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

 

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Opened Access Algorithm to Compute a Minimal Length Basis of Representative Cocycles of Cohomology Generators
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Author: Iglesias Ham, Mabel
García Reyes, Edel
Kropatsch, Walter G.
González Díaz, Rocío
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I
Date: 2010
Published in: Image-A : Applicable Mathematics in Image Engineering, 1 (3), 121-128
Document type: Article
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.
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URI: http://hdl.handle.net/11441/26215

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