Probabilistic image processing and Bayesian network

The basic frameworks and practical schemes of the Bayesian network and the belief propagation to the probabilistic image processing are reviewed. The probabilistic image processing is formulated by means of Bayesian statistics and Markov random fields. The system is regarded as one of Bayesian networks. In general, the Bayesian network has serious computational complexity because the probabilistic models include a number of random variables for nodes or pixels. Recently, many researchers in the intermediate region of the mathematical sciences and the computer sciences are interested in the belief propagations, which is one of powerful approximate methods for probabilistic inference. In the present paper, we briefly explain the formulation of the probabilistic image processing and the theoretical structure of the belief propagation. As two examples of the applications of the probabilistic image processing, we introduce a noise reduction and a segmentation, and extend the segmentation to a motion detection.