Chapter of Book
Advanced homology computation of digital volumes via cell complexes
Author/s | Molina Abril, Helena
![]() ![]() ![]() ![]() ![]() ![]() ![]() Real Jurado, Pedro ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2008 |
Deposit Date | 2015-12-10 |
Published in |
|
Abstract | Given a 3D binary voxel-based digital object V, an algorithm for computing homological information for V via a polyhedral cell complex is designed. By homological information we understand not only Betti numbers, representative ... Given a 3D binary voxel-based digital object V, an algorithm for computing homological information for V via a polyhedral cell complex is designed. By homological information we understand not only Betti numbers, representative cycles of homology classes and homological classification of cycles but also the computation of homology numbers related additional algebraic structures defined on homology (coproduct in homology, product in cohomology, (co)homology operations,...). The algorithm is mainly based on the following facts: a) a local 3D-polyhedrization of any 2×2×2 configuration of mutually 26-adjacent black voxels providing a coherent cell complex at global level; b) a description of the homology of a digital volume as an algebraic-gradient vector field on the cell complex (see Discrete Morse Theory [5], AT-model method [7,5]). Saving this vector field, we go further obtaining homological information at no extra time processing cost. |
Files | Size | Format | View | Description |
---|---|---|---|---|
Advanced homology computation.pdf | 1.298Mb | ![]() | View/ | |
This item appears in the following collection(s)
Except where otherwise noted, this item's license is described as: Atribución-NoComercial-CompartirIgual 4.0 Internacional
Related items
Showing items related by title, author, creator and subject.
-
Article
Adaptative parallel simulators for bioinspired computing models
Martínez del Amor, Miguel Ángel; Pérez Hurtado de Mendoza, Ignacio; Orellana Martín, David; Pérez Jiménez, Mario de Jesús (Elsevier, 2020)In the Membrane Computing area, P systems are unconventional devices of computation inspired by the structure and processes ...
-
Chapter of Book
Cell AT-models for digital volumes
Real Jurado, Pedro; Molina Abril, Helena (2009)In [4], given a binary 26-adjacency voxel-based digital volume V, the homological information (that related to n-dimensional ...
-
Article
Evolutionary membrane computing: A comprehensive survey and new results
Zhang, Gexiang; Gheorghe, Marian; Pan, Linqiang; Pérez Jiménez, Mario de Jesús (Elsevier, 2014)Evolutionary membrane computing is an important research direction of membrane computing that aims to explore the complex ...