and their kind hospitality during a visit of their department in 2014.","month":"01","has_accepted_license":"1","date_updated":"2026-04-09T14:26:05Z","pubrep_id":"774","oa_version":"Published Version","file_date_updated":"2020-07-14T12:45:10Z","oa":1,"status":"public","volume":287,"citation":{"chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” <i>Advances in Mathematics</i>. Academic Press, 2016. <a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">https://doi.org/10.1016/j.aim.2015.10.004</a>.","ieee":"H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” <i>Advances in Mathematics</i>, vol. 287. Academic Press, pp. 674–703, 2016.","apa":"Edelsbrunner, H., &#38; Pausinger, F. (2016). Approximation and convergence of the intrinsic volume. <i>Advances in Mathematics</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">https://doi.org/10.1016/j.aim.2015.10.004</a>","ama":"Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic volume. <i>Advances in Mathematics</i>. 2016;287:674-703. doi:<a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">10.1016/j.aim.2015.10.004</a>","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” <i>Advances in Mathematics</i>, vol. 287, Academic Press, 2016, pp. 674–703, doi:<a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">10.1016/j.aim.2015.10.004</a>.","short":"H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.","ista":"Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","quality_controlled":"1","scopus_import":"1","related_material":{"record":[{"relation":"dissertation_contains","id":"1399","status":"public"}]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"date_created":"2018-12-11T11:53:20Z","publication":"Advances in Mathematics","corr_author":"1","title":"Approximation and convergence of the intrinsic volume","file":[{"access_level":"open_access","file_id":"4928","creator":"system","checksum":"f8869ec110c35c852ef6a37425374af7","file_name":"IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf","file_size":248985,"relation":"main_file","content_type":"application/pdf","date_updated":"2020-07-14T12:45:10Z","date_created":"2018-12-12T10:12:10Z"}],"language":[{"iso":"eng"}],"year":"2016","type":"journal_article","date_published":"2016-01-10T00:00:00Z","page":"674 - 703","intvolume":"       287","publist_id":"5488","isi":1,"department":[{"_id":"HeEd"}],"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/"},{"month":"06","date_updated":"2022-01-28T08:01:22Z","oa_version":"None","doi":"10.1007/978-3-319-39441-1_23","abstract":[{"lang":"eng","text":"Discretization of sphere in the integer space follows a particular discretization scheme, which, in principle, conforms to some topological model. This eventually gives rise to interesting topological properties of a discrete spherical surface, which need to be investigated for its analytical characterization. This paper presents some novel results on the local topological properties of the naive model of discrete sphere. They follow from the bijection of each quadraginta octant of naive sphere with its projection map called f -map on the corresponding functional plane and from the characterization of certain jumps in the f-map. As an application, we have shown how these properties can be used in designing an efficient reconstruction algorithm for a naive spherical surface from an input voxel set when it is sparse or noisy."}],"article_processing_charge":"No","place":"Cham","day":"02","conference":{"end_date":"2016-06-17","location":"Marseille, France","start_date":"2016-06-15","name":"CTIC: Computational Topology in Image Context"},"publication_status":"published","_id":"5805","publisher":"Springer Nature","author":[{"full_name":"Sen, Nabhasmita","first_name":"Nabhasmita","last_name":"Sen"},{"last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","first_name":"Ranita"},{"full_name":"Bhowmick, Partha","first_name":"Partha","last_name":"Bhowmick"}],"extern":"1","alternative_title":["LNCS"],"date_published":"2016-06-02T00:00:00Z","page":"253-264","intvolume":"      9667","publication_identifier":{"isbn":["978-3-319-39440-4"],"issn":["0302-9743"],"eissn":["1611-3349"],"eisbn":["978-3-319-39441-1"]},"department":[{"_id":"HeEd"}],"status":"public","volume":9667,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"ista":"Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol. 9667, 253–264.","short":"N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context, Springer Nature, Cham, 2016, pp. 253–264.","ama":"Sen N, Biswas R, Bhowmick P. On some local topological properties of naive discrete sphere. In: <i>Computational Topology in Image Context</i>. Vol 9667. Cham: Springer Nature; 2016:253-264. doi:<a href=\"https://doi.org/10.1007/978-3-319-39441-1_23\">10.1007/978-3-319-39441-1_23</a>","mla":"Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete Sphere.” <i>Computational Topology in Image Context</i>, vol. 9667, Springer Nature, 2016, pp. 253–64, doi:<a href=\"https://doi.org/10.1007/978-3-319-39441-1_23\">10.1007/978-3-319-39441-1_23</a>.","ieee":"N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties of naive discrete sphere,” in <i>Computational Topology in Image Context</i>, vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.","apa":"Sen, N., Biswas, R., &#38; Bhowmick, P. (2016). On some local topological properties of naive discrete sphere. In <i>Computational Topology in Image Context</i> (Vol. 9667, pp. 253–264). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-39441-1_23\">https://doi.org/10.1007/978-3-319-39441-1_23</a>","chicago":"Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological Properties of Naive Discrete Sphere.” In <i>Computational Topology in Image Context</i>, 9667:253–64. Cham: Springer Nature, 2016. <a href=\"https://doi.org/10.1007/978-3-319-39441-1_23\">https://doi.org/10.1007/978-3-319-39441-1_23</a>."