On restricting planar curve evolution to finite dimensional implicit subspaces with non-Euclidean metric

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This paper deals with restricting curve evolution to a finite and not necessarily flat space of curves, obtained as a subspace of the infinite dimensional space of planar curves endowed with the usual but weak parametrization invariant curve L 2-metric.
We first show how to solve differential equations on a finite dimensional Riemannian manifold defined implicitly as a submanifold of a parameterized one, which in turn may be a Riemannian submanifold of an infinite dimensional one, using some optimal control techniques.
We give an elementary example of the technique on a spherical submanifold of a 3-sphere and then a series of examples on a highly non-linear subspace of the space of closed spline curves, where we have restricted mean curvature motion, Geodesic Active contours and compute geodesic between two curves.
TidsskriftJournal of Mathematical Imaging and Vision
Udgave nummer3
Sider (fra-til)226-240
Antal sider15
StatusUdgivet - 2010

ID: 23090366