最近看到一篇介绍利用“主成份分析实现人脸识别”的matlab应用实例。
学习了一遍，对主成份分析和图像识别有了一个概念性的认识。
这个例子可能是最简单的人脸识别例子了，暂且不考虑实用性，单单起到认识和了解。
下面matlab程序进行学习注释，希望能帮助记忆。同时加强交流。
程序使用的人脸库来自Essex大学的人脸数据库的face94部分。选择了10个人，每人选择3张照片。1张放入测试集合。
2张放入训练集合。照片比较理想化，绿色背景的大头照片，表情略有不同，光照均匀。
程序的链接如下：
http://www.mathworks.com/matlabcentral/fileexchange/17032-pca-based-face-recognition-system/all_files
内部包含的文件如下
红色的文件是主程序，绿色的是测试集合，蓝色的是训练集合。
license.txt PCA_based Face Recognition System/CreateDatabase.m PCA_based Face Recognition System/EigenfaceCore.m PCA_based Face Recognition System/example.m PCA_based Face Recognition System/Readme.txt PCA_based Face Recognition System/Recognition.m PCA_based Face Recognition System/TestDatabase/1.jpg PCA_based Face Recognition System/TestDatabase/10.jpg PCA_based Face Recognition System/TestDatabase/2.jpg PCA_based Face Recognition System/TestDatabase/3.jpg PCA_based Face Recognition System/TestDatabase/4.jpg PCA_based Face Recognition System/TestDatabase/5.jpg PCA_based Face Recognition System/TestDatabase/6.jpg PCA_based Face Recognition System/TestDatabase/7.jpg PCA_based Face Recognition System/TestDatabase/8.jpg PCA_based Face Recognition System/TestDatabase/9.jpg PCA_based Face Recognition System/TrainDatabase/1.jpg PCA_based Face Recognition System/TrainDatabase/10.jpg PCA_based Face Recognition System/TrainDatabase/11.jpg PCA_based Face Recognition System/TrainDatabase/12.jpg PCA_based Face Recognition System/TrainDatabase/13.jpg PCA_based Face Recognition System/TrainDatabase/14.jpg PCA_based Face Recognition System/TrainDatabase/15.jpg PCA_based Face Recognition System/TrainDatabase/16.jpg PCA_based Face Recognition System/TrainDatabase/17.jpg PCA_based Face Recognition System/TrainDatabase/18.jpg PCA_based Face Recognition System/TrainDatabase/19.jpg PCA_based Face Recognition System/TrainDatabase/2.jpg PCA_based Face Recognition System/TrainDatabase/20.jpg PCA_based Face Recognition System/TrainDatabase/3.jpg PCA_based Face Recognition System/TrainDatabase/4.jpg PCA_based Face Recognition System/TrainDatabase/5.jpg PCA_based Face Recognition System/TrainDatabase/6.jpg PCA_based Face Recognition System/TrainDatabase/7.jpg PCA_based Face Recognition System/TrainDatabase/8.jpg PCA_based Face Recognition System/TrainDatabase/9.jpg
训练集合照片
10个人的训练集合照片差别是比较大的，表情、头部的位置都不相同。
测试集合照片 的差别也是比较大的，与训练集合相似度也不大，远远达不到利用像素对比实现图像识别的能力。
主程序包含下面几个文件
PCA_based Face Recognition System/example.m
用于设定训练集合目录、测试集合目录，链接其余函数。
PCA_based Face Recognition System/CreateDatabas.m
用于将训练集合照片转为灰度照片，然后将照片转换为列向量，最后将所有的训练集合照片形成矩阵
PCA_based Face Recognition System/EigenfaceCore.m
用于对训练集合矩阵标准化，然后求标准化矩阵的相关矩阵的特征根和特征向量。
根据特征值的贡献率，选择大于1的特征根作为主成份分量。 组合主成份分量对应的特征向量为特征向量矩阵。
标准化后的训练集合矩阵与特征向量矩阵相乘得到特征脸核函数。
PCA_based Face Recognition System/Recognition.m
将原始的训练集合彩色照片与特征脸核函数相乘，映射训练集合照片到特征脸空间中。
将测试照片与特征脸核函数相乘，映射测试照片到特征脸空间中。
在特征脸空间求测试照片与每一个训练集合照片的方差，方差最小的训练集合照片编号，就是测试照片鉴别结果。
下面对代码进行注释
example.m
% A sample script, which shows the usage of functions, included in
% PCA-based face recognition system (Eigenface method)
%
% See also: CREATEDATABASE, EIGENFACECORE, RECOGNITION
% Original version by Amir Hossein Omidvarnia, October 2007
% Email: [email protected]
// 清理运行环境
clear all
clc
close all
// 定义训练集合、测试集合的位置以及测试照片的编号
% You can customize and fix initial directory paths
TrainDatabasePath = uigetdir(‘D:\Program Files\MATLAB\R2006a\work‘, ‘Select training database path‘ );
TestDatabasePath = uigetdir(‘D:\Program Files\MATLAB\R2006a\work‘, ‘Select test database path‘);
prompt = {‘Enter test image name (a number between 1 to 10):‘};
dlg_title = ‘Input of PCA-Based Face Recognition System‘;
num_lines= 1;
def = {‘1‘};
TestImage = inputdlg(prompt,dlg_title,num_lines,def);
TestImage = strcat(TestDatabasePath,‘\‘,char(TestImage),‘.jpg‘);
// 读入测试照片
im = imread(TestImage);
// 将训练集合照片转换为灰度的训练集合矩阵.
