Unsupervised Segmentation of Markov Random Fields Corrupted by Nonstationary Noise

Hidden Markov fields have been widely used in image processing thanks to their ability to characterize spatial information. In such models, the process of interest $X$ is hidden and is to be estimated from an observable process $Y$. One common way to achieve the associated inference tasks is to define, on one hand, the prior distribution $p(x)$ ; and on the other hand, the noise distribution $p(y|x)$. While it is commonly established that the prior distribution is given by a Markov random field, the noise distribution is usually given through a set of Gaussian densities; one per each label. Hence, observed pixels belonging to the same class are assumed to be generated by the same Gaussian density. Such assumption turns out, however, to be too restrictive in some situations. For instance, due to light conditions, pixels belonging to a same label may present quite different visual aspects. In this letter, we overcome this drawback by considering an auxiliary field $U$ in accordance with the triplet Markov field formalism. Experimental results on simulated and real images demonstrate the interest of the proposed model with respect to the common hidden Markov fields.