Curve cuspless reconstruction via sub-Riemannian geometry - Archive ouverte HAL
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.
Fichier principal
Vignette du fichier
cocv130082.pdf (1.21 Mo) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte
Licence
Copyright (Tous droits réservés)

Dates et versions

hal-01097159 , version 1 (03-09-2024)

Licence

Copyright (Tous droits réservés)

Identifiants

Citer

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⟩
311 Consultations
13 Téléchargements

Altmetric

Partager

More