Ponencia
Generating Second Order (Co)homological Information within AT-Model Context
Autor/es | Real Jurado, Pedro
Molina Abril, Helena Díaz del Río, Fernando Onchis, Darian M. |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Arquitectura y Tecnología de Computadores |
Fecha de publicación | 2019 |
Fecha de depósito | 2020-02-26 |
Publicado en |
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ISBN/ISSN | 978-3-030-10827-4 0302-9743 |
Resumen | In this paper we design a new family of relations between
(co)homology classes, working with coefficients in a field and starting
from an AT-model (Algebraic Topological Model) AT(C) of a finite cell
complex C These ... In this paper we design a new family of relations between (co)homology classes, working with coefficients in a field and starting from an AT-model (Algebraic Topological Model) AT(C) of a finite cell complex C These relations are induced by elementary relations of type “to be in the (co)boundary of” between cells. This high-order connectivity information is embedded into a graph-based representation model, called Second Order AT-Region-Incidence Graph (or AT-RIG) of C. This graph, having as nodes the different homology classes of C, is in turn, computed from two generalized abstract cell complexes, called primal and dual AT-segmentations of C. The respective cells of these two complexes are connected regions (set of cells) of the original cell complex C, which are specified by the integral operator of AT(C). In this work in progress, we successfully use this model (a) in experiments for discriminating topologically different 3D digital objects, having the same Euler characteristic and (b) in designing a parallel algorithm for computing potentially significant (co)homological information of 3D digital objects. |
Identificador del proyecto | MTM2016-81030-P
TEC2012-37868-C04-02 |
Cita | Real Jurado, P., Molina Abril, H., Díaz del Río, F. y Onchis, D.M. (2019). Generating Second Order (Co)homological Information within AT-Model Context. En CTIC 2019 : 7th International Workshop on Computational Topology in Image Contex (68-81), Málaga, España: Springer. |
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