Stochastic models for generic images

The idea of using statistical inference for analyzing and understanding images has been used for at least 20 years, going back, for instance, to the work of Grenander Gr and Cooper Co. To apply these techniques, one needs, of course, a probabilistic model for some class of images or some class of structures present in images. Many models of this type have been introduced. There are stochastic models for image textures GGGD, ZMW, for contours in images Mu, GCK, for the decomposition of an image into regions G-G, M-S, for disparity maps, for grammatical parsing of shapes Fu, for template matching, and for specific tasks such as face recognition HGYGM. The common framework for all these studies is to describe some class of images I (x, y) by means of a set of auxiliary variables xa representing the salient structures in the images, e. g. , edges, texture statistics, inferred depth values or relations, illumination features, medial axes or shape features, locations of key points such as eyes in a face, labels (as in character recognition), etc. Then i) a prior probability model for the "hidden" variables p (xQ) and ii) an imaging model p (I\xQ) for /, given the hidden variables, are defined. Finally, an image is analyzed using Bayes's rule p (xa) cxp (/|: ra) p (: rQ) which is applied to infer, e. g. , the MAP estimate for the hidden variables, given the image. Implicit in this approach is the deduction that there is a well-defined marginal distribution Pi1) = / PCMzaDjIctea JXc on all images that are likely to be seen.