Hidden Markov chains and fields with observations in Riemannian manifolds

Hidden Markov chain, or field, models, with observations in a Euclidean space, play major role across signal and image processing. The present work provides statistical framework which can be used to extend these along related, popular algorithms (such as the Baum-Welch algorithm), case where lie Riemannian manifold. It is motivated by potential use of hidden chains fields, manifolds, models for complex signals images.