Curve evolution in subspaces

Authors:
Aditya Tatu;François Lauze;Mads Nielsen;Ole Fogh Olsen
Affiliations:
DIKU, University of Copenhagen, Copenhagen East, Denmark;Nordic Bioscience Imaging A/S, Herlev, Denmark;DIKU, University of Copenhagen, Copenhagen East, Denmark and Nordic Bioscience Imaging A/S, Herlev, Denmark;IT University of Copenhagen, Copenhagen South, Denmark
Venue:
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Year:
2007

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Abstract

Curve evolution forms the basis of active contour algorithms used for image segmentation. In many applications the curve under evolution needs to be restricted to the shape space given by some example shapes, or some linear space given by a set of basis vectors. Also, when a curve evolution is carried out on a computer, the evolution is approximated by some suitable discretization. Here too, the evolution is implicitly carried out in some subspace and not in the space of all curves. Hence it is important to study curve evolution in subspace of all curves. We look at a formulation that describes curve evolution restricted to subspaces. We give numerical methods and examples of a formulation for curvature flow for curves restricted to the B-spline subspace.