Occlusion models for natural images: A statistical study of a scale-invariant dead leaves model

We develop a scale-invariant version of Matheron's dead leaves model for the statistics of natural images. The model takes occlusions into account and resembles the image formation process by randomly adding independent elementary shapes, such as disks, in layers. We compare the empirical statistics of two large databases of natural images with the statistics of the occlusion model, and find an excellent qualitative, and good quantitative agreement. At this point, this is the only image model which comes close to duplicating the simplest, elementary statistics of natural images-such as, the scale invariance property of marginal distributions of filter responses, the full co-occurrence statistics of two pixels, and the joint statistics of pairs of Haar wavelet responses.