Abstract: An effective algorithm for detection and classification of cyclic and dihedral symmetric images in DoG wavelet domain is presented.The proposed algorithm is very robust to noise for the noisy images corrupted by Additive White Gaussian Noise（AWGN）.Combined with the modified ridgelet transform，the proposed method can successfully detect and classify the noisy images with cyclic and dihedral symmetries，even under the situation of high-level noise（for example，noise deviation is σ=70）.

Key words: cyclic group, dihedral group, symmetry classification, DoG wavelet transform

摘要： 提出了一种DoG小波域的循环群、二面体群对称性图像的识别与分类技术。该技术具有很好的噪声（仅讨论加性的白高斯噪声）鲁棒性特点，甚至在高噪声情况下（例如噪声偏差σ=70），结合修改的脊波变换能实现对噪声图像包含的循环群、二面体群对称性进行识别和分类。

关键词: 循环群, 二面体群, 对称性分类, DoG小波变换