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首页> 外文期刊>Turkish Journal of Electrical Engineering and Computer Sciences >An algorithm to minimize within-class scatter and to reduce common matrix dimension for image recognition
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An algorithm to minimize within-class scatter and to reduce common matrix dimension for image recognition

机译：一种最小化类内散射并减小用于图像识别的公共矩阵尺寸的算法

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In this paper, a new algorithm using 2DPCA and Gram-SchmidtOrthogonalization Procedure for recognition of face images isproposed. The algorithm consists of two parts. In the first part, acommon feature matrix is obtained; and in the second part, thedimension of the common feature matrix is reduced. Resulting commonfeature matrix with reduced dimension is used for face recognition.Column and row covariance matrices are obtained by applying 2DPCA onthe column and row vectors of images, respectively. The algorithmthen applies eigenvalue-eigenvector decomposition to each of these twocovariance matrices. Total scatter maximization is achieved takingthe projection of images onto d eigenvectors corresponding to thelargest d eigenvalues of column covariance matrix, yielding thefeature matrix. The each column of the feature matrix represents afeature vector. Minimization of within class scatter is achieved byreducing the redundancy of the corresponding feature vectors of thedifferent images in the same class. A common feature vector for eachd^{th} eigenvector direction is obtained by applying Gram-SchmidtOrthogonalization Procedure. A common feature matrix is establishedby gathering d common feature vectors in a matrix form. Then, thedimension of common feature matrix is reduced to d imes d taking theprojection of common feature matrix onto d eigenvectors whichcorresponds to the largest d eigenvalues of row covariance matrix.The performance of the proposed algorithm is evaluated experimentallyby measuring the recognition rates. The developed algorithm producedbetter recognition rates compared to Eigenface, Fisherface and 2DPCAmethods. Ar-Face and ORL face databases are used in the experimentalevaluations.
机译：提出了一种基于2DPCA和Gram-Schmidt正交化算法的人脸图像识别新算法。该算法包括两部分。第一部分，得到一个公共特征矩阵。第二部分减少了公共特征矩阵的维数。将得到的尺寸减小的公共特征矩阵用于人脸识别。通过在图像的列和行向量上分别应用2DPCA，获得列和行协方差矩阵。该算法然后将特征值-特征向量分解应用于这两个协方差矩阵中的每一个。通过将图像投影到与列协方差矩阵的最大d个特征值相对应的d个特征向量上，可以实现总散射最大化，从而生成特征矩阵。特征矩阵的每一列代表特征向量。通过减少同一类别中不同图像的相应特征向量的冗余，可以实现类别内散布的最小化。通过应用Gram-Schmidt正交化过程获得每个特征向量方向的公共特征向量。通过以矩阵形式收集d个公共特征向量来建立公共特征矩阵。然后，通过将共同特征矩阵投影到对应于行协方差矩阵的最大特征值的d个特征向量上，将共同特征矩阵的维数减小为d times d。通过测量识别率，对算法的性能进行了实验评估。与Eigenface，Fisherface和2DPCA方法相比，开发的算法产生了更好的识别率。实验评估中使用Ar-Face和ORL人脸数据库。

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