黎曼几何在计算机视觉中的应用研究进展

A Review of Research on Riemannian Geometry and Intelligent Image Recognition

在计算机视觉领域,许多任务相关数据具有非欧结构。近年来,基于黎曼几何的数据表征与应用研究受到了越来越广泛的关注。如何充分利用数据的几何结构,提高目标识别、目标跟踪及目标检测算法的性能,是其中的一些研究热点。主要从三个方面介绍了黎曼流形在计算机视觉中的应用进展。首先,从数学基本概念出发,阐述了黎曼流形与图像的关系,以及视觉应用的可行性,并介绍了在计算机视觉中获得重要应用的几种黎曼流形;其次,对黎曼流形在计算机视觉中的若干常见应用进行了概述,重点介绍了其与深度学习相结合的相关进展;最后,对引入黎曼流形的机器学习方法的未来发展进行了分析和讨论。

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 Riemannian 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.