2DPCA在图像特征提取中优于PCA的判定条件  

Criteria for 2DPCA Superior to PCA in Image Feature Extraction

作　　者：程正东[1,2] 章毓晋[1] 樊祥[2,3] 

机构地区：[1]清华大学电子工程系,北京100084 [2]合肥电子工程学院,合肥230037 [3]中国科技大学六系,合肥230027

出　　处：《工程数学学报》2009年第6期951-961,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(60872084);高等学校博士学科点专项科研基金(SRFDP-20060003102)

摘　　要：主元分析(PCA)与二维主元分析(2DPCA)是两种典型的图像特征提取方法,它们所提取的图像特征的优劣可由重建误差来衡量。通过对PCA和2DPCA的重建误差分析发现,二者的重建误差在理论上相同,但在实际应用中取决于它们的样本协方差阵的估计准确度。本文以均方误差为度量给出了PCA与2DPCA样本协方差阵的估计准确度表达式,并由此得到2DPCA图像特征优于PCA的判定条件是2DPCA协方差阵的特征值平方和大于PCA。本文还指出行2DPCA与列2DPCA所提取的图像特征孰优孰劣也取决于它们各自协方差阵的特征值平方和的大小。在人脸图像库与人脸表情图像库上的实验验证了上述判定条件的正确性。PCA and 2DPCA are two typical image feature extraction methods. The wellness of image features extracted by PCA and 2DPCA can be judged by their reconstruction errors. Our analysis shows that the reconstruction errors of PCA and 2DPCA are equal in theory, but depend on the estimation accuracy of their covariance matrices in practice. This paper gives the accuracy expressions for estimations of covariance matrices for PCA and 2DPCA, respectively, based on the criterion of mean square error. Further, it is shown that the criterion for 2DPCA to be superior to PCA is that the square sum of eigenvalues of the covariance matrix of 2DPCA is larger than that of PCA. This paper also points out that the same criterion can be used to judge the superiority between the column 2DPCA and row 2DPCA. Experiments on the face correctness of the decision conditions. database and facial expression database verify the

关 键 词：PCA 2DPCA 图像特征 协方差阵 重建误差 均方误差 

分 类 号：O212.7[理学—概率论与数理统计]