[{"date_updated":"2023-05-22T08:15:19Z","department":[{"_id":"HeEd"}],"_id":"13048","conference":{"end_date":"2023-06-23","location":"Orlando, FL, United States","start_date":"2023-06-20","name":"STOC: Symposium on Theory of Computing"},"type":"conference","status":"public","publication_status":"published","publication_identifier":{"isbn":["9781450399135"]},"language":[{"iso":"eng"}],"ec_funded":1,"abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2303.04014"}],"month":"06","citation":{"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.","chicago":"Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis.” In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, 1768–76. Association for Computing Machinery, 2023. https://doi.org/10.1145/3564246.3585113.","ieee":"A. Lieutier and M. Wintraecken, “Hausdorff and Gromov-Hausdorff stable subsets of the medial axis,” in Proceedings of the 55th Annual ACM Symposium on Theory of Computing, Orlando, FL, United States, 2023, pp. 1768–1776.","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.","ama":"Lieutier A, Wintraecken M. Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. In: Proceedings of the 55th Annual ACM Symposium on Theory of Computing. Association for Computing Machinery; 2023:1768-1776. doi:10.1145/3564246.3585113","apa":"Lieutier, A., & Wintraecken, M. (2023). Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing (pp. 1768–1776). Orlando, FL, United States: Association for Computing Machinery. https://doi.org/10.1145/3564246.3585113","mla":"Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis.” Proceedings of the 55th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–76, doi:10.1145/3564246.3585113."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"arxiv":["2303.04014"]},"author":[{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"title":"Hausdorff and Gromov-Hausdorff stable subsets of the medial axis","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Learning and triangulating manifolds via collapses","grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"year":"2023","publication":"Proceedings of the 55th Annual ACM Symposium on Theory of Computing","day":"02","page":"1768-1776","date_created":"2023-05-22T08:02:02Z","date_published":"2023-06-02T00:00:00Z","doi":"10.1145/3564246.3585113","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.","oa":1,"publisher":"Association for Computing Machinery","quality_controlled":"1"},{"citation":{"chicago":"Edelsbrunner, Herbert, and Georg F Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” Algorithmica. Springer Nature, 2023. https://doi.org/10.1007/s00453-022-01027-6.","ista":"Edelsbrunner H, Osang GF. 2023. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 85, 277–295.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” Algorithmica, vol. 85, Springer Nature, 2023, pp. 277–95, doi:10.1007/s00453-022-01027-6.","apa":"Edelsbrunner, H., & Osang, G. F. (2023). A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. Springer Nature. https://doi.org/10.1007/s00453-022-01027-6","ama":"Edelsbrunner H, Osang GF. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 2023;85:277-295. doi:10.1007/s00453-022-01027-6","short":"H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.","ieee":"H. Edelsbrunner and G. F. Osang, “A simple algorithm for higher-order Delaunay mosaics and alpha shapes,” Algorithmica, vol. 85. Springer Nature, pp. 277–295, 2023."},"user_id":"2EBD1598-F248-11E8-B48F-1D18A9856A87","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F","last_name":"Osang"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000846967100001"]},"title":"A simple algorithm for higher-order Delaunay mosaics and alpha shapes","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","grant_number":"Z00342"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"has_accepted_license":"1","isi":1,"year":"2023","day":"01","publication":"Algorithmica","page":"277-295","date_published":"2023-01-01T00:00:00Z","doi":"10.1007/s00453-022-01027-6","date_created":"2022-09-11T22:01:57Z","acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"date_updated":"2023-06-27T12:53:43Z","ddc":["510"],"file_date_updated":"2023-01-20T10:02:48Z","department":[{"_id":"HeEd"}],"_id":"12086","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"publication_status":"published","file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"12322","checksum":"71685ca5121f4c837f40c3f8eb50c915","creator":"dernst","file_size":911017,"date_updated":"2023-01-20T10:02:48Z","file_name":"2023_Algorithmica_Edelsbrunner.pdf","date_created":"2023-01-20T10:02:48Z"}],"language":[{"iso":"eng"}],"volume":85,"ec_funded":1,"abstract":[{"lang":"eng","text":"We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets."