Geometric curve flows on parametric manifolds

Planar geometric curve evolution equations are the basis for many image processing and computer vision algorithms. In order to extend the use of these algorithms to images painted on manifolds it is necessary to devise numerical schemes for the implementation of the geodesic generalizations of these equations. We present efficient numerical schemes for the implementation of the classical geodesic curve evolution equations on parametric manifolds. The efficiency of the schemes is due to their implementation on the parameterization plane rather than on the manifold itself. We demonstrate these flows on various manifolds and use them to implement two applications: scale space of images painted on manifolds and segmentation by an active contour model.

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