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Irregular graph pyramids and representative cocycles of cohomology generators


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Opened Access Irregular graph pyramids and representative cocycles of cohomology generators

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Author: González Díaz, Rocío
Ion, Adrián
Iglesias Ham, Mabel
Kropatsch, Walter G.
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I
Date: 2009
Published in: Graph-Based Representations in Pattern Recognition, 5534, 263-272.
Document type: Article
Abstract: Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed.
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