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M. Iglesias-Ham, E. Garcia, W. Kropatsch, R. González-Díaz:
"Algorithm to Compute a Minimal Length Basis of Representative Cocycles of Cohomology Generators";
Vortrag: 3rd International Workshop on Computational Topology in Image Context - CTIC 2010, Chipiona; 10.09.2010 - 12.09.2010; in: "3rd Workshop on Computational Topology in Image Context (CTIC)", Roc\'io Gonz\'alez D\'iaz and Pedro Real Jurado, University of Sevilla, Spain (2010), ISSN: 1885-4508; S. 121 - 127.

Abstract An algorithm to compute a minimal length basis of representative cocycles of
cohomology generators for 2D images is proposed. We based the computations on combinatorial
pyramids foreseeing its future extension to 3D objects. In our research we are looking
for a more refined topological description of deformable 2D and 3D shapes, than they are
the often used Betti numbers. We define contractions on the object edges toward the inner
of the object until the boundaries touch each other, building an irregular pyramid with
this purpose. We show the possible use of the algorithm seeking the minimal cocycles that
connect the convex deficiencies on a human silhouette. We used minimality in the number
of cocycle edges in the basis, which is a robust description to rotations and noise.
Keyworks cohomology; combinatorial pyramids; representative cocycles of cohomology
generators.