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International Symposium on Visual Computing

ISVC 2006: Advances in Visual Computing pp 235–244Cite as

Computing Homology for Surfaces with Generalized Maps: Application to 3D Images

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4292))

Abstract

In this paper, we present an algorithm which allows to compute efficiently generators of the first homology group of a closed surface, orientable or not. Starting with an initial subdivision of a surface, we simplify it to its minimal form (minimal refers to the number of cells), while preserving its homology. Homology generators can thus be directly deduced from the minimal representation of the initial surface. Finally, we show how this algorithm can be used in a 3D labelled image in order to compute homology of each region described by its boundary.

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Author information

Authors and Affiliations

  1. SIC – bât. SP2MI, Bvd M. et P. Curie, BP 30179, 86962 Futuroscope Chasseneuil Cedex, France

    Guillaume Damiand & Laurent Fuchs

  2. PRIP, Vienna University of Technology, Favoritenstr. 9/1832, A-1040, Vienna, Austria

    Samuel Peltier

Authors
  1. Guillaume Damiand
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  2. Samuel Peltier
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  3. Laurent Fuchs
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada, Reno, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. Digital Image Research Center, Kingston University, London, UK

    Paolo Remagnino

  6. Intel, 95052, Santa Clara, CA, USA

    Ara Nefian

  7. University of California, 430, Computer Science Building, 92697-3425, Irvine, CA, USA

    Gopi Meenakshisundaram

  8. Institute for Data Analysis and Visualization, P.O. Box

    Valerio Pascucci

  9. Department of Computer Science and Engineering, Czech Technical University in Prague, Czech

    Jiri Zara

  10. Rockwell Scientific, 1049 Camino Dos Rios, 91360, Thousand Oaks, CA, USA

    Jose Molineros

  11. Computer Graphics Group, Bielefeld University, D-33501, Bielefeld, Germany

    Holger Theisel

  12. Hewlett Packard Labs, Palo Alto, CA, USA

    Tom Malzbender

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© 2006 Springer-Verlag Berlin Heidelberg

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Cite this paper

Damiand, G., Peltier, S., Fuchs, L. (2006). Computing Homology for Surfaces with Generalized Maps: Application to 3D Images. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2006. Lecture Notes in Computer Science, vol 4292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11919629_25

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  • DOI: https://doi.org/10.1007/11919629_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-48626-8

  • Online ISBN: 978-3-540-48627-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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