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.