A Bayesian approach to binocular steropsis

Abstract

We develop a computational model for binocular stereopsis, attempting to explain the process by which the information detailing the 3-D geometry of object surfaces is encoded in a pair of stereo images. We design our model within a Bayesian framework, making explicit all of our assumptions about the nature of image coding and the structure of the world. We start by deriving our model for image formation, introducing a definition of half-occluded regions and deriving simple equations relating these regions to the disparity function. We show that the disparity function alone contains enough information to determine the half-occluded regions. We use these relations to derive a model for image formation in which the half-occluded regions are explicitly represented and computed. Next, we present our prior model in a series of three stages, or “worlds,” where each world considers an additional complication to the prior. We eventually argue that the prior model must be constructed from all of the local quantities in the scene geometry-i.e., depth, surface orientation, object boundaries, and surface creases. In addition, we present a new dynamic programming strategy for estimating these quantities. Throughout the article, we provide motivation for the development of our model by psychophysical examinations of the human visual system.