Unsupervised Image Classification with a Hierarchical EM Algorithm

Abstract

This work is undertaken in the context of hierarchical stochastic models for the resolution of discrete inverse problems from low level vision. Some of these models lie on the nodes of a quadtree which leads to non-iterative inference procedures. Nevertheless, if they circumvent the algorithmic drawbacks of grid-based models (computational load and/or great dependance on the initialization), they admit modeling shortcomings (cumbersome and somehow artificial). We investigate a new hierarchical stochastic model which benefits from both the spatial and hierarchical prior modeling. The independence graph is based on a tree which has been pollarded with nodes at the coarsest resolution exhibiting a grid-based interaction structure. For this class of model, we address the critical problem of parameter estimation. To this end, we derive an EM algorithm on the hybrid structure which mixes an exact EM algorithm on each subtree and a low cost Gibbs EM algorithm on the coarse spatial grid. Experiments on a synthetic image and multispectral satellite images are reported.