摘 要：近十年来，传统的图像检测与匹配算法进入瓶颈期，以深度学习为首的图像特征检测与匹配正展露尖角，将传统算法和深度学习相互融合已是大势所趋。文章简要叙述了几种经典检测算法中特征描述子的生成流程，从数学角度严谨地阐述了局部描述子对图像存在噪声、光照和旋转变化等干扰因素具有良好鲁棒性的原理，并分析讨论了其性能及优缺点。
关键词：局部特征；特征描述子；光照不变性；旋转不变性；PCA
DOI:10.19850/j.cnki.2096-4706.2021.14.027
中图分类号：TP391.4 文献标识码：A 文章编号：2096-4706（2021）14-00103-06
Mathematical Principles in Local Feature Descriptors
SUN Zhuoting, WANG Fulong
(School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510630, China)
Abstract: In recent ten years, traditional image detection and matching algorithms have entered a bottleneck period. Image feature detection and matching led by deep learning are showing sharp corners. It is a general trend to integrate traditional algorithms and deep learning. This paper briefly describes the generation process of feature descriptors in several classic detection algorithms, rigorously expounds the principle that local descriptors have good robustness to image interference factors such as noise, illumination, and rotation changes from a mathematical point of view, and analyzes and discusses its performance, advantages and disadvantages.
Keywords: local feature; feature descriptor; illumination invariance; rotation invariance; PCA
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作者简介：孙卓婷（1996—），女，汉族，广东惠州人，硕士在读，研究方向：图像处理、模式识别；王福龙（1968—），男， 汉族，广东广州人，教授，博士，研究方向：图像处理、模式识别 和智能控制及应用。