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Homological Tree-Based Strategies for Image Analysis

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Computer Analysis of Images and Patterns (CAIP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5702))

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Abstract

Homological characteristics of digital objects can be obtained in a straightforward manner computing an algebraic map φ 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 φ is described in combinatorial terms using a mixed three-level forest. Different strategies changing only two parameters of this algorithm for computing φ 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.

This work has been partially supported by PAICYT research project FQM-296, “Andalusian research project” PO6-TIC-02268, Spanish MEC project MTM2006-03722 and the Austrian Science Fund under grant P20134-N13.

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Authors and Affiliations

  1. Departamento de Matematica Aplicada I, Universidad de Sevilla,  

    P. Real & H. Molina-Abril

  2. Faculty of Informatics, PRIP Group, Vienna University of Technology,  

    H. Molina-Abril & Walter Kropatsch

Authors
  1. P. Real
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  2. H. Molina-Abril
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  3. Walter Kropatsch
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Münster, Einsteinstrasse 62, 48149, Münster, Germany

    Xiaoyi Jiang

  2. Institute of Mathematics and Computing Science, University of Groningen, Nijenborgh 9, 9747, Groningen, AG, The Netherlands

    Nicolai Petkov

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© 2009 Springer-Verlag Berlin Heidelberg

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Real, P., Molina-Abril, H., Kropatsch, W. (2009). Homological Tree-Based Strategies for Image Analysis. In: Jiang, X., Petkov, N. (eds) Computer Analysis of Images and Patterns. CAIP 2009. Lecture Notes in Computer Science, vol 5702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03767-2_40

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  • DOI: https://doi.org/10.1007/978-3-642-03767-2_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03766-5

  • Online ISBN: 978-3-642-03767-2

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