Learn More
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)
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 "(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)
This paper presents a set of tools to compute topological information of sim-plicial 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)
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)
—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)(More)