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⛄ 内容介绍
人脸识别是计算机视觉和模式识别领域的一个活跃课题,有着十分广泛的应用前景.给出了一种基于PCA和LDA方法的人脸识别系统的实现.首先该算法采用奇异值分解技术提取主成分,然后用Fisher线性判别分析技术来提取最终特征,最后将测试图像的投影与每一训练图像的投影相比较,与测试图像最接近的训练图像被系统识别出,图像的比较采用了欧几里德距离,仿真结果表明了该方法的有效性.
⛄ 部分代码
function [m_database V_PCA V_Fisher ProjectedImages_Fisher] = FisherfaceCore(T)
% Use Principle Component Analysis (PCA) and Fisher Linear Discriminant (FLD) to determine the most
% discriminating features between images of faces.
%
% Description: This function gets a 2D matrix, containing all training image vectors
% and returns 4 outputs which are extracted from training database.
% Suppose Ti is a training image, which has been reshaped into a 1D vector.
% Also, P is the total number of MxN training images and C is the number of
% classes. At first, centered Ti is mapped onto a (P-C) linear subspace by V_PCA
% transfer matrix: Zi = V_PCA * (Ti - m_database).
% Then, Zi is converted to Yi by projecting onto a (C-1) linear subspace, so that
% images of the same class (or person) move closer together and images of difference
% classes move further apart: Yi = V_Fisher' * Zi = V_Fisher' * V_PCA' * (Ti - m_database)
%
% Argument: T - (M*NxP) A 2D matrix, containing all 1D image vectors.
% All of 1D column vectors have the same length of M*N
% and 'T' will be a MNxP 2D matrix.
%
% Returns: m_database - (M*Nx1) Mean of the training database
% V_PCA - (M*Nx(P-C)) Eigen vectors of the covariance matrix of the
% training database
% V_Fisher - ((P-C)x(C-1)) Largest (C-1) eigen vectors of matrix J = inv(Sw) * Sb
% ProjectedImages_Fisher - ((C-1)xP) Training images, which are projected onto Fisher linear space
%
% See also: EIG
% Original version by Amir Hossein Omidvarnia, October 2007
% Email: aomidvar@ece.ut.ac.ir
Class_number = ( size(T,2) )/2; % Number of classes (or persons) 矩阵 T 的列数 除以2，也就是 训练图片数量的一半
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); %样本均值
%%%%%%%%%%%%%%%%%%%%%%%% Calculating the deviation of each image from mean image 每张图片与均值图片的背离程度
A = T - repmat(m_database,1,P);
%%%%%%%%%%%%%%%%%%%%%%%% Snapshot method of Eigenface algorithm
L = A'*A; % L is the surrogate（代理人） of covariance matrix C=A*A'.协方差矩阵
[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
⛄ 运行结果
⛄ 参考文献
[1] 钟向阳, 胡仕明. 基于主分量线性判别方法人脸识别系统的实现[J]. 嘉应学院学报:自然科学版, 2006.
[2] 张凯歌. 基于线性判别分析的人脸识别系统研究与实现[D]. 广东工业大学.
[3] 乐丹, 罗文兵, 叶继华,等. 基于2DPCA和Fisher的嵌入式人脸识别系统的实现[J]. 科技广场, 2011(1):4.
[4] 曾贤灏, 李向伟. 基于Fisher准则改进线性判别回归分类的人脸识别[J]. 计算机应用与软件, 2014, 31(9):4.
[5] 马祥, 王映卓, 樊强. 基于LLE与Fisher线性判别的人脸识别算法[J]. 现代电子技术, 2012, 35(8):3.
