Also in common with more general AI, probabilistic approaches have much to offer in dealing with the pervasive problems of uncertainty and in allowing information integration. In probabilistic reasoning, the likelihood of classes of objects or events is inferred by propagation of belief values in the light of changing evidence. The two main frameworks for such reasoning used in knowledge-based vision are Bayesian Belief Networks (BBNs) advocated by Pearl [48] and the Dempster-Shafer theory of evidence [24]. For example, early work by Binford [5] used Bayesian inference to make model-based vision reliable while remaining computationally tractable. Dempster-Shafer theory has also been used [4], but the computational complexity of the scheme means that it is only practical at the level of conceptual evaluation. BBNs, on the other hand, have been more widely adopted in vision systems as they are applicable to all levels of the visual processing because of the fast updating possible with singly connected trees. For example, Rimey and Brown [52] used them to model geometric constraints for active control of camera movements and Gong and Buxton [27] grouped optic flow vectors for segmentation and tracking. BBNs provide a clear mapping of contextual knowledge onto the computation to constrain interpretation by combining known causal dependencies with estimated statistical knowledge. They also support closed-loop control and attentional processing using both top-down and bottom up messages in the propagation of belief values, as well as the possibility of learning and refining representations by observation [13].
Bayesian belief nets are now being used in many demanding applications such as BATmobile [23] and TEA [53] to provide essential information integration. Buxton and Gong [13] have also developed a systematic methodology for the design, integration and implementation of advanced vision systems using BBNs . These networks allow dynamic updating of values in visual evidence and interpretation nodes, but not specification of the temporal constraints themselves. Howarth and Buxton [32] used dynamically reconfigured networks to model the evolving spatial relationships of vehicles as they move through the scene. However, others [23] adopt dynamic probabilistic networks [21] with the simple Markov property that the future is independent of the past given the present. BBNs support the active control of visual processing and off-line learning of the prior and conditional probabilities in many applications, see Spiegelhalter and Cowell [58]. They have even been learnt on-line using reinforcement learning by Whitehead and Ballard [69]. These approaches, then, are very promising for advanced vision systems that require ongoing exploitation and acquisition of knowledge.