},"quality_controlled":"1","date_created":"2019-01-08T20:44:24Z","publication":"Computational Topology in Image Context","title":"On some local topological properties of naive discrete sphere","language":[{"iso":"eng"}],"type":"book_chapter","year":"2016"},{"oa_version":"None","date_updated":"2022-01-28T08:10:11Z","month":"04","place":"Cham","doi":"10.1007/978-3-319-32360-2_20","abstract":[{"text":"Although the concept of functional plane for naive plane is studied and reported in the literature in great detail, no similar study is yet found for naive sphere. This article exposes the first study in this line, opening up further prospects of analyzing the topological properties of sphere in the discrete space. We show that each quadraginta octant Q of a naive sphere forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as the functional plane of Q, and hence gives rise to merely mono-jumps during back projection. The other two coordinate planes serve as para-functional and dia-functional planes for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds neither of the two. Owing to this, the quadraginta octants form symmetry groups and subgroups with equivalent jump conditions. We also show a potential application in generating a special class of discrete 3D circles based on back projection and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry, uniqueness, and bounded distance from the underlying real sphere and real plane.","lang":"eng"}],"article_processing_charge":"No","publication_status":"published","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890"},{"last_name":"Bhowmick","first_name":"Partha","full_name":"Bhowmick, Partha"}],"publisher":"Springer Nature","_id":"5806","extern":"1","conference":{"name":"DGCI: International Conference on Discrete Geometry for Computer Imagery","start_date":"2016-04-18","location":"Nantes, France","end_date":"2016-04-20"},"day":"09","department":[{"_id":"HeEd"}],"publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["978-3-319-32359-6"],"eisbn":["978-3-319-32360-2"]},"page":"256-267","alternative_title":["LNCS"],"date_published":"2016-04-09T00:00:00Z","intvolume":"      9647","language":[{"iso":"eng"}],"publication":"Discrete Geometry for Computer Imagery","title":"On functionality of quadraginta octants of naive sphere with application to circle drawing","type":"conference","year":"2016","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"apa":"Biswas, R., &#38; Bhowmick, P. (2016). On functionality of quadraginta octants of naive sphere with application to circle drawing. In <i>Discrete Geometry for Computer Imagery</i> (Vol. 9647, pp. 256–267). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-32360-2_20\">https://doi.org/10.1007/978-3-319-32360-2_20</a>","ieee":"R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive sphere with application to circle drawing,” in <i>Discrete Geometry for Computer Imagery</i>, Nantes, France, 2016, vol. 9647, pp. 256–267.","chicago":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” In <i>Discrete Geometry for Computer Imagery</i>, 9647:256–67. Cham: Springer Nature, 2016. <a href=\"https://doi.org/10.1007/978-3-319-32360-2_20\">https://doi.org/10.1007/978-3-319-32360-2_20</a>.","ista":"Biswas R, Bhowmick P. 2016. On functionality of quadraginta octants of naive sphere with application to circle drawing. Discrete Geometry for Computer Imagery. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 9647, 256–267.","short":"R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer Nature, Cham, 2016, pp. 256–267.","mla":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” <i>Discrete Geometry for Computer Imagery</i>, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:<a href=\"https://doi.org/10.1007/978-3-319-32360-2_20\">10.1007/978-3-319-32360-2_20</a>.","ama":"Biswas R, Bhowmick P. On functionality of quadraginta octants of naive sphere with application to circle drawing. In: <i>Discrete Geometry for Computer Imagery</i>. Vol 9647. Cham: Springer Nature; 2016:256-267. doi:<a href=\"https://doi.org/10.1007/978-3-319-32360-2_20\">10.1007/978-3-319-32360-2_20</a>"},"status":"public","volume":9647,"date_created":"2019-01-08T20:44:37Z","quality_controlled":"1"},{"department":[{"_id":"HeEd"}],"publication_identifier":{"eisbn":["978-3-319-26145-4"],"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["978-3-319-26144-7"]},"oa_version":"None","date_updated":"2022-01-28T08:13:03Z","month":"01","intvolume":"      9448","page":"86-100","date_published":"2016-01-06T00:00:00Z","type":"book_chapter","year":"2016","language":[{"iso":"eng"}],"publication":"Combinatorial image analysis","title":"On the connectivity and smoothness of discrete spherical circles","_id":"5809","date_created":"2019-01-08T20:45:19Z","author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas"},{"full_name":"Bhowmick, Partha","first_name":"Partha","last_name":"Bhowmick"},{"last_name":"Brimkov","first_name":"Valentin E.","full_name":"Brimkov, Valentin E."}],"publisher":"Springer Nature","publication_status":"published","extern":"1","quality_controlled":"1","day":"06","conference":{"end_date":"2015-11-27","name":"IWCIA: International Workshop on Combinatorial Image Analysis","location":"Kolkata, India","start_date":"2015-11-24"},"citation":{"mla":"Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical Circles.” <i>Combinatorial Image Analysis</i>, vol. 9448, Springer Nature, 2016, pp. 86–100, doi:<a href=\"https://doi.org/10.1007/978-3-319-26145-4_7\">10.1007/978-3-319-26145-4_7</a>.","ama":"Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete spherical circles. In: <i>Combinatorial Image Analysis</i>. Vol 9448. Cham: Springer Nature; 2016:86-100. doi:<a href=\"https://doi.org/10.1007/978-3-319-26145-4_7\">10.1007/978-3-319-26145-4_7</a>","ista":"Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.","short":"R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2016, pp. 86–100.","chicago":"Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity and Smoothness of Discrete Spherical Circles.” In <i>Combinatorial Image Analysis</i>, 9448:86–100. Cham: Springer Nature, 2016. <a href=\"https://doi.org/10.1007/978-3-319-26145-4_7\">https://doi.org/10.1007/978-3-319-26145-4_7</a>.","apa":"Biswas, R., Bhowmick, P., &#38; Brimkov, V. E. (2016). On the connectivity and smoothness of discrete spherical circles. In <i>Combinatorial image analysis</i> (Vol. 9448, pp. 86–100). