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

- Authors:
- DOI:
- 10.1007/s10851-010-0218-2
- Abstract:
- 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.
- Type:
- Journal article
- Language:
- English
- Published in:
- Journal of Mathematical Imaging and Vision, 2010, Vol 38, Issue 3, p. 226-240
- Keywords:
- The Faculty of Science
- Main Research Area:
- Science/technology
- Publication Status:
- Published
- Review type:
- Peer Review
- Submission year:
- 2010
- Scientific Level:
- Scientific
- ID:
- 103463719