Modeling Occlusion and Scaling in Natural Images

Abstract

The dead leaves model, introduced by the mathematical morphology school, consists of the superposition of random closed sets (the objects) and enables one to model the occlusion phenomena. When combined with specific size distributions for objects, one obtains random fields providing adequate models for natural images. However, this framework imposes bounds on the sizes of objects. We consider the limits of these random fields when letting the cutoff sizes tend to zero and infinity. As a result we obtain a random field that contains homogeneous regions, satisfies scaling properties, and is statistically relevant for modeling natural images. We then investigate the combined effect of these features on the regularity of images in the framework of Besov spaces.