| Attributs | Valeurs |
|---|
| type
| |
| Is Part Of
| |
| Subject
| |
| Title
| - Curve cuspless reconstruction via sub-Riemannian geometry
|
| Date
| |
| has manifestation of work
| |
| related by
| |
| Author
| |
| Abstract
| - We consider the problem of minimizing \hbox{$\int_{0}^ell \sqrt{\xi^2 +K^2(s)}\, {\rm d}s $} 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.
|
| article type
| |
| publisher identifier
| |
| Date Copyrighted
| |
| Rights
| - © EDP Sciences, SMAI, 2014
|
| Rights Holder
| |
| is part of this journal
| |
| is primary topic
of | |
