Integral Operators for Computing Homology Generators at Any Dimension

Authors:
Rocio Gonzalez-Diaz;Maria Jose Jimenez;Belen Medrano;Helena Molina-Abril;Pedro Real
Affiliations:
Applied Math Department, University of Seville, Spain;Applied Math Department, University of Seville, Spain;Applied Math Department, University of Seville, Spain;Applied Math Department, University of Seville, Spain;Applied Math Department, University of Seville, Spain
Venue:
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Year:
2008

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Abstract

Starting from an nDgeometrical 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 based on the construction of a sequence of elementary chain homotopies (integral operators) which algebraically connect the initial object with a simplified one with the same homological information than the former.