face-recongize.zip_camera face matlab

function [m_database V_PCA V_Fisher ProjectedImages_Fisher] = FisherfaceCore(T) Class_number = ( size(T,2) )/2; % Number of classes (or persons) Class_population = 2; % Number of images in each class P = Class_population * Class_number; % Total number of training images %%%%%%%%%%%%%%%%%%%%%%%% calculating the mean image m_database = mean(T,2); %%%%%%%%%%%%%%%%%%%%%%%% Calculating the deviation of each image from mean image A = T - repmat(m_database,1,P); %%%%%%%%%%%%%%%%%%%%%%%% Snapshot method of Eigenface algorithm 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 small eigenvalues L_eig_vec = []; for i = 1 : P-Class_number L_eig_vec = [L_eig_vec V(:,i)]; end %%%%%%%%%%%%%%%%%%%%%%%% Calculating the eigenvectors of covariance matrix 'C' V_PCA = A * L_eig_vec; % A: centered image vectors %%%%%%%%%%%%%%%%%%%%%%%% Projecting centered image vectors onto eigenspace % Zi = V_PCA' * (Ti-m_database) ProjectedImages_PCA = []; for i = 1 : P temp = V_PCA'*A(:,i); ProjectedImages_PCA = [ProjectedImages_PCA temp]; end %%%%%%%%%%%%%%%%%%%%%%%% Calculating the mean of each class in eigenspace m_PCA = mean(ProjectedImages_PCA,2); % Total mean in eigenspace m = zeros(P-Class_number,Class_number); Sw = zeros(P-Class_number,P-Class_number); % Initialization os Within Scatter Matrix Sb = zeros(P-Class_number,P-Class_number); % Initialization of Between Scatter Matrix for i = 1 : Class_number m(:,i) = mean( ( ProjectedImages_PCA(:,((i-1)*Class_population+1):i*Class_population) ), 2 )'; S = zeros(P-Class_number,P-Class_number); for j = ( (i-1)*Class_population+1 ) : ( i*Class_population ) S = S + (ProjectedImages_PCA(:,j)-m(:,i))*(ProjectedImages_PCA(:,j)-m(:,i))'; end Sw = Sw + S; % Within Scatter Matrix Sb = Sb + (m(:,i)-m_PCA) * (m(:,i)-m_PCA)'; % Between Scatter Matrix end %%%%%%%%%%%%%%%%%%%%%%%% Calculating Fisher discriminant basis's % We want to maximise the Between Scatter Matrix, while minimising the % Within Scatter Matrix. Thus, a cost function J is defined, so that this condition is satisfied. [J_eig_vec, J_eig_val] = eig(Sb,Sw); % Cost function J = inv(Sw) * Sb J_eig_vec = fliplr(J_eig_vec); %%%%%%%%%%%%%%%%%%%%%%%% Eliminating zero eigens and sorting in descend order for i = 1 : Class_number-1 V_Fisher(:,i) = J_eig_vec(:,i); % Largest (C-1) eigen vectors of matrix J end %%%%%%%%%%%%%%%%%%%%%%%% Projecting images onto Fisher linear space % Yi = V_Fisher' * V_PCA' * (Ti - m_database) for i = 1 : Class_number*Class_population ProjectedImages_Fisher(:,i) = V_Fisher' * ProjectedImages_PCA(:,i); end