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-26145-4_7\">https://doi.org/10.1007/978-3-319-26145-4_7</a>","ieee":"R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness of discrete spherical circles,” in <i>Combinatorial image analysis</i>, vol. 9448, Cham: Springer Nature, 2016, pp. 86–100."},"place":"Cham","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","doi":"10.1007/978-3-319-26145-4_7","status":"public","abstract":[{"text":"A discrete spherical circle is a topologically well-connected 3D circle in the integer space, which belongs to a discrete sphere as well as a discrete plane. It is one of the most important 3D geometric primitives, but has not possibly yet been studied up to its merit. This paper is a maiden exposition of some of its elementary properties, which indicates a sense of its profound theoretical prospects in the framework of digital geometry. We have shown how different types of discretization can lead to forbidden and admissible classes, when one attempts to define the discretization of a spherical circle in terms of intersection between a discrete sphere and a discrete plane. Several fundamental theoretical results have been presented, the algorithm for construction of discrete spherical circles has been discussed, and some test results have been furnished to demonstrate its practicality and usefulness.","lang":"eng"}],"volume":9448,"article_processing_charge":"No"},{"alternative_title":["ISTA Thesis"],"date_published":"2015-06-01T00:00:00Z","page":"144","month":"06","publist_id":"5808","date_updated":"2026-04-16T10:09:04Z","OA_place":"publisher","oa_version":"None","supervisor":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"}],"publication_identifier":{"issn":["2663-337X"]},"department":[{"_id":"HeEd"}],"status":"public","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."}],"article_processing_charge":"No","citation":{"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.","short":"F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science and Technology Austria, 2015.","ista":"Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","chicago":"Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015.","apa":"Pausinger, F. (2015). <i>On the approximation of intrinsic volumes</i>. Institute of Science and Technology Austria.","ieee":"F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015."},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","related_material":{"record":[{"id":"1662","status":"public","relation":"part_of_dissertation"},{"id":"1792","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"2255","relation":"part_of_dissertation"}]},"day":"01","degree_awarded":"PhD","_id":"1399","publisher":"Institute of Science and Technology Austria","author":[{"full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger"}],"publication_status":"published","date_created":"2018-12-11T11:51:48Z","corr_author":"1","title":"On the approximation of intrinsic volumes","language":[{"iso":"eng"}],"type":"dissertation","year":"2015"},{"oa_version":"Submitted Version","oa":1,"department":[{"_id":"HeEd"}],"main_file_link":[{"url":"https://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective","open_access":"1"}],"page":"3070 - 3078","alternative_title":["Advances in Neural Information Processing Systems"],"date_published":"2015-12-01T00:00:00Z","acknowledgement":"This work was partially supported by the Austrian Science FUnd, project no. KLI 00012.","publist_id":"5782","date_updated":"2025-06-03T11:41:36Z","month":"12","intvolume":"        28","language":[{"iso":"eng"}],"title":"Statistical topological data analysis-A kernel perspective","type":"conference","year":"2015","citation":{"chicago":"Kwitt, Roland, Stefan Huber, Marc Niethammer, Weili Lin, and Ulrich Bauer. “Statistical Topological Data Analysis-A Kernel Perspective,” 28:3070–78. Neural Information Processing Systems Foundation, 2015.","apa":"Kwitt, R., Huber, S., Niethammer, M., Lin, W., &#38; Bauer, U. (2015). Statistical topological data analysis-A kernel perspective (Vol. 28, pp. 3070–3078). Presented at the NIPS: Neural Information Processing Systems, Montreal, Canada: Neural Information Processing Systems Foundation.","ieee":"R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, “Statistical topological data analysis-A kernel perspective,” presented at the NIPS: Neural Information Processing Systems, Montreal, Canada, 2015, vol. 28, pp. 3070–3078.","mla":"Kwitt, Roland, et al. <i>Statistical Topological Data Analysis-A Kernel Perspective</i>. Vol. 28, Neural Information Processing Systems Foundation, 2015, pp. 3070–78.","ama":"Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. Statistical topological data analysis-A kernel perspective. In: Vol 28. Neural Information Processing Systems Foundation; 2015:3070-3078.","short":"R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information Processing Systems Foundation, 2015, pp. 3070–3078.","ista":"Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. 2015. Statistical topological data analysis-A kernel perspective. NIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 28, 3070–3078."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","volume":28,"article_processing_charge":"No","abstract":[{"lang":"eng","text":"We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel enabling a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in twosample hypothesis testing on synthetic as well as real-world data."