Hidden Markov chains and fields with observations in Riemannian manifolds

Hidden Markov chain, or Markov field, models, with observations in a Euclidean space, play a major role across signal and image processing. The present work provides a statistical framework which can be used to extend these models, along with related, popular algorithms (such as the Baum-Welch algorithm), to the case where the observations lie in a Riemannian manifold. It is motivated by the potential use of hidden Markov chains and fields, with observations in Riemannian manifolds, as models for complex signals and images. Copyright (C) 2021 The Authors.