Polynomial shift-invariant operators for texture segmentation

Marking boundaries in an image between regions that are differently textured depends on computing descriptions of the regions that show them to be differently textured. Many texture description functions have been introduced in the literature; however, the texture description problem has never been treated in full generality. The author proposed shift-invariant vector-valued piecewise continuous functions of bounded support on images as a general class of texture description functions, and consider approximating functions in this class with polynomials. He proves a theorem that relates the degree of such a polynomial description function to the statistical properties of textured regions it can discriminate, and discusses some implications of the theorem