When a vision system creates an interpretation of some input datn, it assigns truth values or probabilities to intcrnal hypothcses about the world. We present a non-dctcrministic method for assigning truth values that avoids many of the problcms encountered by existing relaxation methods. Instead of rcprcscnting probabilitics with real-numbers, we usc a more dircct encoding in which thc probability associated with a hypotlmis is rcprcscntcd by the probability hat it is in one of two states, true or false. Wc give a particular non-deterministic operator, based on statistical mechanics, for updating the truth values of hypothcses. The operator ensures that the probability of discovering a particular combination of hypothcscs is a simplc function of how good that combination is. Wc show that thcrc is a simple relationship bctween this operator and Bayesian inference, and we describe a learning rule which allows a parallel system to converge on a set ofweights that optimizes its perccptt~al inferences. lnt roduction One way of interpreting images is to formulate hypotheses about parts or aspects of the imagc and then decide which of these hypotheses are likely to be correct. Thc probability that each hypothesis is correct is determined partly by its fit to the imagc and partly by its fit to other hypothcses (hat are taken to be correct, so the truth'value of an individual hypothesis cannot be decided in isolation. One method of searching for the most plausible combination of hypotheses is to use a rclaxation process in which a probability is associated with each hypothesis, and the probabilities arc then iteratively modified on the basis of the fit to the imagc and the known relationships bctwcen hypotheses. An attractive property of rclaxation methods is that they can be implemented in parallel hardwarc where one computational unit is used for each possible hypothcsis, and the interactions betwcen hypotheses are implemented by dircct hardwarc connections betwcen the units. Many variations of the basic relaxation idea have becn However, all the current methods suffer from one or more of the following problems: