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Equi-affine Invariant Geometries of Articulated Objects

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Outdoor and Large-Scale Real-World Scene Analysis

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7474))

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Abstract

We introduce an (equi-)affine invariant geometric structure by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to evaluate a new form of geodesic distances and to construct an invariant Laplacian from which local and global diffusion geometry is constructed. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis.

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Author information

Authors and Affiliations

  1. Computer Science Department, Technion, Israel

    Dan Raviv & Ron Kimmel

  2. School of Electrical Engineering, Tel Aviv University, Israel

    Alexander M. Bronstein

  3. Faculty of Informatics, Università della Svizzera Italiana, Switzerland

    Michael M. Bronstein

  4. Department of Applied Mathematics, Tel Aviv University, Israel

    Nir Sochen

Authors
  1. Dan Raviv
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  2. Alexander M. Bronstein
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  3. Michael M. Bronstein
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  4. Ron Kimmel
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  5. Nir Sochen
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Editor information

Editors and Affiliations

  1. College of Computing Building, Georgia Institute of Technology, 801 Atlantic Drive, 30332-0280, Atlanta, GA, USA

    Frank Dellaert

  2. Department of Computer Science, University of North Carolina at Chapel Hill, Brooks Computer Science Building, CB#3175, 27599, Chapel Hill, NC, USA

    Jan-Michael Frahm

  3. CVG - Institute of Visual Computing, Department of Computer Science, ETH Zurich, CNB G105, Universitaetstrasse 6, 8092, Zurich, Switzerland

    Marc Pollefeys

  4. Institute for Information Processing (TNT), Leibniz Universität, Appelstr. 9A, 30167, Hannover, Germany

    Laura Leal-Taixé

  5. Institute for Information Processing (TNT), Leibniz Universität, Appelstr. 9A, 30167, Hannover, Germany

    Bodo Rosenhahn

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© 2012 Springer-Verlag Berlin Heidelberg

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Raviv, D., Bronstein, A.M., Bronstein, M.M., Kimmel, R., Sochen, N. (2012). Equi-affine Invariant Geometries of Articulated Objects. In: Dellaert, F., Frahm, JM., Pollefeys, M., Leal-Taixé, L., Rosenhahn, B. (eds) Outdoor and Large-Scale Real-World Scene Analysis. Lecture Notes in Computer Science, vol 7474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34091-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-34091-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34090-1

  • Online ISBN: 978-3-642-34091-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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