We present a variational Bayesian framework for performing inference, density estimation and model selection in a special class of graphical models—Hidden Markov Random Fields (HMRFs). HMRFs are particularly well suited to image modelling and in this paper, we apply them to the problem of image segmentation. Unfortunately, HMRFs are notoriously hard to train and use because the exact inference problems they create are intractable. Our main contribution is to introduce an efficient variational approach for performing approximate inference of the Bayesian formulation of HMRFs, which we can then apply to the density estimation and model selection problems that arise when learning image models from data. With this variational approach, we can conveniently tackle the problem of image segmentation. We present experimental results which show that our technique outperforms recent HMRF-based segmentation methods on real world images.
& Wang, S.
(2005). Variational Bayesian Image Modelling. ICML 2005 Proceedings of the 22nd International Conference on Machine Learning, 129-136.