Curve cuspless reconstruction via sub-Riemannian geometry

U. Boscain, R. Duits, F. Rossi, Y. Sachkov

Research output: Book/ReportReportAcademic

91 Downloads (Pure)


We consider the problem of minimizing {formula omitted} for a planar curve having fixed initial and final positions and directions. The total length L is free. Here s is the variable of arclength parametrization, K(s) is the curvature of the curve and ¿>0 a parameter. 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.
Original languageEnglish
Number of pages28
Publication statusPublished - 2012

Publication series
Volume1203.3089 [math.OC]


Dive into the research topics of 'Curve cuspless reconstruction via sub-Riemannian geometry'. Together they form a unique fingerprint.

Cite this