[{"related_material":{"record":[{"id":"15090","status":"public","relation":"earlier_version"}]},"publisher":"Springer Nature","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"corr_author":"1","article_processing_charge":"Yes (via OA deal)","article_type":"original","project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"month":"01","department":[{"_id":"HeEd"}],"volume":75,"author":[{"full_name":"Biswas, Ranita","last_name":"Biswas","orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano"},{"id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","first_name":"Ondrej","orcid":"0000-0003-0464-3823","last_name":"Draganov","full_name":"Draganov, Ondrej"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"acknowledgement":"The fourth author thanks Boris Aronov for insightful discussions on the size of the overlay of Voronoi tessellations. Open access funding provided by Institute of Science and Technology (IST Austria). 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.","oa":1,"doi":"10.1007/s00454-025-00778-7","oa_version":"Published Version","OA_type":"hybrid","date_created":"2025-10-12T22:01:26Z","title":"On the size of chromatic Delaunay mosaics","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"arxiv":1,"file":[{"file_name":"2026_DiscreteCompGeom_Biswas.pdf","checksum":"0addb5c1b78142f9fb453bfa04695400","date_updated":"2026-01-05T13:21:20Z","creator":"dernst","relation":"main_file","file_id":"20952","access_level":"open_access","date_created":"2026-01-05T13:21:20Z","file_size":570922,"success":1,"content_type":"application/pdf"}],"publication_status":"published","scopus_import":"1","ec_funded":1,"status":"public","page":"24-47","PlanS_conform":"1","isi":1,"publication":"Discrete and Computational Geometry","date_updated":"2026-01-05T13:21:56Z","file_date_updated":"2026-01-05T13:21:20Z","date_published":"2026-01-01T00:00:00Z","OA_place":"publisher","year":"2026","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        75","has_accepted_license":"1","day":"01","citation":{"mla":"Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” <i>Discrete and Computational Geometry</i>, vol. 75, Springer Nature, 2026, pp. 24–47, doi:<a href=\"https://doi.org/10.1007/s00454-025-00778-7\">10.1007/s00454-025-00778-7</a>.","ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” <i>Discrete and Computational Geometry</i>, vol. 75. Springer Nature, pp. 24–47, 2026.","short":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 75 (2026) 24–47.","apa":"Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (2026). On the size of chromatic Delaunay mosaics. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-025-00778-7\">https://doi.org/10.1007/s00454-025-00778-7</a>","ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. <i>Discrete and Computational Geometry</i>. 2026;75:24-47. doi:<a href=\"https://doi.org/10.1007/s00454-025-00778-7\">10.1007/s00454-025-00778-7</a>","ista":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2026. On the size of chromatic Delaunay mosaics. Discrete and Computational Geometry. 75, 24–47.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00454-025-00778-7\">https://doi.org/10.1007/s00454-025-00778-7</a>."},"type":"journal_article","quality_controlled":"1","language":[{"iso":"eng"}],"_id":"20456","abstract":[{"lang":"eng","text":"Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications."}],"external_id":{"arxiv":["2212.03121"],"isi":["001584166900001"]}},{"OA_type":"hybrid","oa_version":"Published Version","date_created":"2024-05-12T22:01:03Z","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"file":[{"checksum":"0ee15c1493a6413cf356ab2f32c81a9e","file_name":"2024_JourApplCompTopo_BiswasRa.pdf","file_id":"19612","creator":"dernst","date_updated":"2025-04-23T08:01:36Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"date_created":"2025-04-23T08:01:36Z","file_size":522831}],"publication_status":"published","related_material":{"record":[{"id":"11658","status":"public","relation":"earlier_version"}]},"pmid":1,"publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","corr_author":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"month":"09","department":[{"_id":"HeEd"}],"article_type":"original","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Mathematics, Computer Science"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"author":[{"full_name":"Biswas, Ranita","last_name":"Biswas","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"last_name":"Cultrera Di Montesano","full_name":"Cultrera Di Montesano, Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","orcid":"0000-0001-6249-0832"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"volume":8,"doi":"10.1007/s41468-024-00173-w","oa":1,"acknowledgement":"The authors thank Uli Wagner and Emo Welzl for comments on an earlier version of this paper, and for pointing out related work in the prior literature.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). 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.","OA_place":"publisher","date_published":"2024-09-01T00:00:00Z","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","intvolume":"         8","citation":{"ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” <i>Journal of Applied and Computational Topology</i>, vol. 8. Springer Nature, pp. 557–578, 2024.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>, vol. 8, Springer Nature, 2024, pp. 557–78, doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Journal of Applied and Computational Topology. 8, 557–578.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. 2024;8:557-578. doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>."},"day":"01","has_accepted_license":"1","quality_controlled":"1","type":"journal_article","external_id":{"pmid":["39308789"]},"_id":"15380","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements."}],"scopus_import":"1","ec_funded":1,"status":"public","page":"557-578","publication":"Journal of Applied and Computational Topology","date_updated":"2025-05-14T09:27:57Z","file_date_updated":"2025-04-23T08:01:36Z"},{"ec_funded":1,"scopus_import":"1","status":"public","page":"1101-1119","date_updated":"2026-04-07T12:58:47Z","publication":"Journal of Applied and Computational Topology","file_date_updated":"2025-01-09T07:39:41Z","OA_place":"publisher","date_published":"2024-10-01T00:00:00Z","intvolume":"         8","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"year":"2024","citation":{"apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). Geometric characterization of the persistence of 1D maps. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>","mla":"Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>, vol. 8, Springer Nature, 2024, pp. 1101–19, doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric characterization of the persistence of 1D maps,” <i>Journal of Applied and Computational Topology</i>, vol. 8. Springer Nature, pp. 1101–1119, 2024.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization of the persistence of 1D maps. <i>Journal of Applied and Computational Topology</i>. 2024;8:1101-1119. doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. 8, 1101–1119."