  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.
