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The opacity of typical objects in the world results in occlusion --- animportant property of natural scenes that makes inference of the full3-dimensional structure of the world challenging. The relationship betweenocclusion and low-level image statistics has been hotly debated in theliterature, and extensive simulations have been used to determine whetherocclusion is responsible for the ubiquitously observed power-law power spectraof natural images. To deepen our understanding of this problem, we haveanalytically computed the 2- and 4-point functions of a generalized "deadleaves" model of natural images with parameterized object transparency.Surprisingly, transparency alters these functions only by a multiplicativeconstant, so long as object diameters follow a power law distribution. Forother object size distributions, transparency more substantially affects thelow-level image statistics. We propose that the universality of power law powerspectra for both natural scenes and radiological medical images -- formed bythe transmission of x-rays through partially transparent tissue -- stems frompower law object size distributions, independent of object opacity.

Dead leaves and the dirty ground: low-level image statistics in transmissive and occlusive imaging environments