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DOI:
飞控与探测:2020,(6):01-10
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黎曼几何在计算机视觉中的应用研究进展
(中国科学院沈阳自动化研究所 中国科学院机器人与智能制造创新研究院 中国科学院光电信息处理重点实验室)
A Review of Research on Riemannian Geometry and Intelligent Image Recognition
SHI Zelin1,2,3,LIU Tianci1,2,3,LIU Yunpeng1,2,3
(1.Shenyang Institute of Automation, Chinese Academy of Sciences;2.Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang;3.Key Laboratory of Opto-Electronic Information Processing, Chinese Academy of Sciences, Shenyang)
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中文摘要: 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多的关注。如何充分利用数据的几何结构,来提高目标识别、目标跟踪及目标检测算法的性能,是其中的一些研究热点。本文主要从三个方面介绍黎曼流形在计算机视觉中的应用研究进展。首先,从数学基本概念出发,阐述黎曼流形与图像的关系以及视觉应用的可行性,并介绍计算机视觉中具有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若干常见应用进行了概述,重点介绍了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。
中文关键词: 黎曼几何;深度学习;智能图像识别;黎曼流形;黎曼优化
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.
keywords: Riemannian geometry; deep learning; intelligent image recognition; Riemannian manifold; Riemannian optimization
文章编号:20200601     中图分类号:TP391    文献标志码:A
基金项目:中国科学院重点创新基金项目,信息感知技术(E01Z040601)
作者单位
史泽林 中国科学院沈阳自动化研究所 中国科学院机器人与智能制造创新研究院 中国科学院光电信息处理重点实验室 
刘天赐 中国科学院沈阳自动化研究所 中国科学院机器人与智能制造创新研究院 中国科学院光电信息处理重点实验室 
刘云鹏 中国科学院沈阳自动化研究所 中国科学院机器人与智能制造创新研究院 中国科学院光电信息处理重点实验室 
Author NameAffiliation
SHI Zelin Shenyang Institute of Automation, Chinese Academy of Sciences
Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang; Key Laboratory of Opto-Electronic Information Processing, Chinese Academy of Sciences, Shenyang 
LIU Tianci Shenyang Institute of Automation, Chinese Academy of Sciences
Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang; Key Laboratory of Opto-Electronic Information Processing, Chinese Academy of Sciences, Shenyang 
LIU Yunpeng Shenyang Institute of Automation, Chinese Academy of Sciences
Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang; Key Laboratory of Opto-Electronic Information Processing, Chinese Academy of Sciences, Shenyang 
引用文本:
史泽林,刘天赐,刘云鹏.黎曼几何在计算机视觉中的应用研究进展[J].飞控与探测,2020,(6):01-10.

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