Spatial size distributions: applications to shape and texture analysis

This paper proposes new descriptors for binary and gray-scale images based on newly defined spatial size distributions (SSD). The main idea consists of combining a granulometric analysis of the image with a comparison between the geometric covariograms for binary images or the auto-correlation function for gray-scale images of the original image and its granulometric transformation; the usual granulometric size distribution then arises as a particular case of this formulation. Examples are given to show that in those cases in which a finer description of the image is required, the more complex descriptors generated from the SSD could be advantageously used. It is also shown that the new descriptors are probability distributions so their intuitive interpretation and properties can be appropriately studied from the probabilistic point of view. The usefulness of these descriptors in shape analysis is illustrated by some synthetic examples and their use in texture analysis is studied. Various cases of SSD and several former methods for texture classification are compared.