/************************************************************************/
/* QR-PCA-FaceRec by John Hany */
/* */
/* A face recognition algorithm using QR based PCA. */
/* */
/* Released under MIT license. */
/* */
/* */
/* Welcome to my blog http://johnhany.net/, if you can read Chinese:) */
/* */
/************************************************************************/
#include
#include
using namespace std ;
int component_num = 7 ;
string orl_path = "G:\\Datasets\\orl_faces" ;
enum distance_type { ECULIDEAN = 0 , MANHATTAN , MAHALANOBIS } ;
//double distance_criterion[3] = { 10.0, 30.0, 3.0};
double distance_criterion [ 3 ] = { 1000.0 , 1000.0 , 1000.0 } ;
bool compDistance ( pair < int , double > a , pair < int , double > b ) ;
double calcuDistance ( const arma :: vec vec1 , const arma :: vec vec2 , distance_type dis_type ) ;
double calcuDistance ( const arma :: vec vec1 , const arma :: vec vec2 , const arma :: mat cov2 , distance_type dis_type ) ;
int main ( int argc , const char * argv [ ] ) {
int class_num = 40 ;
int sample_num = 10 ;
int img_cols = 92 ;
int img_rows = 112 ;
cv :: Size sample_size ( img_cols , img_rows ) ;
arma :: mat mat_sample ( img_rows* img_cols , sample_num* class_num ) ;
//Load samples in one matrix `mat_sample`.
for ( int class_idx = 0 ; class_idx < class_num ; class_idx ++ ) {
for ( int sample_idx = 0 ; sample_idx < sample_num ; sample_idx ++ ) {
string filename = orl_path + "\\s" + to_string ( class_idx + 1 ) + "\\" + to_string ( sample_idx + 1 ) + ".pgm" ;
cv :: Mat img_frame = cv :: imread ( filename , CV_LOAD_IMAGE_GRAYSCALE ) ;
cv :: Mat img_sample ;
cv :: resize ( img_frame , img_sample , sample_size ) ;
for ( int i = 0 ; i < img_rows ; i ++ ) {
uchar* pframe = img_sample . ptr < uchar > ( i ) ;
for ( int j = 0 ; j < img_cols ; j ++ ) {
mat_sample ( i* img_cols + j , class_idx* sample_num + sample_idx ) = ( double ) pframe [ j ] / 255.0 ;
}
}
}
}
// cout << mat_sample.n_rows << endl << mat_sample.n_cols << endl << mat_sample(img_rows*img_cols/2, 0) << endl;
//Calculate PCA transform matrix `mat_pca`.
arma :: mat H = mat_sample ;
arma :: mat mean_x = arma :: mean ( mat_sample , 1 ) ;
for ( int j = 0 ; j < class_num * sample_num ; j ++ ) {
H . col ( j ) -= mean_x . col ( 0 ) ;
}
H /= 1.0 / sqrt ( sample_num - 1 ) ;
arma :: mat Q , R ;
arma :: qr_econ ( Q , R , H ) ;
arma :: mat U , V ;
arma :: vec d ;
arma :: svd_econ ( U , d , V , R . t ( ) ) ;
// cout << "d" << endl << d << endl;
// arma::rowvec vec_eigen = d.head(component_num).t();
// cout << "vec_eigen" << endl << vec_eigen << endl;
arma :: mat V_h ( V . n_rows , component_num ) ;
if ( component_num == 1 ) {
V_h = V . col ( 0 ) ;
} else {
V_h = V . cols ( 0 , component_num - 1 ) ;
}
arma :: mat mat_pca = Q * V_h ;
//Calculate eigenfaces `mat_eigen_vec`.
