Image Segmentation That Optimizes Global Homogeneity in a Variational Framework

Abstract

A two-phase segmentation mechanism is described that allows a global homogeneity-related measure to be optimized in a level-set formulation. The mechanism has uniform treatment toward texture, gray level, and color boundaries. Intensities or colors of the image are first coarsely quantized into a number of classes. Then a class map is formed by having each pixel labeled with the class identity its gray or color level is associated with. With this class map, for any segmented region, it can be determined which pixels inside the region belong to which classes, and it can even be calculated how spread-out each of such classes is inside the region. The average spread-size of the classes in the region, in comparison with the size of the region, then constitutes a good measure in evaluating how homogeneous the region is. With the measure, the segmentation problem can be formulated as the optimization of the average homogeneity of the segmented regions. This work contributes chiefly by expressing the above optimization functional in such a way that allows it to be encoded in a variational formulation and that the solution can be reached by the deformation of an active contour. In addition, to solve the problem of multiple optima, this work incorporates an additional geodesic term into the functional of the optimization to maintain the active contour’s mobility at even adverse condition of the deformation process. Experimental results on synthetic and real images are presented to demonstrate the performance of the mechanism.