Fuzzy Homogeneity Measures for Path-Based Colour Image Segmentation

In this paper we study different measures of path homogeneity for fuzzy path-based image segmentation. We provide fuzzy semantics for the concept of homogeneity in two steps: first, we introduce a fuzzy interpretation of resemblance between feature vectors characterizing neighbor pixels; then, we obtain the homogeneity of a path by aggregating the set of fuzzy resemblances between consecutive pixels in the path. We propose a set of intuitive properties that any suitable aggregation function should verify for this purpose, and we show that these properties are verified by certain families of t-norms. To determine the performance of the proposed functions, a set of experiments is carried out with both synthetic and real images. Finally, the homogeneity functions are used to obtain fuzzy regions in natural images