Unsupervised segmentation of images using bi-dimensional pairwise Markov chains model

The pair-wise Markov chain (PMC) model serves as an extension to the hidden Markov chain (HMC) model and has been widely used in unsupervised restoration tasks associated with reconstructing the hidden data. In fact, the PMC model can treat fairly complicated situations for which application of Bayesian restoration estimators such as maximum A Posteriori (MAP), or maximal Posterior mode (MPM) remains possible. The major novelty in this work is to construct a PMC model with observational data in two dimensions, and subsequently adapt the estimation algorithms, as well as, image restoration methods for that context. Often, the transformation of an image from a two-dimensional format to a one-dimensional sequence occurs via Hilbert-Peano scan (HPS), whereas in the proposed model, the second component of the observed process takes over this role to exceed the situation of pixel missing information after transformation for a to be segmented image. To reconstruct the hidden process, we used the MPM decision criterion after estimating the model's parameters with two algorithms: Stochastic expectation maximization (SEM) and iterative conditional estimation (ICE). In this study, experimental, numerical, and visual results are shown to demonstrate the superiority of the proposed model over the classical PMC for unsupervised restorations.