}],"_id":"1424","date_created":"2018-12-11T11:51:56Z","publisher":"Neural Information Processing Systems Foundation","publication_status":"published","author":[{"last_name":"Kwitt","first_name":"Roland","full_name":"Kwitt, Roland"},{"last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","first_name":"Stefan"},{"full_name":"Niethammer, Marc","first_name":"Marc","last_name":"Niethammer"},{"first_name":"Weili","full_name":"Lin, Weili","last_name":"Lin"},{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","first_name":"Ulrich"}],"quality_controlled":"1","conference":{"location":"Montreal, Canada","start_date":"2015-12-07","name":"NIPS: Neural Information Processing Systems","end_date":"2015-12-12"},"day":"01"},{"title":"A stable multi-scale kernel for topological machine learning","language":[{"iso":"eng"}],"year":"2015","type":"conference","abstract":[{"lang":"eng","text":"Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes."}],"article_processing_charge":"No","status":"public","doi":"10.1109/CVPR.2015.7299106","citation":{"short":"J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748.","ista":"Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel for topological machine learning. CVPR: Computer Vision and Pattern Recognition, 4741–4748.","ama":"Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for topological machine learning. In: IEEE; 2015:4741-4748. doi:<a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">10.1109/CVPR.2015.7299106</a>","mla":"Reininghaus, Jan, et al. <i>A Stable Multi-Scale Kernel for Topological Machine Learning</i>. IEEE, 2015, pp. 4741–48, doi:<a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">10.1109/CVPR.2015.7299106</a>.","ieee":"J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel for topological machine learning,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.","apa":"Reininghaus, J., Huber, S., Bauer, U., &#38; Kwitt, R. (2015). A stable multi-scale kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. <a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">https://doi.org/10.1109/CVPR.2015.7299106</a>","chicago":"Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. <a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">https://doi.org/10.1109/CVPR.2015.7299106</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"name":"CVPR: Computer Vision and Pattern Recognition","start_date":"2015-06-07","location":"Boston, MA, USA","end_date":"2015-06-12"},"day":"14","scopus_import":"1","date_created":"2018-12-11T11:52:17Z","_id":"1483","publication_status":"published","publisher":"IEEE","author":[{"first_name":"Jan","full_name":"Reininghaus, Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","first_name":"Stefan"},{"last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","first_name":"Ulrich"},{"last_name":"Kwitt","first_name":"Roland","full_name":"Kwitt, Roland"}],"external_id":{"arxiv":["1412.6821"]},"oa_version":"Preprint","department":[{"_id":"HeEd"}],"oa":1,"publication_identifier":{"eisbn":["978-1-4673-6964-0 "]},"date_published":"2015-10-14T00:00:00Z","arxiv":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1412.6821"}],"page":"4741 - 4748","month":"10","date_updated":"2025-06-11T06:37:43Z","publist_id":"5709"},{"page":"128-135","arxiv":1,"date_published":"2015-08-01T00:00:00Z","publist_id":"5684","department":[{"_id":"HeEd"}],"citation":{"ama":"Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>. Vol 2015-August. Queen’s University; 2015:128-135.","mla":"Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>, vol. 2015–August, Queen’s University, 2015, pp. 128–35.","ista":"Edelsbrunner H, Iglesias Ham M, Kurlin V. 2015. Relaxed disk packing. Proceedings of the 27th Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry vol. 2015–August, 128–135.","short":"H. Edelsbrunner, M. Iglesias Ham, V. Kurlin, in:, Proceedings of the 27th Canadian Conference on Computational Geometry, Queen’s University, 2015, pp. 128–135.","chicago":"Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed Disk Packing.” In <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>, 2015–August:128–35. Queen’s University, 2015.","ieee":"H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>, Ontario, Canada, 2015, vol. 2015–August, pp. 128–135.","apa":"Edelsbrunner, H., Iglesias Ham, M., &#38; Kurlin, V. (2015). Relaxed disk packing. In <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i> (Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","volume":"2015-August","date_created":"2018-12-11T11:52:21Z","scopus_import":"1","quality_controlled":"1","language":[{"iso":"eng"}],"publication":"Proceedings of the 27th Canadian Conference on Computational Geometry","title":"Relaxed disk packing","year":"2015","type":"conference","main_file_link":[{"url":"https://arxiv.org/abs/1505.03402","open_access":"1"}],"date_updated":"2025-06-11T06:38:01Z","month":"08","oa_version":"Submitted Version","oa":1,"article_processing_charge":"No","abstract":[{"lang":"eng","text":"Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations. 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The perturbations are arbitrary continuous maps within L_infty distance r from f for a given r &gt; 0. The main drawback of the approach is that the computability of well groups was shown only when dim K = n or n = 1. Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of R^n by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and dim K &lt; 2n-2, our approximation of the (dim K-n)th well group is exact. For the second part, we find examples of maps f, f' from K to R^n with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status. 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Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–56, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">10.4230/LIPIcs.SOCG.2015.842</a>.","ama":"Franek P, Krcál M. On computability and triviality of well groups. In: Vol 34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">10.4230/LIPIcs.SOCG.2015.842</a>","short":"P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–856.","ista":"Franek P, Krcál M. 2015. On computability and triviality of well groups. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. <a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">https://doi.org/10.4230/LIPIcs.SOCG.2015.842</a>.","apa":"Franek, P., &#38; Krcál, M. (2015). On computability and triviality of well groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">https://doi.org/10.4230/LIPIcs.SOCG.2015.842</a>","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands, 2015, vol. 34, pp. 842–856."