  To understand the computations of our visual system, it is important to
understand also the natural environment it evolved to interpret. Unfortunately,
existing models of the visual environment are either unrealistic or too complex
for mathematical description. Here we describe a naturalistic image model and
present a mathematical solution for the statistical relationships between the
image features and model variables. The world described by this model is
composed of independent, opaque, textured objects which occlude each other.
This simple structure allows us to calculate the joint probability distribution
of image values sampled at multiple arbitrarily located points, without
approximation. This result can be converted into probabilistic relationships
between observable image features as well as between the unobservable
properties that caused these features, including object boundaries and relative
depth. Using these results we explain the causes of a wide range of natural
scene properties, including highly non-gaussian distributions of image features
and causal relations between pairs of edges. We discuss the implications of
this description of natural scenes for the study of vision.
