Scale-based formulations of statistical self-similarity in images

Statistically self-similar images that are segments of two dimensional self-similar random fields, have been useful in the analysis and synthesis of certain types of textures. Whereas a rigorous definition of self-similarity in continuous-space is based on spatial scaling, current treatments in digital image processing are based on ad-hoc approaches rather than on spatial scaling mainly because of the unavailability of continuous scaling in discrete-space. This paper presents a formulation based on such a continuous scaling operator leading to a more general and versatile characterization of statistical self-similarity in images.