},"day":"01","has_accepted_license":"1","external_id":{"pmid":["39678706"]},"abstract":[{"text":"We characterize critical points of 1-dimensional maps paired in persistent homology\r\ngeometrically and this way get elementary proofs of theorems about the symmetry\r\nof persistence diagrams and the variation of such maps. In particular, we identify\r\nbranching points and endpoints of networks as the sole source of asymmetry and\r\nrelate the cycle basis in persistent homology with a version of the stable marriage\r\nproblem. Our analysis provides the foundations of fast algorithms for maintaining a\r\ncollection of sorted lists together with its persistence diagram.","lang":"eng"}],"_id":"13182","language":[{"iso":"eng"}],"quality_controlled":"1","type":"journal_article","related_material":{"record":[{"status":"public","id":"15094","relation":"dissertation_contains"}]},"pmid":1,"article_processing_charge":"Yes (via OA deal)","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"corr_author":"1","publisher":"Springer Nature","author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","last_name":"Cultrera Di Montesano","full_name":"Cultrera Di Montesano, Sebastiano"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"volume":8,"department":[{"_id":"HeEd"}],"month":"10","article_type":"original","project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"name":"Persistent Homology, Algorithms and Stochastic Geometry","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"doi":"10.1007/s41468-023-00126-9","oa":1,"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. The authors of this paper thank anonymous reviewers for their constructive criticism and Monika Henzinger for detailed comments on an earlier version of this paper.","title":"Geometric characterization of the persistence of 1D maps","date_created":"2023-07-02T22:00:44Z","OA_type":"hybrid","oa_version":"Published Version","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"file":[{"content_type":"application/pdf","success":1,"date_created":"2025-01-09T07:39:41Z","file_size":476896,"access_level":"open_access","relation":"main_file","file_id":"18783","creator":"dernst","date_updated":"2025-01-09T07:39:41Z","checksum":"d493df5088c222b88d9ca46b623ad0ee","file_name":"2024_JourApplCompTopo_Biswas.pdf"}],"publication_status":"published"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","intvolume":"       142","article_number":"109693","date_published":"2023-10-01T00:00:00Z","quality_controlled":"1","type":"journal_article","external_id":{"isi":["001013526000001"]},"_id":"13134","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"}],"language":[{"iso":"eng"}],"citation":{"chicago":"Čomić, Lidija, Gaëlle Largeteau-Skapin, Rita Zrour, Ranita Biswas, and Eric Andres. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” <i>Pattern Recognition</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">https://doi.org/10.1016/j.patcog.2023.109693</a>.","ama":"Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. Discrete analytical objects in the body-centered cubic grid. <i>Pattern Recognition</i>. 2023;142(10). doi:<a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">10.1016/j.patcog.2023.109693</a>","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.","apa":"Čomić, L., Largeteau-Skapin, G., Zrour, R., Biswas, R., &#38; Andres, E. (2023). Discrete analytical objects in the body-centered cubic grid. <i>Pattern Recognition</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">https://doi.org/10.1016/j.patcog.2023.109693</a>","mla":"Čomić, Lidija, et al. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” <i>Pattern Recognition</i>, vol. 142, no. 10, 109693, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">10.1016/j.patcog.2023.109693</a>.","ieee":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, and E. Andres, “Discrete analytical objects in the body-centered cubic grid,” <i>Pattern Recognition</i>, vol. 142, no. 10. Elsevier, 2023.","short":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023)."},"day":"01","status":"public","scopus_import":"1","issue":"10","isi":1,"publication":"Pattern Recognition","date_updated":"2025-04-15T07:45:32Z","publication_identifier":{"issn":["0031-3203"]},"oa_version":"None","date_created":"2023-06-18T22:00:45Z","title":"Discrete analytical objects in the body-centered cubic grid","publication_status":"published","publisher":"Elsevier","article_processing_charge":"No","corr_author":"1","doi":"10.1016/j.patcog.2023.109693","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.","department":[{"_id":"HeEd"}],"month":"10","project":[{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"},{"name":"Persistent Homology, Algorithms and Stochastic Geometry","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"}],"article_type":"original","author":[{"first_name":"Lidija","last_name":"Čomić","full_name":"Čomić, Lidija"},{"last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle","first_name":"Gaëlle"},{"first_name":"Rita","last_name":"Zrour","full_name":"Zrour, Rita"},{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","full_name":"Biswas, Ranita","last_name":"Biswas"},{"first_name":"Eric","last_name":"Andres","full_name":"Andres, Eric"}],"volume":142},{"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"oa_version":"Published Version","date_created":"2022-02-20T23:01:34Z","title":"Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics","publication_status":"published","file":[{"access_level":"open_access","file_size":2518111,"date_created":"2022-08-02T06:07:55Z","content_type":"application/pdf","success":1,"file_name":"2022_DiscreteCompGeometry_Biswas.pdf","checksum":"9383d3b70561bacee905e335dc922680","relation":"main_file","file_id":"11718","date_updated":"2022-08-02T06:07:55Z","creator":"dernst"}],"publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","corr_author":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"doi":"10.1007/s00454-022-00371-2","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","month":"04","department":[{"_id":"HeEd"}],"article_type":"original","author":[{"first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas"},{"orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","last_name":"Cultrera Di Montesano","full_name":"Cultrera Di Montesano, Sebastiano"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"first_name":"Morteza","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"volume":67,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"year":"2022","intvolume":"        67","date_published":"2022-04-01T00:00:00Z","quality_controlled":"1","type":"journal_article","external_id":{"isi":["000752175300002"]},"abstract":[{"lang":"eng","text":"The Voronoi tessellation in Rd is defined by locally minimizing the power distance to given weighted points. Symmetrically, the Delaunay mosaic can be defined by locally maximizing the negative power distance to other such points. We prove that the average of the two piecewise quadratic functions is piecewise linear, and that all three functions have the same critical points and values. Discretizing the two piecewise quadratic functions, we get the alpha shapes as sublevel sets of the discrete function on the Delaunay mosaic, and analogous shapes as superlevel sets of the discrete function on the Voronoi tessellation. For the same non-critical value, the corresponding shapes are disjoint, separated by a narrow channel that contains no critical points but the entire level set of the piecewise linear function."}],"_id":"10773","language":[{"iso":"eng"}],"day":"01","citation":{"ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics,” <i>Discrete and Computational Geometry</i>, vol. 67. Springer Nature, pp. 811–842, 2022.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 67 (2022) 811–842.","mla":"Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” <i>Discrete and Computational Geometry</i>, vol. 67, Springer Nature, 2022, pp. 811–42, doi:<a href=\"https://doi.org/10.1007/s00454-022-00371-2\">10.1007/s00454-022-00371-2</a>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2022). Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00371-2\">https://doi.org/10.1007/s00454-022-00371-2</a>","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2022. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 67, 811–842.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. <i>Discrete and Computational Geometry</i>. 