}],"oa_version":"Published Version","scopus_import":"1","month":"01","intvolume":" 85"},{"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"name":"Learning and triangulating manifolds via collapses","grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"external_id":{"isi":["000862193600001"]},"article_processing_charge":"No","author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"first_name":"Ramsay","full_name":"Dyer, Ramsay","last_name":"Dyer"},{"full_name":"Ghosh, Arijit","last_name":"Ghosh","first_name":"Arijit"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"title":"Local criteria for triangulating general manifolds","citation":{"mla":"Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.” Discrete & Computational Geometry, vol. 69, Springer Nature, 2023, pp. 156–91, doi:10.1007/s00454-022-00431-7.","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for triangulating general manifolds,” Discrete & Computational Geometry, vol. 69. Springer Nature, pp. 156–191, 2023.","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete & Computational Geometry 69 (2023) 156–191.","apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., & Wintraecken, M. (2023). Local criteria for triangulating general manifolds. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00431-7","ama":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 2023;69:156-191. doi:10.1007/s00454-022-00431-7","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken. “Local Criteria for Triangulating General Manifolds.” Discrete & Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00431-7.","ista":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 69, 156–191."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"quality_controlled":"1","publisher":"Springer Nature","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).","page":"156-191","date_created":"2023-01-16T10:04:06Z","doi":"10.1007/s00454-022-00431-7","date_published":"2023-01-01T00:00:00Z","year":"2023","isi":1,"has_accepted_license":"1","publication":"Discrete & Computational Geometry","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"status":"public","_id":"12287","department":[{"_id":"HeEd"}],"file_date_updated":"2023-02-02T11:01:10Z","date_updated":"2023-08-01T12:47:32Z","ddc":["510"],"scopus_import":"1","intvolume":" 69","month":"01","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"}],"oa_version":"Published Version","ec_funded":1,"volume":69,"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":582850,"date_updated":"2023-02-02T11:01:10Z","file_name":"2023_DiscreteCompGeometry_Boissonnat.pdf","date_created":"2023-02-02T11:01:10Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"12488","checksum":"46352e0ee71e460848f88685ca852681"}]},{"publisher":"Institute of Electrical and Electronics Engineers","quality_controlled":"1","oa":1,"date_published":"2023-02-08T00:00:00Z","doi":"10.1109/icdmw58026.2022.00093","date_created":"2023-02-14T07:56:21Z","isi":1,"has_accepted_license":"1","year":"2023","day":"08","publication":"2022 IEEE International Conference on Data Mining Workshops","article_number":"00093","author":[{"full_name":"Forghani, Mohammad","last_name":"Forghani","first_name":"Mohammad"},{"full_name":"Claramunt, Christophe","last_name":"Claramunt","first_name":"Christophe"},{"first_name":"Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","last_name":"Karimipour","full_name":"Karimipour, Farid","orcid":"0000-0001-6746-4174"},{"first_name":"Georg","last_name":"Heiler","full_name":"Heiler, Georg"}],"article_processing_charge":"No","external_id":{"isi":["000971492200145"]},"title":"Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic","citation":{"ista":"Forghani M, Claramunt C, Karimipour F, Heiler G. 2023. Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic. 2022 IEEE International Conference on Data Mining Workshops. ICDMW: Conference on Data Mining Workshops, 00093.","chicago":"Forghani, Mohammad, Christophe Claramunt, Farid Karimipour, and Georg Heiler. “Visual Analytics of Mobility Network Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” In 2022 IEEE International Conference on Data Mining Workshops. Institute of Electrical and Electronics Engineers, 2023. https://doi.org/10.1109/icdmw58026.2022.00093.","apa":"Forghani, M., Claramunt, C., Karimipour, F., & Heiler, G. (2023). Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic. In 2022 IEEE International Conference on Data Mining Workshops. Orlando, FL, United States: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/icdmw58026.2022.00093","ama":"Forghani M, Claramunt C, Karimipour F, Heiler G. Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic. In: 2022 IEEE International Conference on Data Mining Workshops. Institute of Electrical and Electronics Engineers; 2023. doi:10.1109/icdmw58026.2022.00093","ieee":"M. Forghani, C. Claramunt, F. Karimipour, and G. Heiler, “Visual analytics of mobility network changes observed using mobile phone data during COVID-19 pandemic,” in 2022 IEEE International Conference on Data Mining Workshops, Orlando, FL, United States, 2023.","short":"M. Forghani, C. Claramunt, F. Karimipour, G. Heiler, in:, 2022 IEEE International Conference on Data Mining Workshops, Institute of Electrical and Electronics Engineers, 2023.","mla":"Forghani, Mohammad, et al. “Visual Analytics of Mobility Network Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” 2022 IEEE International Conference on Data Mining Workshops, 00093, Institute of Electrical and Electronics Engineers, 2023, doi:10.1109/icdmw58026.2022.00093."