Regional Covariance Matrix Based On Dimension Reduction And Its Application In Face Recognition

With the continuous development of science and technology and innovation,more and more scholars have joined the field of face recognition research.Because the covariance matrix has the characteristics of rotation invariance,some scholars have presents some method for human face recognition by utilizing Gabor-based region covariance matrices:One method is to obtain the region covariance matrix of face image,and then to recognize the human face by the generalized eigenvalue distance of the region covariance matrix,however,the method does not reduce the dimension of the region covariance matrix,since the dimensionality of the feature matrix obtained by Gabor wavelet transform is very large,the covariance matrix obtained by covariance matrix is still large,and it is easy to fall into the dimension disaster problem,which causes the image recognition rate to decrease;Another method is an improved method,based on the above method,approximate joint diagonalization of the covariance matrix,then the face recognition is realized by the generalized eigenvalue distance,the method due to the covariance matrix of dimension reduction into approximate diagonalization matrix,It caused too much dimensionality reduction and may cause the loss of image information much.It may affect the recognition rate results.This article embarks from the 2D face databse,the face database is divided into five regions,and the feature information of the face image is obtained by the twodimensional Gabor wavelet transform.In order to verify the effectiveness of face recognition after adding Gabor features,7 different feature mapping functions are proposed,and the regional covariance matrices under different feature mappings functions are calculated respectively.Aiming at the defects of the above two methods,in this paper,three kinds of face recognition methods based on region covariance matrix are proposed,that is European distance classification based on two-dimensional principal component analysis,Mahalanobis distance classification based on twodimensional principal component analysis and generalized eigenvalue distance classification based on two-dimensional principal component analysis.Because the two-dimensional principal component analysis method can construct the scattering matrix of the image directly by using the image matrix,unlike the principal component analysis method,the image matrix needs to be transformed into the corresponding vector before the feature extraction,it is helpful to extract the important facial features for face recognition after analyzing the dimensionality matrix after dimensionality reduction by two-dimensional principal component analysis.It not only brings the important information of the image,but also not causes the dimension disaster and improves the face recognition the recognition rate.In this paper,in order to verify the effectiveness of the proposed method,in this paper,we use the Euclidean distance classification method,the Mahalanobis distance classification method and the generalized eigenvalue classification method to perform face recognition in the region covariance matrix face recognition method without dimension reduction,the three kinds of regional covariance matrix methods without dimensionality reduction,the face recognition method based on the regional covariance matrix approximation joint diagonalization and the three kinds of face recognition methods based on dimension reduction are applied to ORL,YALE,PIE and FERET Four face databases.The experiment shows that feature mapping function to add Gabor,the recognition rate is higher.The recognition rate of the face recognition method based on three kinds of region covariance matrix based on dimensionality reduction is higher than the face recognition rate of the face recognition method of region covariance matrix without dimension and the face recognition rate of approximate joint diagonalized face recognition method based on region covariance matrix.