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"intvolume":"        34","publist_id":"5667","alternative_title":["LIPIcs"],"date_published":"2015-06-11T00:00:00Z","page":"842 - 856"},{"date_published":"2015-01-01T00:00:00Z","alternative_title":["Mathematics and Visualization"],"page":"257 - 267","intvolume":"        40","publist_id":"5640","publication_identifier":{"isbn":["978-3-319-15089-5"]},"department":[{"_id":"HeEd"}],"volume":40,"status":"public","citation":{"ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature,” in <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>, 1st ed., vol. 40, I. Hotz and T. Schultz, Eds. Springer, 2015, pp. 257–267.","apa":"Zobel, V., Reininghaus, J., &#38; Hotz, I. (2015). Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In I. Hotz &#38; T. Schultz (Eds.), <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i> (1st ed., Vol. 40, pp. 257–267). Springer. <a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">https://doi.org/10.1007/978-3-319-15090-1_13</a>","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>, edited by Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. <a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">https://doi.org/10.1007/978-3-319-15090-1_13</a>.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer, 2015, pp. 257–267.","ista":"Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization, vol. 40, 257–267.","ama":"Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>. Vol 40. 1st ed. Springer; 2015:257-267. doi:<a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">10.1007/978-3-319-15090-1_13</a>","mla":"Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>, edited by Ingrid Hotz and Thomas Schultz, 1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:<a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">10.1007/978-3-319-15090-1_13</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","scopus_import":"1","date_created":"2018-12-11T11:52:33Z","title":"Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature","publication":"Visualization and Processing of Higher Order Descriptors for Multi-Valued Data","language":[{"iso":"eng"}],"type":"book_chapter","year":"2015","month":"01","date_updated":"2022-06-10T09:50:14Z","editor":[{"first_name":"Ingrid","full_name":"Hotz, Ingrid","last_name":"Hotz"},{"last_name":"Schultz","first_name":"Thomas","full_name":"Schultz, Thomas"}],"oa_version":"None","abstract":[{"text":"The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece.","lang":"eng"}],"article_processing_charge":"No","doi":"10.1007/978-3-319-15090-1_13","day":"01","_id":"1531","author":[{"full_name":"Zobel, Valentin","first_name":"Valentin","last_name":"Zobel"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Hotz","full_name":"Hotz, Ingrid","first_name":"Ingrid"}],"publisher":"Springer","publication_status":"published","edition":"1"},{"date_published":"2015-01-01T00:00:00Z","page":"980 - 1017","intvolume":"        14","publist_id":"5616","isi":1,"department":[{"_id":"HeEd"}],"publication_identifier":{"eissn":["1536-0040"]},"status":"public","volume":14,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” <i>SIAM Journal on Applied Dynamical Systems</i>. Society for Industrial and Applied Mathematics , 2015. <a href=\"https://doi.org/10.1137/140993934\">https://doi.org/10.1137/140993934</a>.","apa":"Knipl, D., Pilarczyk, P., &#38; Röst, G. (2015). Rich bifurcation structure in a two patch vaccination model. <i>SIAM Journal on Applied Dynamical Systems</i>. Society for Industrial and Applied Mathematics . <a href=\"https://doi.org/10.1137/140993934\">https://doi.org/10.1137/140993934</a>","ieee":"D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two patch vaccination model,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015.","mla":"Knipl, Diána, et al. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 14, no. 2, Society for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:<a href=\"https://doi.org/10.1137/140993934\">10.1137/140993934</a>.","ama":"Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination model. <i>SIAM Journal on Applied Dynamical Systems</i>. 2015;14(2):980-1017. doi:<a href=\"https://doi.org/10.1137/140993934\">10.1137/140993934</a>","short":"D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems 14 (2015) 980–1017.","ista":"Knipl D, Pilarczyk P, Röst G. 2015. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 14(2), 980–1017."},"scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:52:42Z","publication":"SIAM Journal on Applied Dynamical Systems","title":"Rich bifurcation structure in a two patch vaccination model","language":[{"iso":"eng"}],"year":"2015","type":"journal_article","issue":"2","acknowledgement":"Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria (pawel.pilarczyk@ist.ac.at). This author’s work was partially supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement 622033, by Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC), by the Portuguese national funds through Funda ̧caoparaaCiˆencia e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008), and by European Research Council through StG 259559 in the framework of the EPIDELAY project.","main_file_link":[{"url":"http://discovery.ucl.ac.uk/1473750/1/99393.pdf","open_access":"1"}],"month":"01","date_updated":"2025-09-23T10:37:17Z","oa_version":"Published Version","oa":1,"article_type":"original","doi":"10.1137/140993934","abstract":[{"lang":"eng","text":"We show that incorporating spatial dispersal of individuals into a simple vaccination epidemic model may give rise to a model that exhibits rich dynamical behavior. Using an SIVS (susceptible-infected-vaccinated-susceptible) model as a basis, we describe the spread of an infectious disease in a population split into two regions. In each subpopulation, both forward and backward bifurcations can occur. This implies that for disconnected regions the two-patch system may admit several steady states. We consider traveling between the regions and investigate the impact of spatial dispersal of individuals on the model dynamics. We establish conditions for the existence of multiple nontrivial steady states in the system, and we study the structure of the equilibria. The mathematical analysis reveals an unusually rich dynamical behavior, not normally found in the simple epidemic models. In addition to the disease-free equilibrium, eight endemic equilibria emerge from backward transcritical and saddle-node bifurcation points, forming an interesting bifurcation diagram. Stability of steady states, their bifurcations, and the global dynamics are investigated with analytical tools, numerical simulations, and rigorous set-oriented numerical computations."