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International Workshop on Algebraic Frames for the Perception-Action Cycle

AFPAC 1997: Algebraic Frames for the Perception-Action Cycle pp 207–218Cite as

Algebraic and geometric tools to compute projective and permutation invariants

  • Processing of the 3D Visual Space
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1315))

Abstract

This paper studies the computation of projective invariants in pairs of images from uncalibrated cameras, and presents a detailed study of the projective and permutation invariants for configurations of points and/or lines. We give two basic computational approaches, one algebraic and one geometric, and also the relations between the invariants computed by different approaches. In each case, we show how to compute invariants in projective space assuming that the points and lines have already been reconstructed in an arbitrary projective basis, and also, how to compute them directly from image coordinates in a pair of views using only point and line correspondences and the fundamental matrix. Finally, we develop combinations of those projective invariants which are insensitive to permutations of the geometric primitives of each of the basic configurations.

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Author information

Authors and Affiliations

  1. INRIA Rhône-Alpes, 655 Av. de l'Europe, 38330, Montbonnot Saint Martin, France

    Gabriella Csurka

  2. INRIA Sophia-Antipolis, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Olivier Faugeras

Authors
  1. Gabriella Csurka
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  2. Olivier Faugeras
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Editor information

Gerald Sommer Jan J. Koenderink

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© 1997 Springer-Verlag Berlin Heidelberg

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Csurka, G., Faugeras, O. (1997). Algebraic and geometric tools to compute projective and permutation invariants. In: Sommer, G., Koenderink, J.J. (eds) Algebraic Frames for the Perception-Action Cycle. AFPAC 1997. Lecture Notes in Computer Science, vol 1315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017869

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  • DOI: https://doi.org/10.1007/BFb0017869

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63517-8

  • Online ISBN: 978-3-540-69589-9

  • eBook Packages: Springer Book Archive

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