Many researchers have been using belief networks as a convenient mechanism for managing uncertainty in expert systems. Most of these expert systems to date have dealt with the tasks of classification or diagnosis in a temporally static problem domain. To a lesser extent, researchers have also been able to model dynamic properties using belief networks in an effort to simulate and predict the behavior of time-varying systems. Furthermore, real world image interpretation requires the ability to handle millions of features in a statistically efficient manner, using an accurate and rigorous mathematical model of uncertainty. Levitt and Binford argue that the belief network fits naturally into the hierarchical image understanding model, where objects are composed of parts and joints.
Joints specify the relationships among parts, which in turn are composed of subparts and joints.
In this manner, a sufficient set of probabilistic evidence, even if it is incomplete or ambiguous, can be amalgamated to support or deny hypotheses about the objects in the image. Competing hypotheses can be rank ordered by their overall probability, or likelihood of occurrence. The two DAGs shown in Figure represent the belief networks for these two objects. Given a photograph of a cube, we would expect to see at most three faces, nine edges and seven vertices. For a three-sided pyramid, we would expect to see at most three faces, six edges, and four vertices.