Vector (self) snakes: A geometric framework for color, texture, and multiscale image segmentation

A partial-differential-equations (PDE') based geometric framework for segmentation of vector-valued images is described in this paper. The first component of this approach is based on two dimensional geometric active contours deforming from their initial position towards objects in the image. The boundaries of these objects are then obtained as geodesics or minimal weighted distance curves in a Riemannian space. The metric in this space is given by a definition of edges in vector-valued images, incorporating information from all the image components. The curve flow corresponding to these active contours holds formal existence, uniqueness, stability, and correctness results. Then, embedding the deforming curve as the level-set of the image, that is, deforming each one of the image components level-sets according to these active contours, a system of coupled PDE's is obtained. This system deforms the image towards uniform regions, obtaining a simplified (or segmented) image. The flow is related to a number of PDE's based image processing algorithms as anisotropic diffusion and shock filters. The technique is applicable to color and texture images, as well as to vector data obtained from general image decompositions.