The Study On The Bilateral Angle Two-dimensional Principal Component Analysis Algorithm And Its Application

With the development of science and technology,a fast and safe identification plays an increasingly important role in people’s daily life.As a biometric identification technology,face recognition attracts much attention for its image acquisition convenience and non-invade.As an important step in face recognition,feature extraction determines the level of recognition rate.Principal component analysis(PCA)is a classical feature extraction algorithm,but it needs the transformation of image matrix into a 1D vector column by column or row by row as its inputs,such transformation will not only destroy the spatial information embedded in pixels and their neighbors of image,but also lead a high-dimensional vector space,where it is difficult to evaluate the covariance matrix accurately due its large size and relatively small number of training samples.Two-dimensional principal component analysis(2DPCA),as an improved approach of PCA,directly uses image matrix as inputs,and then avoids the above problems emerging in PCA.However,2DPCA is very sensitivity to outliers since it employs squared F-norm as distance metric,which is least squares loss in nature.Angle 2DPCA is an effective method to solve this problem.In this paper,we introduce the algorithms about angle2DPCA in detail,the main results obtained are as follows:Firstly,PCA and its modified algorithms are introduced in detail,including 2DPCA,L1-norm-based 2DPCA(2DPCA-L1),and F-norm-based 2DPCA(F-2DPCA).The advantages and disadvantages of each method are analyzed.Secondly,angel PCA(APCA)and tangent angle 2DPCA(Tan-2DPCA)algorithms are researched,then a new sine angle 2DPCA(Sin-2DPCA)method is proposed,which obtains the optimal projection matrix by minimizing the reconstructed relative error of the image and gives a reasonable explanation for the robustness of the original angle method in theory.Experimental results on Extended Yale B and a subset of CUM PIE face image datasets indicate that Sin-2DPCA has the similar performance with Tan-2DPCA,and the model of the former is simper than the latter,so it can improve the efficiency.Finally,two-directional 2DPCA((2D)~2PCA)is presented.Following this,we develop a bilateral angle 2DPCA(BA2DPCA)approach,which obtains more useful information for identification and saves the image’s storage because it uses the new angel method given above to extract features and reduce dimensions from column and row direction of image matrix respectively.Experimental results on Extended Yale B,AR and a subset of CUM PIE face image datasets illustrate BA2DPCA can obtain the highest recognition accuracy with the minimal number of representation coefficients and reconstructive image quality in all compared algorithms.