2022;67:811-842. doi:<a href=\"https://doi.org/10.1007/s00454-022-00371-2\">10.1007/s00454-022-00371-2</a>","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00454-022-00371-2\">https://doi.org/10.1007/s00454-022-00371-2</a>."},"has_accepted_license":"1","page":"811-842","status":"public","scopus_import":"1","file_date_updated":"2022-08-02T06:07:55Z","isi":1,"publication":"Discrete and Computational Geometry","date_updated":"2024-10-09T21:01:38Z"},{"ec_funded":1,"status":"public","publication":"LIPIcs","date_updated":"2026-04-07T12:58:47Z","file_date_updated":"2022-07-27T09:30:30Z","date_published":"2022-07-25T00:00:00Z","year":"2022","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","day":"25","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, n.d.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. <i>LIPIcs</i>.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. LIPIcs.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","mla":"Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” <i>LIPIcs</i>, Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs,” <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.)."},"type":"journal_article","quality_controlled":"1","_id":"11660","abstract":[{"lang":"eng","text":"We characterize critical points of 1-dimensional maps paired in persistent homology geometrically and this way get elementary proofs of theorems about the symmetry of persistence diagrams and the variation of such maps. In particular, we identify branching points and endpoints of networks as the sole source of asymmetry and relate the cycle basis in persistent homology with a version of the stable marriage problem. Our analysis provides the foundations of fast algorithms for maintaining collections of interrelated sorted lists together with their persistence diagrams. "}],"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"15094","status":"public"}]},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","corr_author":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_processing_charge":"No","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"Mathematics, Computer Science"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"month":"07","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza"}],"acknowledgement":"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. ","oa":1,"oa_version":"Submitted Version","title":"A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs","alternative_title":["LIPIcs"],"date_created":"2022-07-27T09:31:15Z","file":[{"relation":"main_file","creator":"scultrer","file_id":"11661","date_updated":"2022-07-27T09:30:30Z","checksum":"95903f9d1649e8e437a967b6f2f64730","file_name":"window 1.pdf","content_type":"application/pdf","date_created":"2022-07-27T09:30:30Z","file_size":564836,"access_level":"open_access"}],"publication_status":"submitted"},{"date_created":"2022-07-27T09:27:34Z","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","oa_version":"Submitted Version","file":[{"access_level":"open_access","content_type":"application/pdf","date_created":"2022-07-27T09:25:53Z","file_size":639266,"checksum":"b2f511e8b1cae5f1892b0cdec341acac","file_name":"D-S-E.pdf","creator":"scultrer","relation":"main_file","file_id":"11659","date_updated":"2022-07-27T09:25:53Z"}],"publication_status":"draft","related_material":{"record":[{"relation":"later_version","id":"15380","status":"public"},{"relation":"dissertation_contains","status":"public","id":"15094"}]},"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"corr_author":"1","article_processing_charge":"No","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"project":[{"grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"month":"07","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"acknowledgement":"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.","oa":1,"date_published":"2022-07-27T00:00:00Z","year":"2022","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"has_accepted_license":"1","day":"27","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Leibniz International Proceedings on Mathematics</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, n.d.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Leibniz International Proceedings on Mathematics</i>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Leibniz International Proceedings on Mathematics</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” <i>Leibniz International Proceedings on Mathematics</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Leibniz International Proceedings on Mathematics</i>, Schloss Dagstuhl - Leibniz-Zentrum für Informatik."},"_id":"11658","abstract":[{"text":"The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements.","lang":"eng"}],"language":[{"iso":"eng"}],"type":"journal_article","quality_controlled":"1","ec_funded":1,"status":"public","publication":"Leibniz International Proceedings on Mathematics","date_updated":"2026-04-07T12:58:48Z","file_date_updated":"2022-07-27T09:25:53Z"},{"publication_status":"draft","arxiv":1,"date_created":"2024-03-08T09:54:20Z","title":"On the size of chromatic Delaunay mosaics","oa_version":"Preprint","oa":1,"author":[{"first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","last_name":"Biswas","full_name":"Biswas, Ranita"},{"orcid":"0000-0001-6249-0832","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano"},{"full_name":"Draganov, Ondrej","last_name":"Draganov","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","first_name":"Ondrej","orcid":"0000-0003-0464-3823"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"name":"Persistent Homology, Algorithms and Stochastic Geometry","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342"}],"month":"12","department":[{"_id":"HeEd"}],"corr_author":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_processing_charge":"No","related_material":{"record":[{"relation":"later_version","id":"20456","status":"public"},{"id":"15094","status":"public","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"_id":"15090","abstract":[{"text":"Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications.","lang":"eng"}],"external_id":{"arxiv":["2212.03121"]},"type":"preprint","day":"06","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.” <i>ArXiv</i>, n.d.","ista":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv, 2212.03121.","ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. <i>arXiv</i>.","apa":"Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). On the size of chromatic Delaunay mosaics. <i>arXiv</i>.","ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” <i>arXiv</i>. .","short":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","mla":"Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” <i>ArXiv</i>, 2212.03121."},"article_number":"2212.03121","year":"2022","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2022-12-06T00:00:00Z","OA_place":"repository","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2212.03121"}],"publication":"arXiv","date_updated":"2026-04-07T12:58:47Z","status":"public","ec_funded":1},{"type":"conference","quality_controlled":"1","abstract":[{"lang":"eng","text":"Generalizing Lee’s inductive argument for counting the cells of higher order Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse theoretic quantities for piecewise constant functions on planar arrangements. Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for 1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s first k-1 sublevel sets. We get similar expressions for the vertices, edges, and polygons of the order-k Voronoi tessellation."}],"_id":"9604","language":[{"iso":"eng"}],"has_accepted_license":"1","citation":{"ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells of order-k voronoi tessellations in ℝ<sup>3</sup> with morse theory. In: <i>Leibniz International Proceedings in Informatics</i>. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.16\">10.4230/LIPIcs.SoCG.2021.16</a>","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting cells of order-k voronoi tessellations in ℝ<sup>3</sup> with morse theory. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 16.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ<sup>3</sup> with Morse Theory.” In <i>Leibniz International Proceedings in Informatics</i>, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.16\">https://doi.org/10.4230/LIPIcs.SoCG.2021.16</a>.","mla":"Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in ℝ<sup>3</sup> with Morse Theory.” <i>Leibniz International Proceedings in Informatics</i>, vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.16\">10.4230/LIPIcs.SoCG.2021.16</a>.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting cells of order-k voronoi tessellations in ℝ<sup>3</sup> with morse theory,” in <i>Leibniz International Proceedings in Informatics</i>, Online, 2021, vol. 189.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2021). Counting cells of order-k voronoi tessellations in ℝ<sup>3</sup> with morse theory. In <i>Leibniz International Proceedings in Informatics</i> (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.16\">https://doi.org/10.4230/LIPIcs.SoCG.2021.16</a>"},"day":"02","year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["516"],"intvolume":"       189","article_number":"16","date_published":"2021-06-02T00:00:00Z","file_date_updated":"2021-06-28T13:11:39Z","date_updated":"2025-07-10T12:01:56Z","publication":"Leibniz International Proceedings in Informatics","status":"public","scopus_import":"1","ec_funded":1,"conference":{"name":"SoCG: International Symposium on Computational Geometry","start_date":"2021-06-07","end_date":"2021-06-11","location":"Online"},"publication_status":"published","file":[{"date_updated":"2021-06-28T13:11:39Z","file_id":"9611","relation":"main_file","creator":"asandaue","checksum":"22b11a719018b22ecba2471b51f2eb40","file_name":"2021_LIPIcs_Biswas.pdf","success":1,"content_type":"application/pdf","file_size":727817,"date_created":"2021-06-28T13:11:39Z","access_level":"open_access"}],"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959771849"]},"oa_version":"Published Version","title":"Counting cells of order-k voronoi tessellations in ℝ<sup>3</sup> with morse theory","alternative_title":["LIPIcs"],"date_created":"2021-06-27T22:01:48Z","doi":"10.4230/LIPIcs.SoCG.2021.16","oa":1,"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"Mathematics, Computer Science"},{"grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Persistent Homology, Algorithms and Stochastic Geometry"}],"department":[{"_id":"HeEd"}],"month":"06","author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastiano","orcid":"0000-0001-6249-0832"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza"}],"volume":189,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_processing_charge":"No"},{"article_processing_charge":"No","publisher":"Springer Nature","acknowledgement":"This work has been partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia through the project no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35 (RB).","doi":"10.1007/978-3-030-76657-3_10","volume":12708,"author":[{"first_name":"Lidija","full_name":"Čomić, Lidija","last_name":"Čomić"},{"first_name":"Rita","last_name":"Zrour","full_name":"Zrour, Rita"},{"last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle","first_name":"Gaëlle"},{"last_name":"Biswas","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","orcid":"0000-0002-5372-7890"},{"first_name":"Eric","full_name":"Andres, Eric","last_name":"Andres"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"department":[{"_id":"HeEd"}],"month":"05","publication_identifier":{"isbn":["9783030766566"],"eissn":["1611-3349"],"issn":["0302-9743"]},"title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","date_created":"2021-08-08T22:01:29Z","alternative_title":["LNCS"],"oa_version":"None","publication_status":"published","conference":{"end_date":"2021-05-27","location":"Uppsala, Sweden","name":"DGMM: International Conference on Discrete Geometry and Mathematical Morphology","start_date":"2021-05-24"},"status":"public","page":"152-163","ec_funded":1,"scopus_import":"1","date_updated":"2026-04-16T09:26:30Z","publication":"Discrete Geometry and Mathematical Morphology","isi":1,"intvolume":"     12708","year":"2021","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_published":"2021-05-16T00:00:00Z","_id":"9824","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We define a new compact coordinate system in which each integer triplet addresses a voxel in the BCC grid, and we investigate some of its properties. We propose a characterization of 3D discrete analytical planes with their topological features (in the Cartesian and in the new coordinate system) such as the interrelation between the thickness of the plane and the separability constraint we aim to obtain."}],"external_id":{"isi":["001286400400010"]},"type":"conference","quality_controlled":"1","citation":{"ieee":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered cubic grid - coordinate system and discrete analytical plane definition,” in <i>Discrete Geometry and Mathematical Morphology</i>, Uppsala, Sweden, 2021, vol. 12708, pp. 152–163.","short":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.","mla":"Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” <i>Discrete Geometry and Mathematical Morphology</i>, vol. 12708, Springer Nature, 2021, pp. 152–63, doi:<a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">10.1007/978-3-030-76657-3_10</a>.","apa":"Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., &#38; Andres, E. (2021). Body centered cubic grid - coordinate system and discrete analytical plane definition. In <i>Discrete Geometry and Mathematical Morphology</i> (Vol. 12708, pp. 152–163). Uppsala, Sweden: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">https://doi.org/10.1007/978-3-030-76657-3_10</a>","ista":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered cubic grid - coordinate system and discrete analytical plane definition. Discrete Geometry and Mathematical Morphology. DGMM: International Conference on Discrete Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163.","ama":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic grid - coordinate system and discrete analytical plane definition. In: <i>Discrete Geometry and Mathematical Morphology</i>. Vol 12708. Springer Nature; 2021:152-163. doi:<a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">10.1007/978-3-030-76657-3_10</a>","chicago":"Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” In <i>Discrete Geometry and Mathematical Morphology</i>, 12708:152–63. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/978-3-030-76657-3_10\">https://doi.org/10.1007/978-3-030-76657-3_10</a>."