}],"article_processing_charge":"No","project":[{"grant_number":"622033","call_identifier":"FP7","name":"Persistent Homology - Images, Data and Maps","_id":"255F06BE-B435-11E9-9278-68D0E5697425"}],"day":"01","_id":"1555","publication_status":"published","external_id":{"isi":["000357310400015"]},"author":[{"last_name":"Knipl","full_name":"Knipl, Diána","first_name":"Diána"},{"id":"3768D56A-F248-11E8-B48F-1D18A9856A87","last_name":"Pilarczyk","first_name":"Pawel","full_name":"Pilarczyk, Pawel"},{"last_name":"Röst","full_name":"Röst, Gergely","first_name":"Gergely"}],"publisher":"Society for Industrial and Applied Mathematics ","ec_funded":1,"ddc":["510"]},{"page":"273 - 286","date_published":"2015-03-01T00:00:00Z","date_updated":"2021-01-12T06:51:37Z","publist_id":"5608","intvolume":"        45","month":"03","oa_version":"None","department":[{"_id":"HeEd"}],"citation":{"ista":"Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 45(1), 273–286.","short":"G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286.","mla":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” <i>Topological Methods in Nonlinear Analysis</i>, vol. 45, no. 1, Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:<a href=\"https://doi.org/10.12775/TMNA.2015.014\">10.12775/TMNA.2015.014</a>.","ama":"Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. <i>Topological Methods in Nonlinear Analysis</i>. 2015;45(1):273-286. doi:<a href=\"https://doi.org/10.12775/TMNA.2015.014\">10.12775/TMNA.2015.014</a>","apa":"Graff, G., &#38; Pilarczyk, P. (2015). An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. <i>Topological Methods in Nonlinear Analysis</i>. Juliusz Schauder Center for Nonlinear Studies. <a href=\"https://doi.org/10.12775/TMNA.2015.014\">https://doi.org/10.12775/TMNA.2015.014</a>","ieee":"G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds,” <i>Topological Methods in Nonlinear Analysis</i>, vol. 45, no. 1. Juliusz Schauder Center for Nonlinear Studies, pp. 273–286, 2015.","chicago":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” <i>Topological Methods in Nonlinear Analysis</i>. Juliusz Schauder Center for Nonlinear Studies, 2015. <a href=\"https://doi.org/10.12775/TMNA.2015.014\">https://doi.org/10.12775/TMNA.2015.014</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":45,"abstract":[{"text":"For a given self-map $f$ of $M$, a closed smooth connected and simply-connected manifold of dimension $m\\geq 4$, we provide an algorithm for estimating the values of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic points in the smooth homotopy class of $f$. Our results are based on the combinatorial scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm programmed in C++ is publicly available at {\\tt http://www.pawelpilarczyk.com/combtop/}.","lang":"eng"}],"status":"public","doi":"10.12775/TMNA.2015.014","_id":"1563","publisher":"Juliusz Schauder Center for Nonlinear Studies","publication_status":"published","date_created":"2018-12-11T11:52:44Z","author":[{"first_name":"Grzegorz","full_name":"Graff, Grzegorz","last_name":"Graff"},{"first_name":"Pawel","full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"day":"01","quality_controlled":"1","scopus_import":1,"language":[{"iso":"eng"}],"title":"An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds","publication":"Topological Methods in Nonlinear Analysis","type":"journal_article","issue":"1","year":"2015"},{"department":[{"_id":"HeEd"}],"oa_version":"None","month":"01","intvolume":"      9411","publist_id":"5604","date_updated":"2022-01-28T08:25:00Z","alternative_title":["LNCS"],"date_published":"2015-01-01T00:00:00Z","type":"conference","year":"2015","publication":"23rd International Symposium","title":"Shape, homology, persistence, and stability","language":[{"iso":"eng"}],"scopus_import":"1","quality_controlled":"1","conference":{"end_date":"2015-09-26","location":"Los Angeles, CA, United States","start_date":"2015-09-24","name":"GD: Graph Drawing and Network Visualization"},"day":"01","publisher":"Springer Nature","_id":"1567","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"}],"publication_status":"published","date_created":"2018-12-11T11:52:46Z","status":"public","abstract":[{"lang":"eng","text":"My personal journey to the fascinating world of geometric forms started more than 30 years ago with the invention of alpha shapes in the plane. It took about 10 years before we generalized the concept to higher dimensions, we produced working software with a graphics interface for the three-dimensional case. At the same time, we added homology to the computations. Needless to say that this foreshadowed the inception of persistent homology, because it suggested the study of filtrations to capture the scale of a shape or data set. Importantly, this method has fast algorithms. The arguably most useful result on persistent homology is the stability of its diagrams under perturbations."