Irregular Graph Pyramids and Representative Cocycles of Cohomology Generators

Authors:
Rocio Gonzalez-Diaz;Adrian Ion;Mabel Iglesias-Ham;Walter G. Kropatsch
Affiliations:
Applied Math Department, University of Seville, Spain and Pattern Recognition and Image Processing Group, Vienna University of Technology,;Pattern Recognition and Image Processing Group, Vienna University of Technology,;Pattern Recognition Department, CENATAV, Havana, Cuba and Pattern Recognition and Image Processing Group, Vienna University of Technology,;Pattern Recognition and Image Processing Group, Vienna University of Technology,
Venue:
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Year:
2009

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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.