Markov Regularization of Mixture of Latent variable Models for Multi-component Image Unsupervised Joint Reduction/Segmentatin

This paper is concerned with multi-component image segmentation which plays an important role in many imagery applications. Unfortunately, we are faced with the Hughes phenomenon when the number of components increases, and a space dimensionality reduction is often carried out as a preprocessing step before segmentation. An interesting solution is the mixtures of latent variable models which recover clusters in the observation structure and establish a local linear mapping on a reduced dimension space for each cluster. Thus, a globally nonlinear model is obtained to reduce dimensionality. Furthermore, a likelihood to each local model is often available which allows a well formulation of the mixture model and a maximum likelihood based decision for the clustering task. However for D-component images classification, such clustering, based only on the distance between observations in the D-dimensional space is not adapted since it neglects the observation spatial locations in the image. We propose to use a Markov a priori associated with such models to regularize D-dimensional pixel classification. Thus segmentation and reduction are performed simultaneously. In this paper, we focus on the probabilistic principal component analysis (PPCA) as latent model, and the hidden Markov quad-tree (HMT) as a Markov a priori