}],"article_processing_charge":"No","volume":9411,"citation":{"chicago":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In <i>23rd International Symposium</i>, Vol. 9411. Springer Nature, 2015.","apa":"Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In <i>23rd International Symposium</i> (Vol. 9411). Los Angeles, CA, United States: Springer Nature.","ieee":"H. Edelsbrunner, “Shape, homology, persistence, and stability,” in <i>23rd International Symposium</i>, Los Angeles, CA, United States, 2015, vol. 9411.","mla":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” <i>23rd International Symposium</i>, vol. 9411, Springer Nature, 2015.","ama":"Edelsbrunner H. Shape, homology, persistence, and stability. In: <i>23rd International Symposium</i>. Vol 9411. Springer Nature; 2015.","ista":"Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.","short":"H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9"},{"author":[{"first_name":"Olga","full_name":"Dunaeva, Olga","last_name":"Dunaeva"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Lukyanov","first_name":"Anton","full_name":"Lukyanov, Anton"},{"first_name":"Michael","full_name":"Machin, Michael","last_name":"Machin"},{"full_name":"Malkova, Daria","first_name":"Daria","last_name":"Malkova"}],"external_id":{"isi":["000366596600074"]},"publication_status":"published","publisher":"IEEE","_id":"1568","conference":{"name":"SYNASC: Symbolic and Numeric Algorithms for Scientific Computing","start_date":"2014-09-22","location":"Timisoara, Romania","end_date":"2014-09-25"},"day":"05","doi":"10.1109/SYNASC.2014.81","article_processing_charge":"No","abstract":[{"lang":"eng","text":"Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI) magnifying endoscopy (ME) images of the stomach, we combine methods from image processing, computational topology, and machine learning to classify patterns into normal, tubular, vessel. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions."}],"oa_version":"None","date_updated":"2025-09-23T13:44:17Z","month":"02","acknowledgement":"This research is supported by the project No. 477 of P.G. Demidov Yaroslavl State University within State Assignment for Research.","type":"conference","year":"2015","language":[{"iso":"eng"}],"publication":"Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","title":"The classification of endoscopy images with persistent homology","date_created":"2018-12-11T11:52:46Z","quality_controlled":"1","scopus_import":"1","related_material":{"record":[{"status":"public","id":"1289","relation":"later_version"}]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.” In <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>, 7034731. IEEE, 2015. <a href=\"https://doi.org/10.1109/SYNASC.2014.81\">https://doi.org/10.1109/SYNASC.2014.81</a>.","ieee":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The classification of endoscopy images with persistent homology,” in <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>, Timisoara, Romania, 2015, p. 7034731.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., &#38; Malkova, D. (2015). The classification of endoscopy images with persistent homology. In <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i> (p. 7034731). Timisoara, Romania: IEEE. <a href=\"https://doi.org/10.1109/SYNASC.2014.81\">https://doi.org/10.1109/SYNASC.2014.81</a>","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification of endoscopy images with persistent homology. In: <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>. IEEE; 2015:7034731. doi:<a href=\"https://doi.org/10.1109/SYNASC.2014.81\">10.1109/SYNASC.2014.81</a>","mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>, IEEE, 2015, p. 7034731, doi:<a href=\"https://doi.org/10.1109/SYNASC.2014.81\">10.1109/SYNASC.2014.81</a>.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731.","ista":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. 2015. The classification of endoscopy images with persistent homology. Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC: Symbolic and Numeric Algorithms for Scientific Computing, 7034731."},"status":"public","isi":1,"department":[{"_id":"HeEd"}],"publist_id":"5603","page":"7034731","date_published":"2015-02-05T00:00:00Z"},{"oa_version":"None","month":"08","date_updated":"2025-09-29T10:58:50Z","acknowledgement":"The research of the second author is partially supported by NSF under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n","day":"01","_id":"1578","external_id":{"isi":["000355887700001"]},"publisher":"Elsevier","author":[{"last_name":"Cao","full_name":"Cao, Thanhtung","first_name":"Thanhtung"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"last_name":"Tan","full_name":"Tan, Tiowseng","first_name":"Tiowseng"}],"publication_status":"published","doi":"10.1016/j.comgeo.2015.04.001","abstract":[{"lang":"eng","text":"We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations."}],"article_processing_charge":"No","isi":1,"department":[{"_id":"HeEd"}],"intvolume":"        48","publist_id":"5593","date_published":"2015-08-01T00:00:00Z","page":"507 - 519","year":"2015","type":"journal_article","issue":"7","publication":"Computational Geometry","title":"Triangulations from topologically correct digital Voronoi diagrams","language":[{"iso":"eng"}],"quality_controlled":"1","scopus_import":"1","date_created":"2018-12-11T11:52:49Z","status":"public","volume":48,"citation":{"chicago":"Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” <i>Computational Geometry</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">https://doi.org/10.1016/j.comgeo.2015.04.001</a>.","apa":"Cao, T., Edelsbrunner, H., &#38; Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. <i>Computational Geometry</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">https://doi.org/10.1016/j.comgeo.2015.04.001</a>","ieee":"T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct digital Voronoi diagrams,” <i>Computational Geometry</i>, vol. 48, no. 7. Elsevier, pp. 507–519, 2015.","mla":"Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” <i>Computational Geometry</i>, vol. 48, no. 7, Elsevier, 2015, pp. 507–19, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">10.1016/j.comgeo.2015.04.001</a>.","ama":"Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital Voronoi diagrams. <i>Computational Geometry</i>. 