},"day":"16"},{"article_processing_charge":"No","corr_author":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publisher":"De Gruyter","doi":"10.1515/mathm-2020-0106","oa":1,"acknowledgement":"This work has been partially supported by the European Research Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. ","volume":4,"author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas","full_name":"Biswas, Ranita"},{"last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle","first_name":"Gaëlle"},{"full_name":"Zrour, Rita","last_name":"Zrour","first_name":"Rita"},{"first_name":"Eric","last_name":"Andres","full_name":"Andres, Eric"}],"department":[{"_id":"HeEd"}],"month":"11","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"article_type":"original","publication_identifier":{"issn":["2353-3390"]},"date_created":"2021-03-16T08:55:19Z","title":"Digital objects in rhombic dodecahedron grid","oa_version":"Published Version","publication_status":"published","file":[{"date_created":"2021-03-22T08:56:37Z","file_size":3668725,"content_type":"application/pdf","success":1,"access_level":"open_access","relation":"main_file","date_updated":"2021-03-22T08:56:37Z","creator":"dernst","file_id":"9272","file_name":"2020_MathMorpholTheoryAppl_Biswas.pdf","checksum":"4a1043fa0548a725d464017fe2483ce0"}],"page":"143-158","status":"public","ec_funded":1,"issue":"1","file_date_updated":"2021-03-22T08:56:37Z","date_updated":"2025-04-14T07:48:35Z","publication":"Mathematical Morphology - Theory and Applications","intvolume":"         4","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"year":"2020","date_published":"2020-11-17T00:00:00Z","abstract":[{"text":"Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system.","lang":"eng"}],"_id":"9249","language":[{"iso":"eng"}],"quality_controlled":"1","type":"journal_article","day":"17","citation":{"mla":"Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” <i>Mathematical Morphology - Theory and Applications</i>, vol. 4, no. 1, De Gruyter, 2020, pp. 143–58, doi:<a href=\"https://doi.org/10.1515/mathm-2020-0106\">10.1515/mathm-2020-0106</a>.","short":"R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158.","ieee":"R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects in rhombic dodecahedron grid,” <i>Mathematical Morphology - Theory and Applications</i>, vol. 4, no. 1. De Gruyter, pp. 143–158, 2020.","apa":"Biswas, R., Largeteau-Skapin, G., Zrour, R., &#38; Andres, E. (2020). Digital objects in rhombic dodecahedron grid. <i>Mathematical Morphology - Theory and Applications</i>. De Gruyter. <a href=\"https://doi.org/10.1515/mathm-2020-0106\">https://doi.org/10.1515/mathm-2020-0106</a>","ama":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic dodecahedron grid. <i>Mathematical Morphology - Theory and Applications</i>. 2020;4(1):143-158. doi:<a href=\"https://doi.org/10.1515/mathm-2020-0106\">10.1515/mathm-2020-0106</a>","ista":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 4(1), 143–158.","chicago":"Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital Objects in Rhombic Dodecahedron Grid.” <i>Mathematical Morphology - Theory and Applications</i>. De Gruyter, 2020. <a href=\"https://doi.org/10.1515/mathm-2020-0106\">https://doi.org/10.1515/mathm-2020-0106</a>."},"has_accepted_license":"1"},{"doi":"10.1007/978-3-030-14085-4_3","month":"02","date_updated":"2022-01-27T14:25:17Z","publication":"21st IAPR International Conference on Discrete Geometry for Computer Imagery","volume":11414,"author":[{"orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita","last_name":"Biswas"},{"full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin","first_name":"Gaëlle"},{"full_name":"Zrour, Rita","last_name":"Zrour","first_name":"Rita"},{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"}],"publisher":"Springer Berlin Heidelberg","status":"public","page":"27-37","article_processing_charge":"No","extern":"1","type":"conference","quality_controlled":"1","conference":{"name":"DGCI: International Conference on Discrete Geometry for Computer Imagery","start_date":"2019-03-26","end_date":"2019-03-28","location":"Marne-la-Vallée, France"},"publication_status":"published","abstract":[{"text":"We propose a new non-orthogonal basis to express the 3D Euclidean space in terms of a regular grid. Every grid point, each represented by integer 3-coordinates, corresponds to rhombic dodecahedron centroid. Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. A characterization of a 3D digital sphere with relevant topological features is proposed as well with the help of a 48 symmetry that comes with the new coordinate system.","lang":"eng"}],"_id":"6163","language":[{"iso":"eng"}],"citation":{"ama":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Rhombic dodecahedron grid—coordinate system and 3D digital object definitions. In: <i>21st IAPR International Conference on Discrete Geometry for Computer Imagery</i>. Vol 11414. Berlin, Heidelberg: Springer Berlin Heidelberg; 2019:27-37. doi:<a href=\"https://doi.org/10.1007/978-3-030-14085-4_3\">10.1007/978-3-030-14085-4_3</a>","ista":"Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2019. Rhombic dodecahedron grid—coordinate system and 3D digital object definitions. 21st IAPR International Conference on Discrete Geometry for Computer Imagery. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 11414, 27–37.","chicago":"Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Rhombic Dodecahedron Grid—Coordinate System and 3D Digital Object Definitions.” In <i>21st IAPR International Conference on Discrete Geometry for Computer Imagery</i>, 11414:27–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2019. <a href=\"https://doi.org/10.1007/978-3-030-14085-4_3\">https://doi.org/10.1007/978-3-030-14085-4_3</a>.","mla":"Biswas, Ranita, et al. “Rhombic Dodecahedron Grid—Coordinate System and 3D Digital Object Definitions.” <i>21st IAPR International Conference on Discrete Geometry for Computer Imagery</i>, vol. 11414, Springer Berlin Heidelberg, 2019, pp. 27–37, doi:<a href=\"https://doi.org/10.1007/978-3-030-14085-4_3\">10.1007/978-3-030-14085-4_3</a>.","ieee":"R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Rhombic dodecahedron grid—coordinate system and 3D digital object definitions,” in <i>21st IAPR International Conference on Discrete Geometry for Computer Imagery</i>, Marne-la-Vallée, France, 2019, vol. 11414, pp. 27–37.","short":"R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, in:, 21st IAPR International Conference on Discrete Geometry for Computer Imagery, Springer Berlin Heidelberg, Berlin, Heidelberg, 2019, pp. 27–37.","apa":"Biswas, R., Largeteau-Skapin, G., Zrour, R., &#38; Andres, E. (2019). Rhombic dodecahedron grid—coordinate system and 3D digital object definitions. In <i>21st IAPR International Conference on Discrete Geometry for Computer Imagery</i> (Vol. 11414, pp. 27–37). Berlin, Heidelberg: Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-030-14085-4_3\">https://doi.org/10.1007/978-3-030-14085-4_3</a>"},"day":"23","year":"2019","publication_identifier":{"isbn":["978-3-6624-6446-5","978-3-6624-6447-2"],"issn":["0302-9743","1611-3349"]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","intvolume":"     11414","place":"Berlin, Heidelberg","oa_version":"None","date_published":"2019-02-23T00:00:00Z","alternative_title":["LNCS"],"title":"Rhombic dodecahedron grid—coordinate system and 3D digital object definitions","date_created":"2019-03-21T12:12:19Z"},{"date_updated":"2022-01-27T15:26:39Z","publication":"19th International Workshop","volume":11255,"author":[{"last_name":"Koshti","full_name":"Koshti, Girish","first_name":"Girish"},{"full_name":"Biswas, Ranita","last_name":"Biswas","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle","first_name":"Gaëlle"},{"last_name":"Zrour","full_name":"Zrour, Rita","first_name":"Rita"},{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"},{"first_name":"Partha","last_name":"Bhowmick","full_name":"Bhowmick, Partha"}],"month":"11","doi":"10.1007/978-3-030-05288-1_7","extern":"1","article_processing_charge":"No","publisher":"Springer","page":"82-96","status":"public","citation":{"chicago":"Koshti, Girish, Ranita Biswas, Gaëlle Largeteau-Skapin, Rita Zrour, Eric Andres, and Partha Bhowmick. “Sphere Construction on the FCC Grid Interpreted as Layered Hexagonal Grids in 3D.” In <i>19th International Workshop</i>, 11255:82–96. Cham: Springer, 2018. <a href=\"https://doi.org/10.1007/978-3-030-05288-1_7\">https://doi.org/10.1007/978-3-030-05288-1_7</a>.","ista":"Koshti G, Biswas R, Largeteau-Skapin G, Zrour R, Andres E, Bhowmick