Probabilistic inference in human and computer vision

This thesis aims to improve the understanding of 3-dimensional geometry from images as a statistical inference problem provides both new explanations for the origins of spontaneous perceptual switching in the human visual system, and new computer vision algorithms with lower 3D reconstruction errors. Perceptual Bistability refers to the phenomenon of spontaneous perceptual switching between two likely interpretations of a single image. Although frequently explained by processes of adaptation or hysteresis, we show that perceptual switching can arise as a natural by-product of performing probabilistic (Bayesian) inference, which interprets images by combining models of image formation with knowledge of scene regularities. We introduce a theoretical model consistent with Bayesian models of vision that involves searching for good interpretations of an image by sampling a bimodal posterior distribution representing the two interpretations of a Necker cube (a cuboidal wire frame object capable of eliciting two distinct percepts). This sampling scheme, coupled with a decay process that favors recent over old interpretations, is capable of producing data that resembles human bistable behavior. Furthermore, we introduce psychophysical experiments that are equivalent to manipulating the prior probability influencing the interpretation of the Necker cube. We show that human bistable switching behavior can be predicted with the equivalent manipulations of the theoretical model. To describe changes in the temporal dynamics of the perceptual alternations beyond traditional static measures like percept durations, we introduce Markov Renewal Processes (MRPs). MRPs provide a general mathematical framework for describing probabilistic switching behavior in finite state processes. Furthermore, we show the MRP is predicted by the Bayesian model. Because the Bayesian model produces the same kind of stochastic process found in human perceptual behavior, we conclude that bistability may represent an unavoidable by-product of normal perceptual inference with ambiguous images. Additionally, this thesis contributes to the computer vision applications of 3D reconstruction by using a Bayesian approach to handling camera calibration error to improve the quality of object reconstruction, discounting the effect of viewpoint. This approach provides a statistically optimal reconstruction for which error from viewpoint has been minimized.