基于PCA人脸识别算法的Matlab实现（1）

基于PCA人脸识别算法的Matlab实现

最近在做人脸识别的项目，一直用别的接口也不是办法，找点论文

 

'Eigenface' Face Recognition System
Written by: Amir Hossein Omidvarnia

This package implements a well-known PCA-based face recognition
method, which is called 'Eigenface' [1].
All functions are easy to use, as they are heavy commented.
Furthermore, a sample script is included to show their usage.
In general, you should follow this order:

1. Select training and test database paths.
2. Select path of the test image.
3. Run 'CreateDatabase' function to create 2D matrix of all training images.
4. Run 'EigenfaceCore' function to produce basis's of facespace.
5. Run 'Recognition' function to get the name of equivalent image in training database.

For your convenience, I have prepared sample training and test databases, which are parts
of 'face94' Essex face database [2]. You just need to copy the above functions, along with
the training and test databases into a specified path (for example 'work' path of your
MATLAB root). Then follow dialog boxes, which will appear upon running 'example.m'.

Enjoy it!

 

References:

[1] P. N. Belhumeur, J. Hespanha, and D. J. Kriegman. Eigenfaces vs. Fisherfaces: Recognition
using class specific linear projection. In ECCV (1), pages 45--58, 1996.

[2] Available at:
http://cswww.essex.ac.uk/mv/allfaces/faces94.zip

 

 

Recognition.m

function OutputName = Recognition(TestImage, m, A, Eigenfaces)
% Recognizing step....
%
% Description: This function compares two faces by projecting the images into facespace and 
% measuring the Euclidean distance between them.
%
% Argument:      TestImage              - Path of the input test image
%
%                m                      - (M*Nx1) Mean of the training
%                                         database, which is output of 'EigenfaceCore' function.
%
%                Eigenfaces             - (M*Nx(P-1)) Eigen vectors of the
%                                         covariance matrix of the training
%                                         database, which is output of 'EigenfaceCore' function.
%
%                A                      - (M*NxP) Matrix of centered image
%                                         vectors, which is output of 'EigenfaceCore' function.
% 
% Returns:       OutputName             - Name of the recognized image in the training database.
%
% See also: RESHAPE, STRCAT

% Original version by Amir Hossein Omidvarnia, October 2007
%                     Email: aomidvar@ece.ut.ac.ir                  

%%%%%%%%%%%%%%%%%%%%%%%% Projecting centered image vectors into facespace
% All centered images are projected into facespace by multiplying in
% Eigenface basis's. Projected vector of each face will be its corresponding
% feature vector.

ProjectedImages = [];
Train_Number = size(Eigenfaces,2);
for i = 1 : Train_Number
    temp = Eigenfaces'*A(:,i); % Projection of centered images into facespace
    ProjectedImages = [ProjectedImages temp]; 
end

%%%%%%%%%%%%%%%%%%%%%%%% Extracting the PCA features from test image
InputImage = imread(TestImage);
temp = InputImage(:,:,1);

[irow icol] = size(temp);
InImage = reshape(temp',irow*icol,1);
Difference = double(InImage)-m; % Centered test image
ProjectedTestImage = Eigenfaces'*Difference; % Test image feature vector

%%%%%%%%%%%%%%%%%%%%%%%% Calculating Euclidean distances 
% Euclidean distances between the projected test image and the projection
% of all centered training images are calculated. Test image is
% supposed to have minimum distance with its corresponding image in the
% training database.

Euc_dist = [];
for i = 1 : Train_Number
    q = ProjectedImages(:,i);
    temp = ( norm( ProjectedTestImage - q ) )^2;
    Euc_dist = [Euc_dist temp];
end

[Euc_dist_min , Recognized_index] = min(Euc_dist);
OutputName = strcat(int2str(Recognized_index),'.jpg');

　　

CreateDatabase.m

 

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: aomidvar@ece.ut.ac.ir                  

%%%%%%%%%%%%%%%%%%%%%%%% File management
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
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!
    str = int2str(i);
    str = strcat('\',str,'.jpg');
    str = strcat(TrainDatabasePath,str);
    
    img = imread(str);
    img = rgb2gray(img);
    
    [irow icol] = size(img);
   
    temp = reshape(img',irow*icol,1);   % Reshaping 2D images into 1D image vectors
    T = [T temp]; % 'T' grows after each turn                    
end

　　

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

　　

 

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: aomidvar@ece.ut.ac.ir                  

clear all
clc
close all

% 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');
im = imread(TestImage);

T = CreateDatabase(TrainDatabasePath);
[m, A, Eigenfaces] = EigenfaceCore(T);
OutputName = Recognition(TestImage, m, A, Eigenfaces);

SelectedImage = strcat(TrainDatabasePath,'\',OutputName);
SelectedImage = imread(SelectedImage);

imshow(im)
title('Test Image');
figure,imshow(SelectedImage);
title('Equivalent Image');

str = strcat('Matched image is :  ',OutputName);
disp(str)