2015;48(7):507-519. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">10.1016/j.comgeo.2015.04.001</a>","short":"T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.","ista":"Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"date_published":"2015-02-01T00:00:00Z","page":"120 - 133","intvolume":"        48","publist_id":"5589","department":[{"_id":"HeEd"}],"isi":1,"volume":48,"status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., &#38; Palfrader, P. (2015). Weighted straight skeletons in the plane. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2014.08.006\">https://doi.org/10.1016/j.comgeo.2014.08.006</a>","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight skeletons in the plane,” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 2. Elsevier, pp. 120–133, 2015.","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Weighted Straight Skeletons in the Plane.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.comgeo.2014.08.006\">https://doi.org/10.1016/j.comgeo.2014.08.006</a>.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(2), 120–133.","mla":"Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 2, Elsevier, 2015, pp. 120–33, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2014.08.006\">10.1016/j.comgeo.2014.08.006</a>.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons in the plane. <i>Computational Geometry: Theory and Applications</i>. 2015;48(2):120-133. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2014.08.006\">10.1016/j.comgeo.2014.08.006</a>"},"related_material":{"record":[{"status":"public","id":"1584","relation":"other"}]},"scopus_import":"1","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_created":"2018-12-11T11:52:51Z","title":"Weighted straight skeletons in the plane","publication":"Computational Geometry: Theory and Applications","language":[{"iso":"eng"}],"file":[{"creator":"system","file_id":"5215","access_level":"open_access","content_type":"application/pdf","date_created":"2018-12-12T10:16:28Z","date_updated":"2020-07-14T12:45:02Z","file_name":"IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf","checksum":"c1ef67f6ec925e12f73a96b8fe285ab4","relation":"main_file","file_size":505987}],"issue":"2","type":"journal_article","year":"2015","month":"02","date_updated":"2025-09-29T11:06:26Z","has_accepted_license":"1","pubrep_id":"474","file_date_updated":"2020-07-14T12:45:02Z","oa_version":"Published Version","oa":1,"abstract":[{"lang":"eng","text":"We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights."}],"article_processing_charge":"No","doi":"10.1016/j.comgeo.2014.08.006","day":"01","_id":"1582","publication_status":"published","external_id":{"isi":["000345056700007"]},"author":[{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"last_name":"Held","full_name":"Held, Martin","first_name":"Martin"},{"full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber"},{"first_name":"Dominik","full_name":"Kaaser, Dominik","last_name":"Kaaser"},{"last_name":"Palfrader","first_name":"Peter","full_name":"Palfrader, Peter"}],"publisher":"Elsevier","ddc":["000"]},{"ddc":["000"],"_id":"1583","author":[{"last_name":"Biedl","full_name":"Biedl, Therese","first_name":"Therese"},{"first_name":"Martin","full_name":"Held, Martin","last_name":"Held"},{"full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber"},{"full_name":"Kaaser, Dominik","first_name":"Dominik","last_name":"Kaaser"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"}],"external_id":{"isi":["000346225300034"]},"publisher":"Elsevier","publication_status":"published","day":"01","article_processing_charge":"No","abstract":[{"text":"We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon.","lang":"eng"}],"doi":"10.1016/j.ipl.2014.09.021","oa":1,"oa_version":"Published Version","file_date_updated":"2020-07-14T12:45:03Z","pubrep_id":"473","date_updated":"2025-09-22T14:35:14Z","has_accepted_license":"1","month":"02","issue":"2","type":"journal_article","year":"2015","language":[{"iso":"eng"}],"file":[{"file_size":270137,"relation":"main_file","checksum":"2779a648610c9b5c86d0b51a62816d23","file_name":"IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf","date_updated":"2020-07-14T12:45:03Z","date_created":"2018-12-12T10:18:45Z","content_type":"application/pdf","access_level":"open_access","file_id":"5367","creator":"system"}],"title":"A simple algorithm for computing positively weighted straight skeletons of monotone polygons","publication":"Information Processing Letters","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_created":"2018-12-11T11:52:51Z","quality_controlled":"1","scopus_import":"1","citation":{"mla":"Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” <i>Information Processing Letters</i>, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:<a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">10.1016/j.ipl.2014.09.021</a>.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. <i>Information Processing Letters</i>. 2015;115(2):243-247. doi:<a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">10.1016/j.ipl.2014.09.021</a>","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247.","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 115(2), 243–247.","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” <i>Information Processing Letters</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">https://doi.org/10.1016/j.ipl.2014.09.021</a>.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., &#38; Palfrader, P. (2015). A simple algorithm for computing positively weighted straight skeletons of monotone polygons. <i>Information Processing Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">https://doi.org/10.1016/j.ipl.2014.09.021</a>","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” <i>Information Processing Letters</i>, vol. 115, no. 2. Elsevier, pp. 243–247, 2015."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":115,"status":"public","department":[{"_id":"HeEd"}],"isi":1,"publist_id":"5588","intvolume":"       115","page":"243 - 247","date_published":"2015-02-01T00:00:00Z"}]