Conference
New Characterizations of Full Convexity
| العنوان: | New Characterizations of Full Convexity |
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| المؤلفون: | Feschet, Fabien, Lachaud, Jacques-Olivier |
| المساهمون: | Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Université Clermont Auvergne 2017-2020 (UCA 2017-2020 )-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques (LAMA), Université Savoie Mont Blanc (USMB Université de Savoie Université de Chambéry )-Centre National de la Recherche Scientifique (CNRS), Sara Brunetti, Andrea Frosini, Simone Rinaldi, ANR-22-CE46-0006,StableProxies,Traitement numérique stable de la géométrie et calcul haute-performance sur des données géométriques hétérogènes(2022) |
| المصدر: | Lecture Notes in Computer Science ; International Conference on Discrete Geometry and Mathematical Morphology ; https://hal.science/hal-04735219 ; International Conference on Discrete Geometry and Mathematical Morphology, Apr 2024, Firenze, Italy, Italy. pp.41-53, ⟨10.1007/978-3-031-57793-2_4⟩ |
| بيانات النشر: | HAL CCSD Springer Nature Switzerland |
| سنة النشر: | 2024 |
| مصطلحات موضوعية: | Digital geometry, Digital convexity, Full convexity, ACM: I.: Computing Methodologies/I.3: COMPUTER GRAPHICS/I.3.5: Computational Geometry and Object Modeling, [INFO]Computer Science [cs], [MATH]Mathematics [math] |
| جغرافية الموضوع: | Firenze, Italy |
| الوصف: | International audience ; Full convexity has been recently proposed as an alternative definition of digital convexity. In contrast to classical definitions, fully convex sets are always connected and even simply connected whatever the dimension, while remaining digitally convex in the usual sense. Several characterizations were proposed in former works, either based on lattice intersection enumeration with several convex hulls, or using the idempotence of an envelope operator. We continue these efforts by studying simple properties of real convex sets whose digital counterparts remain largely misunderstood. First we study if we can define full convexity through variants of the usual continuous convexity via segments inclusion, i.e. “for all pair of points of X, the straight segment joining them must lie within the set X”. We show an equivalence of full convexity with this segment convexity in dimension 2, and counterexamples starting from dimension 3. If we consider now d-simplices instead of a segment (2-simplex), we achieve an equivalence in arbitrary dimension d. Secondly, we exhibit another characterization of full convexity, which is recursive with respect to the dimension and uses simple axis projections. This latter characterization leads to two immediate applications: a proof that digital balls are indeed fully convex, and a natural progressive measure of full convexity for arbitrary digital sets. |
| نوع الوثيقة: | conference object |
| اللغة: | English |
| DOI: | 10.1007/978-3-031-57793-2_4 |
| الاتاحة: | https://hal.science/hal-04735219 https://hal.science/hal-04735219v1/document https://hal.science/hal-04735219v1/file/feschet-2024-dgmm.pdf https://doi.org/10.1007/978-3-031-57793-2_4 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.C27BAD53 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1007/978-3-031-57793-2_4 |
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