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.
Original language | English |
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Journal | Journal of Mathematical Imaging and Vision |
Volume | 38 |
Issue number | 3 |
Pages (from-to) | 226-240 |
Number of pages | 15 |
ISSN | 0924-9907 |
DOIs | |
Publication status | Published - 2010 |
- Faculty of Science
Research areas
ID: 23090366