A hierarchical approach to fuzzy segmentation of colour images

In this paper we introduce a methodology for the segmentation of colour images by means of a nested hierarchy of fuzzy partitions. Colour image segmentation attempts to divide the pixels of an image in several homogeneously-coloured and topologically connected groups, called regions. Our methodology deals with the different (but related) aspects of imprecision that are present in this process. First, the concept of homogeneity in a colour space is imprecise, so a measure of distance/similarity between colours is introduced. As a direct consequence, boundaries between regions are imprecise in general, so it is convenient to define regions as fuzzy subsets of items. The proposed distance in a perceptual colour space is employed to calculate fuzzy regions and membership degrees. In addition, fuzzy segmentation can be different depending on the precision level we consider when looking for homogeneity. Starting from an initial fuzzy segmentation, a hierarchical approach, based on a similarity relation between regions, is employed to obtain a nested hierarchy of regions at different precision levels.