Curve cuspless reconstruction via sub-Riemannian geometry

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

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Abstract

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
Publishers.n.
Number of pages28
Publication statusPublished - 2012

Publication series

NamearXiv.org
Volume1203.3089 [math.OC]

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Boscain, U., Duits, R., Rossi, F., & Sachkov, Y. (2012). Curve cuspless reconstruction via sub-Riemannian geometry. (arXiv.org; Vol. 1203.3089 [math.OC]). s.n.