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

Olivier Faugeras 1
1 ROBOTVIS - Computer Vision and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
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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Rapport
[Research Report] RR-2053, INRIA. 1993
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https://hal.inria.fr/inria-00074619
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Soumis le : mercredi 24 mai 2006 - 15:55:07
Dernière modification le : samedi 27 janvier 2018 - 01:30:56
Document(s) archivé(s) le : mardi 12 avril 2011 - 17:49:52

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Olivier Faugeras. Cartan's moving frame method and its application to the geometry and evolution of curves in the Euclidean, affine and projective planes. [Research Report] RR-2053, INRIA. 1993. 〈inria-00074619〉

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