基于主元分析的对称性检测

对称性在日常生活中广泛存在，对一般物体镜像和对称性的快速检测一直是计算机视觉的难题，至今未有通用性很好且效率较高的算法，本文提出一种新的方法，把对称性检测问题转化为协方差矩阵的特征值分解问题，文中的３个定理及其证明奠定了理论基础。此外不把这一结论推广到旋转对称性的检测问题。仿真表明：这种方法理论基础扎实，操作简便，非常适合于强镜像对称复杂图像的镜像对称轴方向检测。

Principle Component Analysis-Based Symmetry Detection

Symmetry is widely spread in man made objects and objects in nature.Fast and effective symmetry detection is still a difficult problem in computer vision.In this paper,we convert the symmetry detection problem to a Principal Component Analysis (PCA) problem.And six theorems and four corollaries about PCA problem are given and proved.They tell us the conditions symmetry images satisfy.Following the instructions by the theorems and the corollaries,we design an algorithm to find symmetry axles.Experimental results show that the algorithm we given is fast and robustness.