Abstract:In computer vision, many visual data own non-Euclidean geometry. In recent years，the research of data representation based on Riemannian geometry and its applications have received widespread attention. How to make full use of the geometric structure of data to improve the performance of algorithms in the aspect of target recognition, target tracking and target detection has always been focused in the research of Riemann geometry. This article mainly introduces the research progress of Riemannian manifold learning methods in computer vision from three aspects. Firstly, the basic concepts of Riemannian manifolds are explained from a mathematical perspective, and then several types of Riemannian manifolds that have important applications in computer vision are introduced to clarify why mathematically abstract concepts of Riemannian manifold can be combined with computer vision. Secondly, we summarize the development of Riemann manifold methods in the field of computer vision, and emphasize the recent research progress of Riemannian manifold in deep learning. Finally, according to the current research status, the brief analyses and discussion are given for the future development directions of machine learning methods combined with Riemannian manifold.