@inbook{531c78dd20104cb68d8818c75e33a536,

title = "Cuspless sub-Riemannian geodesics within the Euclidean motion group SE(d)",

abstract = "We consider the problem P curve of minimizing TeX for a planar curve having fixed initial and final positions and directions. Here ¿ is the curvature of the curve with free total length l. This problem comes from a 2D model of geometry of vision due to Petitot, Citti and Sarti. Here we will provide a general theory on cuspless sub-Riemannian geodesics within a sub-Riemannian manifold in SE(d), with d¿=¿2, where we solve for their momentum in the general d-dimensional case. We will explicitly solve the curve optimization problem P curve in 2D (i.e. d¿=¿2) with a corresponding cuspless sub-Riemannian geodesic lifted problem defined on a sub-Riemannian manifold within SE(2). We also derive the solutions of P curve in 3D (i.e. d¿=¿3) with a corresponding cuspless sub-Riemannian geodesic problem defined on a sub-Riemannian manifold within SE(3). Besides exact formulas for cuspless sub-Riemannian geodesics, we derive their geometric properties, and we provide a full analysis of the range of admissible end-conditions. Furthermore, we apply this analysis to the modeling of association fields in neurophysiology",

author = "R. Duits and A. Ghosh and {Dela Haije}, T.C.J. and Y. Sachkov",

year = "2014",

doi = "10.1007/978-3-642-34444-2_5",

language = "English",

isbn = "978-3-642-34443-5",

series = "Lecture Notes in Morphogenesis",

publisher = "Springer",

pages = "173--215",

editor = "G. Citti and A. Sarti",

booktitle = "Neuromathematics of Vision",

address = "Germany",

}