Discrete Curve Evolution on Arbitrary Triangulated 3D Mesh

Discrete Curve Evolution (DCE) algorithm is used to eliminate objects’ contour distortions while at the same time preserve the perceptual appearance at a level sufficient for object recognition. This method is widely used for shape similarity measure, skeleton pruning and salient point detection of binary objects on a regular 2D grid. Our paper aims at describing a new DCE algorithm for an arbitrary triangulated 3D mesh. The difficulty lies in the calculation of a vertex cost function for an object contour, as on a 3D surface the notion of Euclidean distance cannot be used. It is also very difficult to compute a geodesic angle between lines connecting vertices. We introduce a new cost function for border vertex which is only based on geodesic distances. We apply the proposed algorithm on vertex sets to compute an approximation of original contours, extract salient points and prune skeletons. The experimental results justify the robustness of our method with respect to noise distortions.