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- Rocío González-Díaz, Pedro Real Jurado
- Discrete Applied Mathematics
- 2005

We propose a method for computing the cohomology ring of three–dimensional (3D) digital binary–valued pictures. We obtain the cohomology ring of a 3D digital binary–valued picture I, via a simplicial complex K(I) topologically representing (up to isomorphisms of pictures) the picture I. The usefulness of a simplicial description of the “digital” cohomology… (More)

- Rocío González-Díaz, Pedro Real Jurado
- DGCI
- 2003

We propose a method for computing the Z2–cohomology ring of a simplicial complex uniquely associated with a three–dimensional digital binary–valued picture I. Binary digital pictures are represented on the standard grid Z, in which all grid points have integer coordinates. Considering a particular 14–neighbourhood system on this grid, we construct a unique… (More)

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in… (More)

In this paper, we deal with the problem of the computation of the homology of a finite simplicial complex after an “elementary simplicial perturbation” process such as the inclusion or elimination of a maximal simplex or an edge contraction. To this aim we compute an algebraic topological model that is an special chain homotopy equivalence connecting the… (More)

- Rocío González-Díaz, Pedro Real Jurado
- J. Symb. Comput.
- 2005

This paper offers an algorithmic solution to the problem of obtaining “economical” formulae for some maps in Simplicial Topology, having, in principle, a high computational cost in their evaluation. In particular, maps of this kind are used for defining cohomology operations at the cochain level. As an example, we obtain an explicit combinatorial… (More)

Starting from an nD geometrical object, a cellular subdivision of such an object provides an algebraic counterpart from which homology information can be computed. In this paper, we develop a process to drastically reduce the amount of data that represent the original object, with the purpose of a subsequent homology computation. The technique applied is… (More)

- Rocío González-Díaz, María José Jiménez, Belén Medrano, Pedro Real Jurado
- Discrete Applied Mathematics
- 2009

This paper presents a set of tools to compute topological information of simplicial complexes, tools that are applicable to extract topological information from digital pictures. A simplicial complex is encoded in a (non-unique) algebraic-topological format called AM-model. An AM-model for a given object K is determined by a concrete chain homotopy and it… (More)

In this paper, algorithms for computing integer (co)homology of a simplicial complex of any dimension are designed, extending the work done in (7; 9). For doing this, the homology of the object is encoded in an algebraic-topological format (that we call AM-model). Moreover, in the case of 3D binary digital images, having as input AM-models for the images I… (More)

This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary{valued images, each of them de ned as 2D arrays of pixels. Our answer is based on an algebraictopological coding, called AT{model, for a nD (n = 2; 3) digital binaryvalued image I consisting simply in taking I together with an algebraic object depending… (More)

In this abstract we extend ideas and results submitted to [3] in which a new codification of Local Binary Patterns (LBP) is given using combinatorial maps and a method for obtaining a representative LBP image is developed based on merging regions and Minimum Contrast Algorithm. The LBP code characterizes the topological category (max, min, slope, saddle) of… (More)