Algorithm to Compute a Minimal Length Basis of Representative Cocycles of Cohomology Generators

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