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.