renlianshibie.zip_parts_人脸识别MATLAB源程序

EigenfaceCore.m function [m, A, Eigenfaces] = EigenfaceCore(T) % Use Principle Component Analysis (PCA) to determine the most? % discriminating features between images of faces. % % Description: This function gets a 2D matrix, containing all training image vectors % and returns 3 outputs which are extracted from training database. % % Argument: ? ? ?T ? ? ? ? ? ? ? ? ? ? ?- A 2D matrix, containing all 1D image vectors. % ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Suppose all P images in the training database? % ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? have the same size of MxN. So the length of 1D? % ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? column vectors is M*N and 'T' will be a MNxP 2D matrix. %? % Returns: ? ? ? m ? ? ? ? ? ? ? ? ? ? ?- (M*Nx1) Mean of the training database % ? ? ? ? ? ? ? ?Eigenfaces ? ? ? ? ? ? - (M*Nx(P-1)) Eigen vectors of the covariance matrix of the training database % ? ? ? ? ? ? ? ?A ? ? ? ? ? ? ? ? ? ? ?- (M*NxP) Matrix of centered image vectors % % See also: EIG % Original version by Amir Hossein Omidvarnia, October 2007 % ? ? ? ? ? ? ? ? ? ? Email: aomidvar@ece.ut.ac.ir ? ? ? ? ? ? ? ? ? %%%%%%%%%%%%%%%%%%%%%%%% Calculating the mean image? m = mean(T,2); % Computing the average face image m = (1/P)*sum(Tj's) ? ?(j = 1 : P) Train_Number = size(T,2); %%%%%%%%%%%%%%%%%%%%%%%% Calculating the deviation of each image from mean image A = []; for i = 1 : Train_Number temp = double(T(:,i)) - m; % Computing the difference image for each image in the training set Ai = Ti - m A = [A temp]; % Merging all centered images end %%%%%%%%%%%%%%%%%%%%%%%% Snapshot method of Eigenface methos % We know from linear algebra theory that for a PxQ matrix, the maximum % number of non-zero eigenvalues that the matrix can have is min(P-1,Q-1). % Since the number of training images (P) is usually less than the number % of pixels (M*N), the most non-zero eigenvalues that can be found are equal % to P-1. So we can calculate eigenvalues of A'*A (a PxP matrix) instead of % A*A' (a M*NxM*N matrix). It is clear that the dimensions of A*A' is much % larger that A'*A. So the dimensionality will decrease. L = A'*A; % L is the surrogate of covariance matrix C=A*A'. [V, D] = eig(L); % Diagonal elements of D are the eigenvalues for both L=A'*A and C=A*A'. %%%%%%%%%%%%%%%%%%%%%%%% Sorting and eliminating eigenvalues % All eigenvalues of matrix L are sorted and those who are less than a % specified threshold, are eliminated. So the number of non-zero % eigenvectors may be less than (P-1). L_eig_vec = []; for i = 1 : size(V,2) if( D(i,i)>1 ) L_eig_vec = [L_eig_vec V(:,i)]; end end %%%%%%%%%%%%%%%%%%%%%%%% Calculating the eigenvectors of covariance matrix 'C' % Eigenvectors of covariance matrix C (or so-called "Eigenfaces") % can be recovered from L's eiegnvectors. Eigenfaces = A * L_eig_vec; % A: centered image vectors