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.
翻译:隐藏的 Markov 链条, 即 Markov 字段, 模型, 在 Euclidean 空间中进行观测, 在信号和图像处理中发挥着主要作用。 目前的工作提供了一个统计框架,可以用来将这些模型及相关的流行算法(如 Baum-Welch 算法) 扩展至 Riemannian 方块中的观测。 其动机是可能使用隐藏的 Markov 链条和字段, 在Riemannian 方块中进行观测, 作为复杂信号和图像的模型。