Curve cuspless reconstruction via sub-Riemannian geometry - Département de mathématiques appliquées
Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2014

Curve cuspless reconstruction via sub-Riemannian geometry

Abstract

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
Origin Publisher files allowed on an open archive
licence
Copyright

Dates and versions

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

Licence

Copyright

Identifiers

Cite

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⟩
300 View
9 Download

Altmetric

Share

More