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Capítulo de Libro
Extending the notion of AT-Model for integer homology computation
(2007)
When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing (co)homology, representative (co)cycles of (co)homology generators and the cup product on cohomology of ...
Capítulo de Libro
A Graph-with-Loop Structure for a Topological Representation of 3D Objects
(2007)
Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the height function), we construct a graph G h (K) which is an extension of the Reeb graph R h (|K|). ...
Capítulo de Libro
A bio-inspired software for segmenting digital images.
(2010)
Segmentation in computer vision refers to the process of partitioning a digital image into multiple segments (sets of pixels). It has several features which make it suitable for techniques inspired by nature. It can be ...
Capítulo de Libro
A homological–based description of subdivided nD objects
(2011)
We present here a topo–geometrical description of a subdivided nD object called homological spanning forest representation. This representation is a convenient tool in order to completely control not only geometrical, but ...
Capítulo de Libro
Homological computation using spanning trees
(2009)
We introduce here a new F2 homology computation algorithm based on a generalization of the spanning tree technique on a finite 3-dimensional cell complex K embedded in ℝ3. We demonstrate that the complexity of this algorithm ...
Capítulo de Libro
Getting topological information for a 80-adjacency doxel-based 4D volume through a polytopal cell complex
(2009)
Given an 80-adjacency doxel-based digital four-dimensional hypervolume V, we construct here an associated oriented 4–dimensional polytopal cell complex K(V), having the same integer homological information (that related ...
Capítulo de Libro
Segmentation in 2D and 3D image using Tissue-Like P System
(2009)
Membrane Computing is a biologically inspired computational model. Its devices are called P systems and they perform computations by applying a finite set of rules in a synchronous, maximally parallel way. In this paper, ...
Capítulo de Libro
Reusing integer homology information of binary digital images
(2006)
In this paper, algorithms for computing integer (co)homology of a simplicial complex of any dimension are designed, extending the work done in [1,2,3]. For doing this, the homology of the object is encoded in an ...
Capítulo de Libro
Cell AT-models for digital volumes
(2009)
In [4], given a binary 26-adjacency voxel-based digital volume V, the homological information (that related to n-dimensional holes: connected components, ”tunnels” and cavities) is extracted from a linear map (called ...
Capítulo de Libro
Reducing Computational Costs in the Basic Perturbation Lemma
(2006)
Homological Perturbation Theory [11, 13] is a well-known general method for computing homology, but its main algorithm, the Basic Perturbation Lemma, presents, in general, high computational costs. In this paper, we ...