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"02","abstract":[{"text":"The limited exchange between human communities is a key factor in preventing the spread of COVID-19. This paper introduces a digital framework that combines an integration of real mobility data at the country scale with a series of modeling techniques and visual capabilities that highlight mobility patterns before and during the pandemic. The findings not only significantly exhibit mobility trends and different degrees of similarities at regional and local levels but also provide potential insight into the emergence of a pandemic on human behavior patterns and their likely socio-economic impacts.","lang":"eng"}],"oa_version":"Submitted Version","publication_identifier":{"eissn":["2375-9259"],"eisbn":["9798350346091"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"c253bee25e6dfe484f96662daa119cb6","file_id":"12549","file_size":1183339,"date_updated":"2023-02-14T07:58:26Z","creator":"fkarimip","file_name":"Visual Analysis_Mobility_COVID19 - SocDM2022.pdf","date_created":"2023-02-14T07:58:26Z"}],"language":[{"iso":"eng"}],"type":"conference","conference":{"name":"ICDMW: Conference on Data Mining Workshops","location":"Orlando, FL, United States","end_date":"2022-12-01","start_date":"2022-11-28"},"status":"public","_id":"12548","file_date_updated":"2023-02-14T07:58:26Z","department":[{"_id":"HeEd"}],"date_updated":"2023-08-01T13:15:48Z","ddc":["600"]},{"intvolume":" 63","month":"02","scopus_import":"1","oa_version":"Published Version","pmid":1,"abstract":[{"lang":"eng","text":"Geometry is crucial in our efforts to comprehend the structures and dynamics of biomolecules. For example, volume, surface area, and integrated mean and Gaussian curvature of the union of balls representing a molecule are used to quantify its interactions with the water surrounding it in the morphometric implicit solvent models. The Alpha Shape theory provides an accurate and reliable method for computing these geometric measures. In this paper, we derive homogeneous formulas for the expressions of these measures and their derivatives with respect to the atomic coordinates, and we provide algorithms that implement them into a new software package, AlphaMol. The only variables in these formulas are the interatomic distances, making them insensitive to translations and rotations. AlphaMol includes a sequential algorithm and a parallel algorithm. In the parallel version, we partition the atoms of the molecule of interest into 3D rectangular blocks, using a kd-tree algorithm. We then apply the sequential algorithm of AlphaMol to each block, augmented by a buffer zone to account for atoms whose ball representations may partially cover the block. The current parallel version of AlphaMol leads to a 20-fold speed-up compared to an independent serial implementation when using 32 processors. For instance, it takes 31 s to compute the geometric measures and derivatives of each atom in a viral capsid with more than 26 million atoms on 32 Intel processors running at 2.7 GHz. The presence of the buffer zones, however, leads to redundant computations, which ultimately limit the impact of using multiple processors. AlphaMol is available as an OpenSource software."}],"ec_funded":1,"volume":63,"issue":"3","language":[{"iso":"eng"}],"file":[{"date_created":"2023-08-16T12:21:13Z","file_name":"2023_JCIM_Koehl.pdf","date_updated":"2023-08-16T12:21:13Z","file_size":8069223,"creator":"dernst","checksum":"7d20562269edff1e31b9d6019d4983b0","file_id":"14070","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","publication_identifier":{"issn":["1549-9596"],"eissn":["1549-960X"]},"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"12544","department":[{"_id":"HeEd"}],"file_date_updated":"2023-08-16T12:21:13Z","ddc":["510","540"],"date_updated":"2023-08-16T12:22:07Z","oa":1,"publisher":"American Chemical Society","quality_controlled":"1","acknowledgement":"P.K. acknowledges support from the University of California Multicampus Research Programs and Initiatives (Grant No. M21PR3267) and from the NSF (Grant No.1760485). H.E. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.\r\nOpen Access is funded by the Austrian Science Fund (FWF).","date_created":"2023-02-12T23:00:59Z","date_published":"2023-02-13T00:00:00Z","doi":"10.1021/acs.jcim.2c01346","page":"973-985","publication":"Journal of Chemical Information and Modeling","day":"13","year":"2023","has_accepted_license":"1","isi":1,"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"title":"Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives","external_id":{"isi":["000920370700001"],"pmid":["36638318"]},"article_processing_charge":"No","author":[{"first_name":"Patrice","full_name":"Koehl, Patrice","last_name":"Koehl"},{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Koehl P, Akopyan A, Edelsbrunner H. 2023. Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical Information and Modeling. 63(3), 973–985.","chicago":"Koehl, Patrice, Arseniy Akopyan, and Herbert Edelsbrunner. “Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.” Journal of Chemical Information and Modeling. American Chemical Society, 2023. https://doi.org/10.1021/acs.jcim.2c01346.","ieee":"P. Koehl, A. Akopyan, and H. Edelsbrunner, “Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives,” Journal of Chemical Information and Modeling, vol. 63, no. 3. American Chemical Society, pp. 973–985, 2023.","short":"P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and Modeling 63 (2023) 973–985.","apa":"Koehl, P., Akopyan, A., & Edelsbrunner, H. (2023). Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical Information and Modeling. American Chemical Society. https://doi.org/10.1021/acs.jcim.2c01346","ama":"Koehl P, Akopyan A, Edelsbrunner H. Computing the volume, surface area, mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical Information and Modeling. 2023;63(3):973-985. doi:10.1021/acs.jcim.2c01346","mla":"Koehl, Patrice, et al. “Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.” Journal of Chemical Information and Modeling, vol. 63, no. 3, American Chemical Society, 2023, pp. 973–85, doi:10.1021/acs.jcim.2c01346."}},{"_id":"12764","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","date_updated":"2023-10-04T11:46:48Z","ddc":["510"],"file_date_updated":"2023-10-04T11:46:24Z","department":[{"_id":"HeEd"}],"abstract":[{"text":"We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi cell corresponding to the singularity. We divide polyhedral surfaces into discrete conformal classes using a generalization of discrete conformal equivalence pioneered by Feng Luo. We subsequently show that, in every discrete conformal class, there exists a polyhedral surface with constant discrete Gaussian curvature. We also provide explicit examples to demonstrate that this surface is in general not unique.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 70","month":"07","publication_status":"published","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"language":[{"iso":"eng"}],"file":[{"success":1,"checksum":"cdbf90ba4a7ddcb190d37b9e9d4cb9d3","file_id":"14396","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2023_DiscreteGeometry_Kourimska.pdf","date_created":"2023-10-04T11:46:24Z","file_size":1026683,"date_updated":"2023-10-04T11:46:24Z","creator":"dernst"}],"volume":70,"project":[{"_id":"26AD5D90-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I04245","name":"Algebraic Footprints of Geometric Features in Homology"}],"citation":{"ista":"Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 70, 123–153.","chicago":"Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00484-2.","apa":"Kourimska, H. (2023). Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00484-2","ama":"Kourimska H. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 2023;70:123-153. doi:10.1007/s00454-023-00484-2","short":"H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153.","ieee":"H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” Discrete and Computational Geometry, vol. 70. Springer Nature, pp. 123–153, 2023.","mla":"Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 123–53, doi:10.1007/s00454-023-00484-2."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000948148000001"]},"author":[{"last_name":"Kourimska","orcid":"0000-0001-7841-0091","full_name":"Kourimska, Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","first_name":"Hana"}],"title":"Discrete yamabe problem for polyhedral surfaces","acknowledgement":"Open access funding provided by the Austrian Science Fund (FWF). This research was supported by the FWF grant, Project number I4245-N35, and by the Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID 195170736 - TRR109.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","year":"2023","has_accepted_license":"1","isi":1,"publication":"Discrete and Computational Geometry","day":"01","page":"123-153","date_created":"2023-03-26T22:01:09Z","date_published":"2023-07-01T00:00:00Z","doi":"10.1007/s00454-023-00484-2"},{"author":[{"first_name":"René","last_name":"Corbet","full_name":"Corbet, René"},{"first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","last_name":"Kerber"},{"last_name":"Lesnick","full_name":"Lesnick, Michael","first_name":"Michael"},{"last_name":"Osang","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000936496800001"],"arxiv":["2103.07823"]},"article_processing_charge":"Yes (via OA deal)","title":"Computing the multicover bifiltration","citation":{"ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2023. Computing the multicover bifiltration. Discrete and Computational Geometry. 70, 376–405.","chicago":"Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00476-8.","ieee":"R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” Discrete and Computational Geometry, vol. 70. Springer Nature, pp. 376–405, 2023.","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, Discrete and Computational Geometry 70 (2023) 376–405.","apa":"Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2023). Computing the multicover bifiltration. