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A distance on curves modulo rigid transformations
Institution:Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
Abstract:We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations). Given two curves, the distance between them is defined as the infimum of an energy functional which, roughly speaking, measures the extent to which the jet field of the first curve needs to be rotated to match up with the jet field of the second curve. We show that this energy functional attains a global minimum on the appropriate function space, and we derive a set of first-order ODEs for the minimizer.
Keywords:primary"}  {"#name":"keyword"  "$":{"id":"kw0020"}  "$$":[{"#name":"text"  "_":"58E30  secondary"}  {"#name":"keyword"  "$":{"id":"kw0030"}  "$$":[{"#name":"text"  "_":"49Q10  53A04
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