Bayesian Modeling of Uncertainty in Low-Level Vision

Over the last decade, many low-level vision algorithms have been devised for extracting depth from one or more intensity images. The output of such algorithms usually contains no indication of the uncertainty associated with the scene reconstruction. In other areas of computer vision and robotics, the need for such error modeling is becoming recognized, both because of the uncertainty inherent in sensing and because of the desire to integrate information from different sensors or viewpoints. In this thesis, we develop a new Bayesian model for the dense fields that are commonly used in low-level vision. The Bayesian model consists of three components: a prior model, a sensor model, and a posterior model. The prior model captures any a priori information about the structure of the dense field. We construct this model by using the smoothness constraints for regularization to define a Markov Random Field. The sensor model describes the behaviour and noise characteristics of our measurement system. We develop a number of sensor models for both sparse depth measurements and dense flow or intensity measurements. The posterior model combines the information from the prior and sensor models using Bayes’ Rule, and can be used as the input to later stages of processing. We show how to compute optimal estimates from the posterior model, and also how to compute the uncertainty (variance) in these estimates. This thesis applies Bayesian modeling to a number of low-level vision problems. The main application is the on-line extraction of depth from motion. For this application, we use a two-dimensional generalization of the Kalman filter to convert the current posterior model into a prior model for the next estimate. The resulting incremental algorithm provides a dense on-line estimate of depth whose uncertainty and error are reduced over time. Other applications of Bayesian modeling, include the choice of optimal smoothing parameter for interpolation; the determination of observer motion from sparse depth measurements without correspondence; and the construction of multiresolution relative surface representations. The approach to uncertainty modeling which we develop, and the utility of this approach in various applications, support our thesis that Bayesian modeling is a useful and practical framework for low-level vision.