  The opacity of typical objects in the world results in occlusion --- an
important property of natural scenes that makes inference of the full
3-dimensional structure of the world challenging. The relationship between
occlusion and low-level image statistics has been hotly debated in the
literature, and extensive simulations have been used to determine whether
occlusion is responsible for the ubiquitously observed power-law power spectra
of natural images. To deepen our understanding of this problem, we have
analytically computed the 2- and 4-point functions of a generalized "dead
leaves" model of natural images with parameterized object transparency.
Surprisingly, transparency alters these functions only by a multiplicative
constant, so long as object diameters follow a power law distribution. For
other object size distributions, transparency more substantially affects the
low-level image statistics. We propose that the universality of power law power
spectra for both natural scenes and radiological medical images -- formed by
the transmission of x-rays through partially transparent tissue -- stems from
power law object size distributions, independent of object opacity.
