Morphological statistics of natural images and consequences

We present statistics on natural images dealing with homogeneous and connected regions, defined as connected components of differences of level sets. We show that their area is distributed according to a power law. From these experimental results, we show precisely how the modeling of images as functions of bounded variation, widely used in image restoration methods, is incompletely adapted to natural images. For this purpose we use a model of convolution and sampling for the formation of images. We also use our experimental results to confirm the scale invariance of natural images.