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Integral operators for computing homology generators at any dimension


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Opened Access Integral operators for computing homology generators at any dimension

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Author: González Díaz, Rocío
Jiménez Rodríguez, María José
Medrano Garfia, Belén
Real Jurado, Pedro
Molina Abril, Helena
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I
Date: 2008
Published in: Progress in Pattern Recognition, Image Analysis and Applications, Lecture Notes in Computer Science, Vol. 5197, p. 356-363
Document type: Chapter of Book
Abstract: Starting from an nD geometrical 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.
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