P. 2018. Sphere construction on the FCC grid interpreted as layered hexagonal grids in 3D. 19th International Workshop. IWCIA: International Workshop on Combinatorial Image Analysis, LNCS, vol. 11255, 82–96.","ama":"Koshti G, Biswas R, Largeteau-Skapin G, Zrour R, Andres E, Bhowmick P. Sphere construction on the FCC grid interpreted as layered hexagonal grids in 3D. In: <i>19th International Workshop</i>. Vol 11255. Cham: Springer; 2018:82-96. doi:<a href=\"https://doi.org/10.1007/978-3-030-05288-1_7\">10.1007/978-3-030-05288-1_7</a>","apa":"Koshti, G., Biswas, R., Largeteau-Skapin, G., Zrour, R., Andres, E., &#38; Bhowmick, P. (2018). Sphere construction on the FCC grid interpreted as layered hexagonal grids in 3D. In <i>19th International Workshop</i> (Vol. 11255, pp. 82–96). Cham: Springer. <a href=\"https://doi.org/10.1007/978-3-030-05288-1_7\">https://doi.org/10.1007/978-3-030-05288-1_7</a>","short":"G. Koshti, R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, P. Bhowmick, in:, 19th International Workshop, Springer, Cham, 2018, pp. 82–96.","ieee":"G. Koshti, R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, and P. Bhowmick, “Sphere construction on the FCC grid interpreted as layered hexagonal grids in 3D,” in <i>19th International Workshop</i>, Porto, Portugal, 2018, vol. 11255, pp. 82–96.","mla":"Koshti, Girish, et al. “Sphere Construction on the FCC Grid Interpreted as Layered Hexagonal Grids in 3D.” <i>19th International Workshop</i>, vol. 11255, Springer, 2018, pp. 82–96, doi:<a href=\"https://doi.org/10.1007/978-3-030-05288-1_7\">10.1007/978-3-030-05288-1_7</a>."},"day":"22","abstract":[{"lang":"eng","text":"In this paper, we propose an algorithm to build discrete spherical shell having integer center and real-valued inner and outer radii on the face-centered cubic (FCC) grid. We address the problem by mapping it to a 2D scenario and building the shell layer by layer on hexagonal grids with additive manufacturing in mind. The layered hexagonal grids get shifted according to need as we move from one layer to another and forms the FCC grid in 3D. However, we restrict our computation strictly to 2D in order to utilize symmetry and simplicity."}],"_id":"6164","language":[{"iso":"eng"}],"type":"conference","conference":{"location":"Porto, Portugal","end_date":"2018-11-24","start_date":"2018-11-22","name":"IWCIA: International Workshop on Combinatorial Image Analysis"},"publication_status":"published","quality_controlled":"1","date_published":"2018-11-22T00:00:00Z","alternative_title":["LNCS"],"title":"Sphere construction on the FCC grid interpreted as layered hexagonal grids in 3D","date_created":"2019-03-21T12:16:58Z","oa_version":"None","intvolume":"     11255","place":"Cham","year":"2018","publication_identifier":{"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["978-3-030-05287-4"],"eisbn":["978-3-030-05288-1"]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9"},{"day":"10","citation":{"chicago":"Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Polyhedra of Graceful Spheres and Circular Geodesics.” <i>Discrete Applied Mathematics</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.dam.2015.11.017\">https://doi.org/10.1016/j.dam.2015.11.017</a>.","ama":"Biswas R, Bhowmick P, Brimkov VE. On the polyhedra of graceful spheres and circular geodesics. <i>Discrete Applied Mathematics</i>. 2017;216:362-375. doi:<a href=\"https://doi.org/10.1016/j.dam.2015.11.017\">10.1016/j.dam.2015.11.017</a>","ista":"Biswas R, Bhowmick P, Brimkov VE. 2017. On the polyhedra of graceful spheres and circular geodesics. Discrete Applied Mathematics. 216, 362–375.","apa":"Biswas, R., Bhowmick, P., &#38; Brimkov, V. E. (2017). On the polyhedra of graceful spheres and circular geodesics. <i>Discrete Applied Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.dam.2015.11.017\">https://doi.org/10.1016/j.dam.2015.11.017</a>","mla":"Biswas, Ranita, et al. “On the Polyhedra of Graceful Spheres and Circular Geodesics.” <i>Discrete Applied Mathematics</i>, vol. 216, Elsevier, 2017, pp. 362–75, doi:<a href=\"https://doi.org/10.1016/j.dam.2015.11.017\">10.1016/j.dam.2015.11.017</a>.","short":"R. Biswas, P. Bhowmick, V.E. Brimkov, Discrete Applied Mathematics 216 (2017) 362–375.","ieee":"R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the polyhedra of graceful spheres and circular geodesics,” <i>Discrete Applied Mathematics</i>, vol. 216. Elsevier, pp. 362–375, 2017."},"type":"journal_article","quality_controlled":"1","publication_status":"published","_id":"5799","abstract":[{"text":"We construct a polyhedral surface called a graceful surface, which provides best possible approximation to a given sphere regarding certain criteria. In digital geometry terms, the graceful surface is uniquely characterized by its minimality while guaranteeing the connectivity of certain discrete (polyhedral) curves defined on it. The notion of “gracefulness” was first proposed in Brimkov and Barneva (1999) and shown to be useful for triangular mesh discretization through graceful planes and graceful lines. In this paper we extend the considerations to a nonlinear object such as a sphere. In particular, we investigate the properties of a discrete geodesic path between two voxels and show that discrete 3D circles, circular arcs, and Mobius triangles are all constructible on a graceful sphere, with guaranteed minimum thickness and the desired connectivity in the discrete topological space.","lang":"eng"}],"language":[{"iso":"eng"}],"oa_version":"None","date_published":"2017-01-10T00:00:00Z","title":"On the polyhedra of graceful spheres and circular geodesics","date_created":"2019-01-08T20:41:12Z","year":"2017","publication_identifier":{"issn":["0166-218X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       216","month":"01","date_updated":"2021-01-12T08:03:33Z","publication":"Discrete Applied Mathematics","volume":216,"author":[{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas","full_name":"Biswas, Ranita"},{"full_name":"Bhowmick, Partha","last_name":"Bhowmick","first_name":"Partha"},{"full_name":"Brimkov, Valentin E.","last_name":"Brimkov","first_name":"Valentin E."}],"doi":"10.1016/j.dam.2015.11.017","extern":"1","publisher":"Elsevier","status":"public","page":"362-375"},{"intvolume":"        59","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2017","publication_identifier":{"issn":["09249907"]},"title":"On the functionality and usefulness of Quadraginta octants of naive sphere","date_created":"2019-01-08T20:42:08Z","date_published":"2017-09-01T00:00:00Z","oa_version":"None","language":[{"iso":"eng"}],"_id":"5800","abstract":[{"lang":"eng","text":"This paper presents a novel study on the functional gradation of coordinate planes in connection with the thinnest and tunnel-free (i.e., naive) discretization of sphere in the integer space. For each of the 48-symmetric quadraginta octants of naive sphere with integer radius and integer center, we show that the corresponding voxel set forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as its functional plane. We use this fundamental property to prove several other theoretical results for naive sphere. First, the quadraginta octants form symmetry groups and subgroups with certain equivalent topological properties. Second, a naive sphere is always unique and consists of fewest voxels. Third, it is efficiently constructible from its functional-plane projection. And finally, a special class of 4-symmetric discrete 3D circles can be constructed on a naive sphere based on back projection from the functional plane."