A STUDY OF A CONVEX VARIATIONAL DIFFUSION APPROACH FOR IMAGE SEGMENTATION AND FEATURE-EXTRACTION

We analyze a variational approach to image segmentation that is based on a strictly convex nonquadratic cost functional. The smoothness term combines a standard first-order measure for image regions with a tota l-variation based measure for signal transitions. Accordingly, the cos ts associated with ''discontinuities'' are given by the length of leve l lines and local image contrast. For real images, this provides a rea sonable approximation of the variational model of Mumford and Shah tha t has been suggested as a generic approach to image segmentation. The global properties of the convex variational model are favorable to app lications: Uniqueness of the solution, continuous dependence of the so lution on both data and parameters, consistent and efficient numerical approximation of the solution with the FEM-method. Various global and local properties of the convex variational model are analyzed and ill ustrated with numerical examples. Apart from the favorable global prop erties, the approach is shown to provide a sound mathematical model of a useful locally adaptive smoothing process. A comparison is carried out with results of a region-growing technique related to the Mumford- Shah model.