Mixture Models and the EM Algorithm for Object Recognition within Compositional Hierarchies. Part 1: Recognition

We apply the Expectation Maximization (EM) algorithm to an assignment problem where in addition to binary assignment variables analog parameters must be estimated. As an example, we use the problem of part labeling in the context of model based object recognition where models are stored in from of a compositional hierarchy. This problem has been formulated previously as a graph matching problem and stated in terms of minimizing an objective function that a recurrent neural network solves. Mjolsness has introduced a "stochastic visual grammar" as a model for this problem; there the matching problem arises from an index renumbering operation via a permutation matrix. The optimization problem w.r.t the match variables is difficult and Mean Field Annealing techniques are used to solve it. Here we propose to model the part labeling problem in terms of a mixture of distributions, each describing the parameters of a part. Under this model, the match variables correspond to the a posteriori estimates of the mixture coefficients. The parts in the input image are unlabeled, this problem can be stated as missing data problem and the EM algorithm can be used to recover the labels and estimate parameters. The resulting update equations are identical to the Elastic Net equations; however, the update dynamics differ.

ICSI Technical Report TR-93-004

Technical Report