T = CreateDatabase(TrainDatabasePath);
// 将灰度的训练集合矩阵转换为特征脸核函数
[m, A, Eigenfaces] = EigenfaceCore(T);
//将测试照片 训练集合 利用特征脸核函数进行鉴别
OutputName = Recognition(TestImage, m, A, Eigenfaces);
//根据鉴别结果从训练集合中选择原始照片
SelectedImage = strcat(TrainDatabasePath,‘\‘,OutputName);
SelectedImage = imread(SelectedImage);
//输出鉴别结果
figure
imshow(im)
title(‘Test Image‘);
figure,imshow(SelectedImage);
title(‘Equivalent Image‘);
str = strcat(‘Matched image is : ‘,OutputName);
disp(str)
CreateDatabas.m
// 定义函数,输入变量为训练集合路径
function T = CreateDatabase(TrainDatabasePath)
% Align a set of face images (the training set T1, T2, ... , TM )
%
% Description: This function reshapes all 2D images of the training database
% into 1D column vectors. Then, it puts these 1D column vectors in a row to
% construct 2D matrix ‘T‘.
%
%
% Argument: TrainDatabasePath - Path of the training database
%
% Returns: 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 MN and ‘T‘ will be a MNxP 2D matrix.
%
% See also: STRCMP, STRCAT, RESHAPE
% Original version by Amir Hossein Omidvarnia, October 2007
% Email: [email protected]
%%%%%%%%%%%%%%%%%%%%%%%% File management
//得到训练集合的文件
TrainFiles = dir(TrainDatabasePath);
Train_Number = 0;
for i = 1:size(TrainFiles,1)
if not(strcmp(TrainFiles(i).name,‘.‘)|strcmp(TrainFiles(i).name,‘..‘)|strcmp(TrainFiles(i).name,‘Thumbs.db‘))
Train_Number = Train_Number + 1; % Number of all images in the training database
end
end
%%%%%%%%%%%%%%%%%%%%%%%% Construction of 2D matrix from 1D image vectors
// 将训练集合照片拼接为矩阵
T = [];
for i = 1 : Train_Number
% I have chosen the name of each image in databases as a corresponding
% number. However, it is not mandatory!
// 拼接训练集合照片 路径和文件名
str = int2str(i);
str = strcat(‘\‘,str,‘.jpg‘);
% strg = strcat(‘\‘,str,‘_g.jpg‘);
str = strcat(TrainDatabasePath,str);
% strg = strcat(TrainDatabasePath,strg);
//读取训练照片,并转为灰度照片
img = imread(str);
img = rgb2gray(img);
% imwrite(img,strg);
[irow icol] = size(img);
// 将照片转为列向量,按照先行再列的顺序转换为irow*icol行的列向量
temp = reshape(img‘,irow*icol,1); % Reshaping 2D images into 1D image vectors
//拼接列向量为矩阵
T = [T temp]; % ‘T‘ grows after each turn
end
EigenfaceCore.m
// 定义函数，输入为的训练集合照片灰度矩阵
输出m为训练集合照片灰度矩阵的行均值的列向量
输出A为训练集合照片灰度矩阵的偏差矩阵
输出Eigenfaces 为训练集合得到的特征脸核函数
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: [email protected]
%%%%%%%%%%%%%%%%%%%%%%%% Calculating the mean image
// 求训练集合灰度照片矩阵的行均值
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
// 利用行均值求的训练集合照片灰度矩阵的偏差值。得到偏差矩阵
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
% normal1 = reshape(temp,180,200);
% imwrite(normal1‘,[num2str(i),‘_normal.jpg‘]);
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.
// 求出偏差矩阵的相关矩阵，以及相关矩阵的特征值D和特征向量V
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‘.
% diag(D)
% V
%%%%%%%%%%%%%%%%%%%%%%%% 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).
// 选择大于1的特征值作为主成份。提取对应的特征向量，拼接为特征向量矩阵。
L_eig_vec = [];
for i = 1 : size(V,2)
if( D(i,i)>1 )
L_eig_vec = [L_eig_vec V(:,i)];
end
end
% L_eig_vec
%%%%%%%%%%%%%%%%%%%%%%%% Calculating the eigenvectors of covariance matrix ‘C‘
% Eigenvectors of covariance matrix C (or so-called "Eigenfaces")
% can be recovered from L‘s eiegnvectors.
// 特征向量与训练集合照片偏差矩阵相乘，得到特征脸核函数
Eigenfaces = A * L_eig_vec; % A: centered image vectors
% for i = 1 : 19
% temp = Eigenfaces(:,i); % Computing the difference image for each image in the training set Ai = Ti - m
% normal1 = reshape(temp,180,200);
% imwrite(normal1‘,[num2str(i),‘_Eigenfaces.jpg‘]);
% end