Curve cuspless reconstruction via sub-Riemannian geometry - Département de mathématiques appliquées
Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2014

Curve cuspless reconstruction via sub-Riemannian geometry

Résumé

We consider the problem of minimizing for a planar curve having fixed initial and final positions and directions. The total length ℓ is free. Here s is the arclength parameter, K(s) is the curvature of the curve and ξ > 0 is a fixed constant. This problem comes from a model of geometry of vision due to Petitot, Citti and Sarti. We study existence of local and global minimizers for this problem. We prove that if for a certain choice of boundary conditions there is no global minimizer, then there is neither a local minimizer nor a geodesic. We finally give properties of the set of boundary conditions for which there exists a solution to the problem.
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hal-01097159 , version 1 (03-09-2024)

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Ugo Boscain, Remco Duits, Francesco Rossi, Yuri Sachkov. Curve cuspless reconstruction via sub-Riemannian geometry. ESAIM: Control, Optimisation and Calculus of Variations, 2014, 20 (3), pp.748-770. ⟨10.1051/cocv/2013082⟩. ⟨hal-01097159⟩
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