Hidden Markov chains (HMC) are a very powerful tool in hidden data restoration and are currently used to solve a wide range of problems. However, when these data are not stationary, estimating the parameters, which are required for unsupervised processing, poses a problem. Moreover, taking into account correlated non-Gaussian noise is difficult without model approximations. The aim of this paper is to propose a simultaneous solution to both of these problems using triplet Markov chains (TMC) and copulas. The interest of the proposed models and related processing is validated by different experiments some of which are related to semi-supervised and unsupervised image segmentation.