Unsupervised statistical image segmentation using bi-dimensional hidden Markov chains model with application to mammography images

Abstract

Hidden Markov chain (HMC) models have been widely used in unsupervised image segmentation. In these models, there is a double process; a hidden one noted X and an observed one, which is often one-dimensional, noted Y. The latter is constituted by pixels of a noisy image after transforming its bi-dimensional form into a mono-dimensional sequence. In this context, these models run into a problem of relationships between pixels which is often solved by applying curves such as the Hilbert-Peano scan when modeling the image under study. We propose enriching the HMC model by introducing a second component to the observed process Y based on the average of two observations which are neighbors in the image but are not in the chain of each considered pixel. This gives a bi-dimensional HMC model which has the same structure as the classical model except for the two-dimensional case of the low modeling noise. The estimation of the parameters of this model is carried out by using a three-algorithm approach: Bayesian one based mainly on the Markov Chain Monte Carlo (MCMC) methods, Expectation-Maximization (EM), and Iterative Conditional Estimation (ICE). We apply the final Bayesian decision criteria Marginal Posterior Mode to come up with a final configuration of the result X. The proposed model is compared to the classical HMC model in combination with the Hilbert-Peano scan numerically through simulated data and visually through synthetic and mammogram images.