Presentation
Euler Well-Composedness
Author/s | Boutry, Nicolas
González Díaz, Rocío Jiménez Rodríguez, María José Paluzo Hidalgo, Eduardo |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2020 |
Deposit Date | 2021-10-06 |
Published in |
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ISBN/ISSN | 978-3-030-51001-5 0302-9743 |
Abstract | In this paper, we de ne a new
avour of well-composedness,
called Euler well-composedness, in the general setting of regular cell
complexes: A regular cell complex is Euler well-composed if the Euler
characteristic of ... In this paper, we de ne a new avour of well-composedness, called Euler well-composedness, in the general setting of regular cell complexes: A regular cell complex is Euler well-composed if the Euler characteristic of the link of each boundary vertex is 1. A cell decomposi- tion of a picture I is a pair of regular cell complexes K(I), K( I) such that K(I) (resp. K( I)) is a topological and geometrical model represent- ing I (resp. its complementary, I). Then, a cell decomposition of a pic- ture I is self-dual Euler well-composed if both K(I) and K( I) are Euler well-composed. We prove in this paper that, rst, self-dual Euler well- composedness is equivalent to digital well-composedness in dimension 2 and 3, and second, in dimension 4, self-dual Euler well-composedness implies digital well-composedness, though the converse is not true. |
Citation | Boutry, N., González Díaz, R., Jiménez Rodríguez, M.J. y Paluzo Hidalgo, E. (2020). Euler Well-Composedness. En IWCIA 2020: 20th International Workshop on Combinatorial Image Analysis (3-19), Novi Sad, Serbia: Springer. |
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