Carving Prior Manifolds Using Inequalities

The use of prior information by learning from training data is used increasingly in image analysis and computer vision. The high dimensionality of the parameter spaces and the complexity of the probability distributions however often makes the exact learning of priors an impossible problem, requiring an excessive amount of training data that is seldom realizable in practise. In this paper we propose a weaker form of prior estimation which tries to learn the boundaries of impossible events from examples. This is equivalent to estimating the support of the prior distribution or the manifold of possible events. The idea is to model the set of possible events by algebraic inequalities. Learning proceeds by selecting those inequalities that show a consistent sign when applied to the training data set. Every such inequality "carves" out a region of impossible events in the parameter space. The manifold of possible events estimated in this way will in general represent the qualitative properties of the events. We give example of this in the problems of restoration of handwritten characters and automatically tracked body locations