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An Elementary Proof of the Equivalence between 2D and 3D Classical Snakes and Geodesic Active Contours

Gilles Aubert 1 Laure Blanc-Féraud
1 ARIANA - Inverse problems in earth monitoring
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : Recently, Caselles et al. have shown in the equivalence between a classical snake problem of Kass et al. and a geodesic active contour model. The PDE derived from the geodesic problem gives an evolution equation for active contours which is very powerfull for image segmentation since changes of topology are allowed using the level set implementation. However in Caselles' paper the equivalence with classical snake is only shown for 2D images with 1D curves, by using concepts of Hamiltonian theory which have no meanings for active contours. This paper propose a proof using only elementary calculus of mathematical analysis. This proof is also valid in the 3D case for active surfaces.
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https://hal.inria.fr/inria-00073349
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Submitted on : Wednesday, May 24, 2006 - 12:35:45 PM
Last modification on : Thursday, February 3, 2022 - 11:16:48 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:43:22 PM

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  • HAL Id : inria-00073349, version 1

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Gilles Aubert, Laure Blanc-Féraud. An Elementary Proof of the Equivalence between 2D and 3D Classical Snakes and Geodesic Active Contours. RR-3340, INRIA. 1998. ⟨inria-00073349⟩

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