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Integral Invariant Signatures

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Part of the book series:Lecture Notes in Computer Science ((LNCS,volume 3024))

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Abstract

For shapes represented as closed planar contours, we introduce a class of functionals that are invariant with respect to the Euclidean and similarity group, obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential cousins, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (in the limit), they are not as sensitive to noise in the data. We exploit the integral invariants to define a unique signature, from which the original shape can be reconstructed uniquely up to the symmetry group, and a notion of scale-space that allows analysis at multiple levels of resolution. The invariant signature can be used as a basis to define various notions of distance between shapes, and we illustrate the potential of the integral invariant representation for shape matching on real and synthetic data.

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Author information

Authors and Affiliations

  1. University of California at Los Angeles, Los Angeles, CA, 90024, USA

    Siddharth Manay & Stefano Soatto

  2. University of Oxford, Oxford, OX1 3BW, UK

    Byung-Woo Hong

  3. Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Anthony J. Yezzi

Authors
  1. Siddharth Manay

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  2. Byung-Woo Hong

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  3. Anthony J. Yezzi

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  4. Stefano Soatto

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Editor information

Editors and Affiliations

  1. Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Prague 6, Czech Republic

    Tomás Pajdla

  2. Center for Machine Perception, Dept. of Cybernetics, Faculty of Elec. Eng., Czech Technical University in Prague, Karlovo nám. 13, 121 35, Prague, Czech Rep.

    Jiří Matas

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© 2004 Springer-Verlag Berlin Heidelberg

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Manay, S., Hong, BW., Yezzi, A.J., Soatto, S. (2004). Integral Invariant Signatures. In: Pajdla, T., Matas, J. (eds) Computer Vision - ECCV 2004. ECCV 2004. Lecture Notes in Computer Science, vol 3024. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24673-2_8

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