}],"publication_status":"published","quality_controlled":"1","type":"journal_article","citation":{"chicago":"Biswas, Ranita, and Partha Bhowmick. “On the Functionality and Usefulness of Quadraginta Octants of Naive Sphere.” <i>Journal of Mathematical Imaging and Vision</i>. Springer Nature, 2017. <a href=\"https://doi.org/10.1007/s10851-017-0718-4\">https://doi.org/10.1007/s10851-017-0718-4</a>.","ista":"Biswas R, Bhowmick P. 2017. On the functionality and usefulness of Quadraginta octants of naive sphere. Journal of Mathematical Imaging and Vision. 59(1), 69–83.","ama":"Biswas R, Bhowmick P. On the functionality and usefulness of Quadraginta octants of naive sphere. <i>Journal of Mathematical Imaging and Vision</i>. 2017;59(1):69-83. doi:<a href=\"https://doi.org/10.1007/s10851-017-0718-4\">10.1007/s10851-017-0718-4</a>","apa":"Biswas, R., &#38; Bhowmick, P. (2017). On the functionality and usefulness of Quadraginta octants of naive sphere. <i>Journal of Mathematical Imaging and Vision</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10851-017-0718-4\">https://doi.org/10.1007/s10851-017-0718-4</a>","ieee":"R. Biswas and P. Bhowmick, “On the functionality and usefulness of Quadraginta octants of naive sphere,” <i>Journal of Mathematical Imaging and Vision</i>, vol. 59, no. 1. Springer Nature, pp. 69–83, 2017.","short":"R. Biswas, P. Bhowmick, Journal of Mathematical Imaging and Vision 59 (2017) 69–83.","mla":"Biswas, Ranita, and Partha Bhowmick. “On the Functionality and Usefulness of Quadraginta Octants of Naive Sphere.” <i>Journal of Mathematical Imaging and Vision</i>, vol. 59, no. 1, Springer Nature, 2017, pp. 69–83, doi:<a href=\"https://doi.org/10.1007/s10851-017-0718-4\">10.1007/s10851-017-0718-4</a>."},"day":"01","status":"public","page":"69-83","publisher":"Springer Nature","extern":"1","issue":"1","doi":"10.1007/s10851-017-0718-4","volume":59,"author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","orcid":"0000-0002-5372-7890"},{"last_name":"Bhowmick","full_name":"Bhowmick, Partha","first_name":"Partha"}],"publication":"Journal of Mathematical Imaging and Vision","date_updated":"2021-01-12T08:03:34Z","month":"09"},{"month":"08","date_updated":"2022-01-27T15:34:25Z","publication":"20th IAPR International Conference","volume":10502,"author":[{"full_name":"Dwivedi, Shivam","last_name":"Dwivedi","first_name":"Shivam"},{"first_name":"Aniket","full_name":"Gupta, Aniket","last_name":"Gupta"},{"first_name":"Siddhant","last_name":"Roy","full_name":"Roy, Siddhant"},{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","full_name":"Biswas, Ranita","last_name":"Biswas"},{"last_name":"Bhowmick","full_name":"Bhowmick, Partha","first_name":"Partha"}],"doi":"10.1007/978-3-319-66272-5_28","extern":"1","publisher":"Springer Nature","page":"347-359","status":"public","article_processing_charge":"No","citation":{"mla":"Dwivedi, Shivam, et al. “Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space.” <i>20th IAPR International Conference</i>, vol. 10502, Springer Nature, 2017, pp. 347–59, doi:<a href=\"https://doi.org/10.1007/978-3-319-66272-5_28\">10.1007/978-3-319-66272-5_28</a>.","ieee":"S. Dwivedi, A. Gupta, S. Roy, R. Biswas, and P. Bhowmick, “Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space,” in <i>20th IAPR International Conference</i>, Vienna, Austria, 2017, vol. 10502, pp. 347–359.","short":"S. Dwivedi, A. Gupta, S. Roy, R. Biswas, P. Bhowmick, in:, 20th IAPR International Conference, Springer Nature, Cham, 2017, pp. 347–359.","apa":"Dwivedi, S., Gupta, A., Roy, S., Biswas, R., &#38; Bhowmick, P. (2017). Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space. In <i>20th IAPR International Conference</i> (Vol. 10502, pp. 347–359). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-66272-5_28\">https://doi.org/10.1007/978-3-319-66272-5_28</a>","ama":"Dwivedi S, Gupta A, Roy S, Biswas R, Bhowmick P. Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space. In: <i>20th IAPR International Conference</i>. Vol 10502. Cham: Springer Nature; 2017:347-359. doi:<a href=\"https://doi.org/10.1007/978-3-319-66272-5_28\">10.1007/978-3-319-66272-5_28</a>","ista":"Dwivedi S, Gupta A, Roy S, Biswas R, Bhowmick P. 2017. Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space. 20th IAPR International Conference. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 10502, 347–359.","chicago":"Dwivedi, Shivam, Aniket Gupta, Siddhant Roy, Ranita Biswas, and Partha Bhowmick. “Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space.” In <i>20th IAPR International Conference</i>, 10502:347–59. Cham: Springer Nature, 2017. <a href=\"https://doi.org/10.1007/978-3-319-66272-5_28\">https://doi.org/10.1007/978-3-319-66272-5_28</a>."},"day":"22","type":"conference","publication_status":"published","quality_controlled":"1","conference":{"name":"DGCI: International Conference on Discrete Geometry for Computer Imagery","start_date":"2017-09-19","end_date":"2017-09-21","location":"Vienna, Austria"},"abstract":[{"lang":"eng","text":"Space filling circles and spheres have various applications in mathematical imaging and physical modeling. In this paper, we first show how the thinnest (i.e., 2-minimal) model of digital sphere can be augmented to a space filling model by fixing certain “simple voxels” and “filler voxels” associated with it. Based on elementary number-theoretic properties of such voxels, we design an efficient incremental algorithm for generation of these space filling spheres with successively increasing radius. The novelty of the proposed technique is established further through circular space filling on 3D digital plane. As evident from a preliminary set of experimental result, this can particularly be useful for parallel computing of 3D Voronoi diagrams in the digital space."}],"_id":"5801","language":[{"iso":"eng"}],"oa_version":"None","date_published":"2017-08-22T00:00:00Z","date_created":"2019-01-08T20:42:22Z","alternative_title":["LNCS"],"title":"Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space","publication_identifier":{"isbn":["978-3-319-66271-8"],"eisbn":["978-3-319-66272-5"],"issn":["0302-9743"],"eissn":["1611-3349"]},"year":"2017","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","intvolume":"     10502","place":"Cham"},{"extern":"1","article_processing_charge":"No","status":"public","page":"388-398","publisher":"Springer Nature","author":[{"first_name":"Eric","full_name":"Andres, Eric","last_name":"Andres"},{"orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","full_name":"Biswas, Ranita"},{"full_name":"Bhowmick, Partha","last_name":"Bhowmick","first_name":"Partha"}],"volume":10502,"publication":"20th IAPR International Conference","date_updated":"2022-01-27T15:38:35Z","month":"08","doi":"10.1007/978-3-319-66272-5_31","title":"Digital primitives defined by weighted focal set","alternative_title":["LNCS"],"date_created":"2019-01-08T20:42:39Z","date_published":"2017-08-22T00:00:00Z","oa_version":"None","place":"Cham","intvolume":"     10502","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publication_identifier":{"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["978-3-319-66271-8"],"eisbn":["978-3-319-66272-5"]},"year":"2017","day":"22","citation":{"chicago":"Andres, Eric, Ranita Biswas, and Partha Bhowmick. “Digital Primitives Defined by Weighted Focal Set.” In <i>20th IAPR International Conference</i>, 10502:388–98. Cham: Springer Nature, 2017. <a href=\"https://doi.org/10.1007/978-3-319-66272-5_31\">https://doi.org/10.1007/978-3-319-66272-5_31</a>.","ama":"Andres E, Biswas R, Bhowmick P. Digital primitives defined by weighted focal set. In: <i>20th IAPR International Conference</i>. Vol 10502. Cham: Springer Nature; 2017:388-398. doi:<a href=\"https://doi.org/10.1007/978-3-319-66272-5_31\">10.1007/978-3-319-66272-5_31</a>","ista":"Andres E, Biswas R, Bhowmick P. 2017. Digital primitives defined by weighted focal set. 20th IAPR International Conference. