Homological Tree-Based Strategies for Image Analysis

Authors:
P. Real;H. Molina-Abril;Walter Kropatsch
Affiliations:
Departamento de Matematica Aplicada I, Universidad de Sevilla, ;Departamento de Matematica Aplicada I, Universidad de Sevilla, and Faculty of Informatics, PRIP Group, Vienna University of Technology, ;Faculty of Informatics, PRIP Group, Vienna University of Technology,
Venue:
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
Year:
2009

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Abstract

Homological characteristics of digital objects can be obtained in a straightforward manner computing an algebraic map 驴 over a finite cell complex K (with coefficients in the finite field $\textbf{F}_2=\{0,1\}$) which represents the digital object [9]. Computable homological information includes the Euler characteristic, homology generators and representative cycles, higher (co)homology operations, etc. This algebraic map 驴 is described in combinatorial terms using a mixed three-level forest. Different strategies changing only two parameters of this algorithm for computing 驴 are presented. Each one of those strategies gives rise to different maps, although all of them provides the same homological information for K. For example, tree-based structures useful in image analysis like topological skeletons and pyramids can be obtained as subgraphs of this forest.