Computer Science – Computer Vision and Pattern Recognition
Scientific paper
2011-05-23
Discrete Applied Mathematics, Volume 147, Issues 2-3, 15 April 2005, Pages 245-263
Computer Science
Computer Vision and Pattern Recognition
Special Issue: Advances in Discrete Geometry and Topology
Scientific paper
10.1016/j.dam.2004.09.014
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 ring of 3D digital binary-valued pictures is tested by means of a small program visualizing the different steps of the method. Some examples concerning topological thinning, the visualization of representative (co)cycles of (co)homology generators and the computation of the cup product on the cohomology of simple pictures are showed.
Gonzalez-Diaz Rocio
Real Pedro
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