Ponencia
One More Step Towards Well-Composedness of Cell Complexes over nD Pictures
Autor/es | Boutry, Nicolas
González Díaz, Rocío Jiménez Rodríguez, María José |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2019 |
Fecha de depósito | 2021-10-06 |
Publicado en |
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ISBN/ISSN | 978-3-030-14084-7 0302-9743 |
Resumen | An nD pure regular cell complex K is weakly well-composed
(wWC) if, for each vertex v of K, the set of n-cells incident to v is
face-connected. In previous work we proved that if an nD picture I is
digitally well composed ... An nD pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K, the set of n-cells incident to v is face-connected. In previous work we proved that if an nD picture I is digitally well composed (DWC) then the cubical complex Q(I) associated to I is wWC. If I is not DWC, we proposed a combinatorial algorithm to “locally repair” Q(I) obtaining an nD pure simplicial complex PS(I) homotopy equivalent to Q(I) which is always wWC. In this paper we give a combinatorial procedure to compute a simplicial complex PS(¯I) which decomposes the complement space of |PS(I)| and prove that PS(¯I) is also wWC. This paper means one more step on the way to our ultimate goal: to prove that the nD repaired complex is continuously well-composed (CWC), that is, the boundary of its continuous analog is an (n − 1)- manifold. |
Agencias financiadoras | Ministerio de Economía y Competitividad (MINECO). España |
Identificador del proyecto | MTM2015-67072-P |
Cita | Boutry, N., González Díaz, R. y Jiménez Rodríguez, M.J. (2019). One More Step Towards Well-Composedness of Cell Complexes over nD Pictures. En DGCI 2019: 21st IAPR International Conference on Discrete Geometry for Computer Imagery (101-114), Marne-la-Vallée, France: Springer. |
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