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Cartan's moving frame method and its application to the geometry and evolution of curves in the euclidean, affine and projective planes

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Applications of Invariance in Computer Vision (AICV 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 825))

Abstract

This article is a general introduction to Cartan's moving frame method which is elegant, simple, and of an algorithmic nature. We have demonstrated how to use it systematically on three examples relevant to computer vision, curves in the euclidean, affine and projective planes, and derived the corresponding Frenet equations. We have then used these equations to show that the analysis of the deformation of plane curves according to an intrinsic heat equation could be done in a common framework, yielding very similar expressions for the evolution of the three curvature invariants.

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Authors and Affiliations

  1. INRIA Sophia-Antipolis, 2004 Route des Lucioles, B.P. 93, 06902, Sophia-Antipolis, France

    Olivier Faugeras

Authors
  1. Olivier Faugeras
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Editor information

Joseph L. Mundy Andrew Zisserman David Forsyth

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© 1994 Springer-Verlag Berlin Heidelberg

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Faugeras, O. (1994). Cartan's moving frame method and its application to the geometry and evolution of curves in the euclidean, affine and projective planes. In: Mundy, J.L., Zisserman, A., Forsyth, D. (eds) Applications of Invariance in Computer Vision. AICV 1993. Lecture Notes in Computer Science, vol 825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58240-1_2

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  • DOI: https://doi.org/10.1007/3-540-58240-1_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58240-3

  • Online ISBN: 978-3-540-48583-4

  • eBook Packages: Springer Book Archive

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