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 10502, 388–398.","apa":"Andres, E., Biswas, R., &#38; Bhowmick, P. (2017). Digital primitives defined by weighted focal set. In <i>20th IAPR International Conference</i> (Vol. 10502, pp. 388–398). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-66272-5_31\">https://doi.org/10.1007/978-3-319-66272-5_31</a>","mla":"Andres, Eric, et al. “Digital Primitives Defined by Weighted Focal Set.” <i>20th IAPR International Conference</i>, vol. 10502, Springer Nature, 2017, pp. 388–98, doi:<a href=\"https://doi.org/10.1007/978-3-319-66272-5_31\">10.1007/978-3-319-66272-5_31</a>.","ieee":"E. Andres, R. Biswas, and P. Bhowmick, “Digital primitives defined by weighted focal set,” in <i>20th IAPR International Conference</i>, Vienna, Austria, 2017, vol. 10502, pp. 388–398.","short":"E. Andres, R. Biswas, P. Bhowmick, in:, 20th IAPR International Conference, Springer Nature, Cham, 2017, pp. 388–398."},"language":[{"iso":"eng"}],"_id":"5802","abstract":[{"text":"This papers introduces a definition of digital primitives based on focal points and weighted distances (with positive weights). The proposed definition is applicable to general dimensions and covers in its gamut various regular curves and surfaces like circles, ellipses, digital spheres and hyperspheres, ellipsoids and k-ellipsoids, Cartesian k-ovals, etc. Several interesting properties are presented for this class of digital primitives such as space partitioning, topological separation, and connectivity properties. To demonstrate further the potential of this new way of defining digital primitives, we propose, as extension, another class of digital conics defined by focus-directrix combination.","lang":"eng"}],"publication_status":"published","conference":{"start_date":"2017-09-19","name":"DGCI: International Conference on Discrete Geometry for Computer Imagery","location":"Vienna, Austria","end_date":"2017-09-21"},"quality_controlled":"1","type":"conference"},{"place":"Cham","publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["978-3-319-59107-0","978-3-319-59108-7"]},"alternative_title":["LNCS"],"title":"Construction of persistent Voronoi diagram on 3D digital plane","date_created":"2019-01-08T20:42:56Z","oa_version":"None","publication_status":"published","conference":{"start_date":"2017-06-19","name":"IWCIA: International Workshop on Combinatorial Image Analysis","location":"Plovdiv, Bulgaria","end_date":"2017-06-21"},"article_processing_charge":"No","publisher":"Springer Nature","extern":"1","doi":"10.1007/978-3-319-59108-7_8","volume":10256,"author":[{"orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita","last_name":"Biswas"},{"last_name":"Bhowmick","full_name":"Bhowmick, Partha","first_name":"Partha"}],"month":"05","department":[{"_id":"HeEd"}],"intvolume":"     10256","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","year":"2017","date_published":"2017-05-17T00:00:00Z","abstract":[{"text":"Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept.","lang":"eng"}],"_id":"5803","language":[{"iso":"eng"}],"quality_controlled":"1","type":"book_chapter","citation":{"apa":"Biswas, R., &#38; Bhowmick, P. (2017). Construction of persistent Voronoi diagram on 3D digital plane. In <i>Combinatorial image analysis</i> (Vol. 10256, pp. 93–104). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-59108-7_8\">https://doi.org/10.1007/978-3-319-59108-7_8</a>","short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104.","ieee":"R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in <i>Combinatorial image analysis</i>, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104.","mla":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” <i>Combinatorial Image Analysis</i>, vol. 10256, Springer Nature, 2017, pp. 93–104, doi:<a href=\"https://doi.org/10.1007/978-3-319-59108-7_8\">10.1007/978-3-319-59108-7_8</a>.","chicago":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In <i>Combinatorial Image Analysis</i>, 10256:93–104. Cham: Springer Nature, 2017. <a href=\"https://doi.org/10.1007/978-3-319-59108-7_8\">https://doi.org/10.1007/978-3-319-59108-7_8</a>.","ista":"Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.","ama":"Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital plane. In: <i>Combinatorial Image Analysis</i>. Vol 10256. Cham: Springer Nature; 2017:93-104. doi:<a href=\"https://doi.org/10.1007/978-3-319-59108-7_8\">10.1007/978-3-319-59108-7_8</a>"},"day":"17","status":"public","page":"93-104","publication":"Combinatorial image analysis","date_updated":"2022-01-28T07:48:24Z"},{"intvolume":"      9667","year":"2016","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_published":"2016-06-02T00:00:00Z","language":[{"iso":"eng"}],"_id":"5805","abstract":[{"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.","lang":"eng"}],"type":"book_chapter","quality_controlled":"1","citation":{"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.","short":"N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context, Springer Nature, Cham, 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>","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>","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.","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>."},"day":"02","page":"253-264","status":"public","date_updated":"2022-01-28T08:01:22Z","publication":"Computational Topology in Image Context","place":"Cham","publication_identifier":{"eisbn":["978-3-319-39441-1"],"isbn":["978-3-319-39440-4"],"eissn":["1611-3349"],"issn":["0302-9743"]},"date_created":"2019-01-08T20:44:24Z","title":"On some local topological properties of naive discrete sphere","alternative_title":["LNCS"],"oa_version":"None","publication_status":"published","conference":{"end_date":"2016-06-17","location":"Marseille, France","name":"CTIC: Computational Topology in Image Context","start_date":"2016-06-15"},"article_processing_charge":"No","publisher":"Springer Nature","extern":"1","doi":"10.1007/978-3-319-39441-1_23","author":[{"last_name":"Sen","full_name":"Sen, Nabhasmita","first_name":"Nabhasmita"},{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas","full_name":"Biswas, Ranita"},{"last_name":"Bhowmick","full_name":"Bhowmick, Partha","first_name":"Partha"}],"volume":9667,"department":[{"_id":"HeEd"}],"month":"06"},{"date_updated":"2022-01-28T08:10:11Z","publication":"Discrete Geometry for Computer Imagery","page":"256-267","status":"public","type":"conference","quality_controlled":"1","_id":"5806","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"}],"language":[{"iso":"eng"}],"citation":{"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.","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>","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>.","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.","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>.","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>"},"day":"09","year":"2016","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","intvolume":"      9647","date_published":"2016-04-09T00:00:00Z","doi":"10.1007/978-3-319-32360-2_20","month":"04","department":[{"_id":"HeEd"}],"volume":9647,"author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Partha","full_name":"Bhowmick, Partha","last_name":"Bhowmick"}],"publisher":"Springer Nature","article_processing_charge":"No","extern":"1","publication_status":"published","conference":{"location":"Nantes, France","end_date":"2016-04-20","start_date":"2016-04-18","name":"DGCI: International Conference on Discrete Geometry for Computer Imagery"},"publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["978-3-319-32359-6"],"eisbn":["978-3-319-32360-2"]},"place":"Cham","oa_version":"None","title":"On functionality of quadraginta octants of naive sphere with application to circle drawing","date_created":"2019-01-08T20:44:37Z","alternative_title":["LNCS"]}]