Semi-supervised clustering: Application to image segmentation

This paper describes a new approach to semi-supervised model-based clustering. The problem is formulated as penalized logistic regression, where the labels are only indirectly observed (via the component densities). This formulation allows deriving a generalized EM algorithm with closed-form update equations, which is in contrast with other related approaches which require expensive Gibbs Sampling or suboptimal algorithms. We show how this approach can be naturally used for image segmentation under spatial priors, avoiding the usual hard combinatorial optimization required by classical Markov random fields; this opens the door to the use of sophisticated spatial priors (such as those based on wavelet representations) in a simple and computationally very efficient way.