The Bayesian Approach to Vision

Bayesian statistical decision theory formulates vision as perceptual inference where the goal is to infer the structure of the viewed scene from input images. The approach an be used not only to model perceptual phenomena but also to design computer vision systems tat perform useful tasks on natural images. This ensures that the models can be extended form the artificial stimuli used in most psychophysical, or neuroscientific experiments to more natural and realistic stimuli. The approach requires specifying likelihood functions for how the viewed scene generates the observed image data and prior probabilities for the state of the scene. We show how this relates to Signal Detection Theory and Machine Learning.

Next, we describe how the probability models (i.e., likelihood functions and priors) can be represented by graphs which makes explicit the statistical dependencies between variables. This representation enables us to account for perceptual phenomena such as discounting, cue integration, and explaining away. We illustrate the techniques involved in the Bayesian approach by two worked examples. The first is the perception of motion where we describe Bayesian theories (Weiss & Adelson, Yuille & Grzywacz) which show that many phenomena can be explained as a trade-off between the likelihood function and the prior of a single model. The second is image parsing where the goal is to segment natural images and to detect and recognize objects. This involves models competing and cooperating to explain the image by combining bottom-up and top-down processing.