Discrete visual features modeling via leave-one-out likelihood estimation and applications

Discrete data are an important component in many image processing and computer vision applications. In this work we propose an unsupervised statistical approach to learn structures of this kind of data. The central ingredient in our model is the introduction of the generalized Dirichlet distribution as a prior to the multinomial. An estimation algorithm, based on leave-one-out likelihood and empirical Bayesian inference, for the parameters is developed. This estimation algorithm can be viewed as a hybrid expectation–maximization (EM) which alternates EM iterations with Newton–Raphson iterations using the Hessian matrix. We propose then the use of our model as a parametric basis for support vector machines within a hybrid generative/discriminative framework. In a series of experiments involving scene modeling and classification using visual words, and color texture modeling we show the efficiency of the proposed approach.