We present results of using Bayesian inference for recovering the 3-D shape and texture of an object based on information extracted from a single 2-D image. We are using a number of different models for specific object classes. The goal is to combine the classes to a hierarchical structure. Instead of searching for the most probable explanation we estimate the entire posterior distribution of the model parameters using Markov chain Monte Carlo methods. The evaluation of model fit is based on combining edge information with intensity difference between the model and the target image.

We study an object recognition system where Bayesian inference is used for estimating the probability distribution of matching object locations on an image. The representation of the object contains two parts: the likelihood part that defines the probability of perceiving a given (gray scale) image corresponding to the matched object detail, and the prior part that defines the probability of variation of the object, including elastic distortions and interclass variations.The application we are studying is related to recognition of faces and recovering the shape of human heads. The prior consists of covariance model for the face, which encodes the correlations of matching point locations over different face images. The approach is closely related to eigenshapes and linear object classes. In the likelihood part, measurement of point correspondence is based on Gabor filter responses. In addition to matching filter amplitudes, we compute also the discrepancy of the filter phases, which increases the spatial accuracy of the matched locations. The similarity is based on measuring the distribution of Gabor filter responses in a given object location, and finding a low dimensional subspace to model the variation. The probability of match is proportional to the angle between the subspace and the vector of Gabor filter responses.The object matching is carried out as Bayesian inference: the goal is to find the posterior probability distribution of the possible matches given the image and the object prior. We use Markov Chain Monte Carlo (MCMC) methods, such as Gibbs and Metropolis sampling, to estimate the posterior probability of matches. In the paper we present MCMC methods suitable for the matching task and present some preliminary results.