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00476-8","ama":"Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. Discrete and Computational Geometry. 2023;70:376-405. doi:10.1007/s00454-022-00476-8","mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” Discrete and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 376–405, doi:10.1007/s00454-022-00476-8."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"We thank the anonymous reviewers for many helpful comments and suggestions, which led to substantial improvements of the paper. The first two authors were supported by the Austrian Science Fund (FWF) grant number P 29984-N35 and W1230. The first author was partly supported by an Austrian Marshall Plan Scholarship, and by the Brummer & Partners MathDataLab. A conference version of this paper was presented at the 37th International Symposium on Computational Geometry (SoCG 2021). Open access funding provided by the Royal Institute of Technology.","page":"376-405","date_published":"2023-09-01T00:00:00Z","doi":"10.1007/s00454-022-00476-8","date_created":"2023-03-05T23:01:06Z","has_accepted_license":"1","isi":1,"year":"2023","day":"01","publication":"Discrete and Computational Geometry","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"12709","file_date_updated":"2023-03-07T14:40:14Z","department":[{"_id":"HeEd"}],"date_updated":"2023-10-04T12:03:40Z","ddc":["000"],"scopus_import":"1","month":"09","intvolume":" 70","abstract":[{"lang":"eng","text":"Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness."}],"oa_version":"Published Version","volume":70,"related_material":{"record":[{"relation":"earlier_version","id":"9605","status":"public"}]},"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"publication_status":"published","file":[{"date_created":"2023-03-07T14:40:14Z","file_name":"2023_DisCompGeo_Corbet.pdf","date_updated":"2023-03-07T14:40:14Z","file_size":1359323,"creator":"cchlebak","file_id":"12715","checksum":"71ce7e59f7ee4620acc704fecca620c2","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}]},{"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses","grant_number":"M03073"}],"article_processing_charge":"No","author":[{"first_name":"Jean Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean Daniel"},{"last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"title":"The reach of subsets of manifolds","citation":{"ista":"Boissonnat JD, Wintraecken M. 2023. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 7, 619–641.","chicago":"Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” Journal of Applied and Computational Topology. Springer Nature, 2023. https://doi.org/10.1007/s41468-023-00116-x.","ieee":"J. D. Boissonnat and M. Wintraecken, “The reach of subsets of manifolds,” Journal of Applied and Computational Topology, vol. 7. Springer Nature, pp. 619–641, 2023.","short":"J.D. Boissonnat, M. Wintraecken, Journal of Applied and Computational Topology 7 (2023) 619–641.","apa":"Boissonnat, J. D., & Wintraecken, M. (2023). The reach of subsets of manifolds. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00116-x","ama":"Boissonnat JD, Wintraecken M. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 2023;7:619-641. doi:10.1007/s41468-023-00116-x","mla":"Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” Journal of Applied and Computational Topology, vol. 7, Springer Nature, 2023, pp. 619–41, doi:10.1007/s41468-023-00116-x."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publisher":"Springer Nature","quality_controlled":"1","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.","page":"619-641","date_created":"2023-03-26T22:01:08Z","date_published":"2023-09-01T00:00:00Z","doi":"10.1007/s41468-023-00116-x","year":"2023","publication":"Journal of Applied and Computational Topology","day":"01","type":"journal_article","article_type":"original","status":"public","_id":"12763","department":[{"_id":"HeEd"}],"date_updated":"2023-10-04T12:07:18Z","main_file_link":[{"open_access":"1","url":"https://inserm.hal.science/INRIA-SACLAY/hal-04083524v1"}],"scopus_import":"1","intvolume":" 7","month":"09","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."}],"oa_version":"Submitted Version","ec_funded":1,"volume":7,"publication_status":"published","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"language":[{"iso":"eng"}]},{"abstract":[{"lang":"eng","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. "}],"oa_version":"Submitted Version","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1"}],"month":"04","intvolume":" 52","publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"publication_status":"published","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"earlier_version","id":"9441","status":"public"}]},"volume":52,"issue":"2","ec_funded":1,"_id":"12960","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-10-10T07:34:35Z","department":[{"_id":"HeEd"}],"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.","quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics","oa":1,"isi":1,"year":"2023","day":"30","publication":"SIAM Journal on Computing","page":"452-486","date_published":"2023-04-30T00:00:00Z","doi":"10.1137/21M1412918","date_created":"2023-05-14T22:01:00Z","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses","grant_number":"M03073"}],"citation":{"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.","chicago":"Boissonnat, Jean Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2023. https://doi.org/10.1137/21M1412918.","short":"J.D. Boissonnat, S. Kachanovich, M. Wintraecken, SIAM Journal on Computing 52 (2023) 452–486.","ieee":"J. D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations,” SIAM Journal on Computing, vol. 52, no. 2. Society for Industrial and Applied Mathematics, pp. 452–486, 2023.","apa":"Boissonnat, J. D., Kachanovich, S., & Wintraecken, M. (2023). Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1412918","ama":"Boissonnat JD, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. 2023;52(2):452-486. doi:10.1137/21M1412918","mla":"Boissonnat, Jean Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing, vol. 52, no. 2, Society for Industrial and Applied Mathematics, 2023, pp. 452–86, doi:10.1137/21M1412918."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Boissonnat, Jean Daniel","last_name":"Boissonnat","first_name":"Jean Daniel"},{"last_name":"Kachanovich","full_name":"Kachanovich, Siargey","first_name":"Siargey"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"article_processing_charge":"No","external_id":{"isi":["001013183000012"]},"title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations"},{"acknowledgement":"The first author has been partially supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia through the project no. 451-03-47/2023-01/200156. The fourth author is funded by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.","publisher":"Elsevier","quality_controlled":"1","isi":1,"year":"2023","day":"01","publication":"Pattern Recognition","date_published":"2023-10-01T00:00:00Z","doi":"10.1016/j.patcog.2023.109693","date_created":"2023-06-18T22:00:45Z","article_number":"109693","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Discretization in Geometry and Dynamics"}],"citation":{"ista":"Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. 2023. Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. 142(10), 109693.","chicago":"Čomić, Lidija, Gaëlle Largeteau-Skapin, Rita Zrour, Ranita Biswas, and Eric Andres. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern Recognition. Elsevier, 2023. https://doi.org/10.1016/j.patcog.2023.109693.","ieee":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, and E. Andres, “Discrete analytical objects in the body-centered cubic grid,” Pattern Recognition, vol. 142, no. 10. Elsevier, 2023.","short":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023).","ama":"Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. 2023;142(10). doi:10.1016/j.patcog.2023.109693","apa":"Čomić, L., Largeteau-Skapin, G., Zrour, R., Biswas, R., & Andres, E. (2023). Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. Elsevier. https://doi.org/10.1016/j.patcog.2023.109693","mla":"Čomić, Lidija, et al. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern Recognition, vol. 142, no. 10, 109693, Elsevier, 2023, doi:10.1016/j.patcog.2023.109693."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Čomić, Lidija","last_name":"Čomić","first_name":"Lidija"},{"full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin","first_name":"Gaëlle"},{"last_name":"Zrour","full_name":"Zrour, Rita","first_name":"Rita"},{"first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas"},{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"}],"external_id":{"isi":["001013526000001"]},"article_processing_charge":"No","title":"Discrete analytical objects in the body-centered cubic grid","abstract":[{"text":"We propose a characterization of discrete analytical spheres, planes and lines in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently proposed alternative compact coordinate system, in which each integer triplet addresses some voxel in the grid. We define spheres and planes through double Diophantine inequalities and investigate their relevant topological features, such as functionality or the interrelation between the thickness of the objects and their connectivity and separation properties. We define lines as the intersection of planes. The number of the planes (up to six) is equal to the number of the pairs of faces of a BCC voxel that are parallel to the line.","lang":"eng"}],"oa_version":"None","scopus_import":"1","month":"10","intvolume":" 142","publication_identifier":{"issn":["0031-3203"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"10","volume":142,"_id":"13134","type":"journal_article","article_type":"original","status":"public","date_updated":"2023-10-10T07:37:16Z","department":[{"_id":"HeEd"}]}]