Belief Propagation (BP) is an algorithm that has found broad application in many areas of computer science. The range of these areas includes Error Correcting Codes, Kalman filters, particle filters, and -- most relevantly -- stereo computer vision. Many of the currently best algorithms for stereo vision benchmarks, e.g. the Middlebury dataset, use Belief Propagation. This dissertation describes improvements to the core algorithm to improve its applicability and usefulness for computer vision applications. A Belief Propagation solution to a computer vision problem is commonly based on specification of a Markov Random Field that it optimizes. Both Markov Random Fields and Belief Propagation have at their core some definition of nodes and neighborhoods' for each node. Each node has a subset of the other nodes defined to be its neighborhood. In common usages for stereo computer vision, the neighborhoods are defined as a pixel's immediate four spatial neighbors. For any given node, this neighborhood definition may or may not be correct for the specific scene. In a setting with video cameras, I expand the neighborhood definition to include corresponding nodes in temporal neighborhoods in addition to spatial neighborhoods. This amplifies the problem of erroneous neighborhood assignments. Part of this dissertation addresses the erroneous neighborhood assignment problem. Often, no single algorithm is always the best. The Markov Random Field formulation appears amiable to integration of other algorithms: I explore that potential here by integrating priors from independent algorithms. This dissertation makes core improvements to BP such that it is more robust to erroneous neighborhood assignments, is more robust in regions with inputs that are near-uniform, and can be biased in a sensitive manner towards higher level priors. These core improvements are demonstrated by the presented results: application to office environments, real-world datasets, and benchmark datasets
