Mixture models and the probabilistic structure of depth cues.

Monocular cues to depth derive their informativeness from a combination of perspective projection and prior constraints on the way scenes in the world are structured. For many cues, the appropriate priors are best described as mixture models, each of which characterizes a different category of objects, surfaces, or scenes. This paper provides a Bayesian analysis of the resulting model selection problem, showing how the mixed structure of priors creates the potential for non-linear, cooperative interactions between cues and how the information provided by a single cue can effectively determine the appropriate constraint to apply to a given image. The analysis also leads to a number of psychophysically testable predictions. We test these predictions by applying the framework to the problem of perceiving planar surface orientation from texture. A number of psychophysical experiments are described that show that the visual system is biased to interpret textures as isotropic, but that when sufficient image data is available, the system effectively turns off the isotropy constraint and interprets texture information using only a homogeneity assumption. Human performance is qualitatively similar to an optimal estimator that assumes a mixed prior on surface textures--some proportion being isotropic and homogeneous and some proportion being anisotropic and homogeneous.