arma :: mat mat_eigen = mat_pca . t ( ) * mat_sample ;
// cout << "mat_eigen" << endl << mat_eigen << endl;
arma :: mat mat_eigen_vec ( component_num , class_num , arma :: fill :: zeros ) ;
vector < arma :: mat > mat_cov_list ;
for ( int class_idx = 0 ; class_idx < class_num ; class_idx ++ ) {
arma :: vec eigen_sum ( component_num , arma :: fill :: zeros ) ;
for ( int sample_idx = 0 ; sample_idx < sample_num ; sample_idx ++ ) {
eigen_sum += mat_eigen . col ( class_idx* sample_num + sample_idx ) ;
}
eigen_sum /= ( double ) sample_num ;
mat_eigen_vec . col ( class_idx ) = eigen_sum ;
mat_cov_list . push_back ( arma :: cov ( ( mat_eigen . cols ( class_idx* sample_num , class_idx* sample_num + sample_num - 1 ) ) . t ( ) ) ) ;
// cout << mat_cov_list[class_idx] << endl;
}
// cout << "mat_eigen_vec" << endl << mat_eigen_vec << endl;
/*
cout << "dis within class" << endl;
for(int class_idx = 0; class_idx < class_num; class_idx++) {
for(int sample_idx = 0; sample_idx < sample_num; sample_idx++) {
double dis = calcuDistance(mat_eigen.col(class_idx*sample_num+sample_idx), mat_eigen_vec.col(class_idx), mat_cov_list[class_idx], distance_type::MAHALANOBIS);
cout << dis << " ";
}
cout << endl;
}
cout << "dis between classes" << endl;
for(int class_idx = 0; class_idx < class_num; class_idx++) {
for(int sample_idx = 0; sample_idx < class_num; sample_idx++) {
double dis = calcuDistance(mat_eigen.col(sample_idx*sample_num), mat_eigen_vec.col(class_idx), mat_cov_list[class_idx], distance_type::MAHALANOBIS);
cout << dis << " ";
}
cout << endl;
}
*/
//Classify new sample.
int correct_count = 0 ;
double max_dis = 0.0 ;
for ( int class_idx = 0 ; class_idx < class_num ; class_idx ++ ) {
for ( int sample_idx = 0 ; sample_idx < sample_num ; sample_idx ++ ) {
arma :: mat mat_new_sample ( img_rows* img_cols , 1 ) ;
string filename = orl_path + "\\s" + to_string ( class_idx + 1 ) + "\\" + to_string ( sample_idx + 1 ) + ".pgm" ;
cv :: Mat img_new_frame = cv :: imread ( filename , CV_LOAD_IMAGE_GRAYSCALE ) ;
cv :: Mat img_new_sample ;
cv :: resize ( img_new_frame , img_new_sample , sample_size ) ;
for ( int i = 0 ; i < img_rows ; i ++ ) {
uchar* pframe = img_new_sample . ptr < uchar > ( i ) ;
for ( int j = 0 ; j < img_cols ; j ++ ) {
mat_new_sample ( i* img_cols + j , 0 ) = ( double ) pframe [ j ] / 255.0 ;
}
}
arma :: mat mat_new_eigen = mat_pca . t ( ) * mat_new_sample ;
vector < pair < int , double >> dis_list ;
for ( int new_class_idx = 0 ; new_class_idx < class_num ; new_class_idx ++ ) {
double dis = calcuDistance ( mat_new_eigen . col ( 0 ) , mat_eigen_vec . col ( new_class_idx ) , mat_cov_list [ new_class_idx ] , distance_type :: MAHALANOBIS ) ;
dis_list . push_back ( make_pair ( new_class_idx , dis ) ) ;
}
sort ( dis_list . begin ( ) , dis_list . end ( ) , compDistance ) ;
if ( dis_list [ 0 ] . first == class_idx && dis_list [ 0 ] . second <= distance_criterion [ distance_type :: MAHALANOBIS ] ) {
correct_count ++ ;
}
if ( dis_list . back ( ) . second > max_dis ) {
max_dis = dis_list . back ( ) . second ;
}
}
}
cout << "Maximum distance: " << max_dis << endl ;
double correct_ratio = ( double ) correct_count / ( class_num * sample_num ) ;
cout << "Correctness ratio: " << correct_ratio * 100.0 << "%" << endl ;
cin . get ( ) ;
return 0 ;
}
bool compDistance ( pair < int , double > a , pair < int , double > b ) {
return ( a . second < b . second ) ;
}
double calcuDistance ( const arma :: vec vec1 , const arma :: vec vec2 , distance_type dis_type ) {
if ( dis_type == ECULIDEAN ) {
return arma :: norm ( vec1 - vec2 , 2 ) ;
} else if ( dis_type == MANHATTAN ) {
return arma :: norm ( vec1 - vec2 , 1 ) ;
} else if ( dis_type == MAHALANOBIS ) {
arma :: mat tmp = ( vec1 - vec2 ) . t ( ) * ( vec1 - vec2 ) ;
return sqrt ( tmp ( 0 , 0 ) ) ;
}
return - 1.0 ;
}
double calcuDistance ( const arma :: vec vec1 , const arma :: vec vec2 , const arma :: mat cov2 , distance_type dis_type ) {
if ( dis_type == ECULIDEAN ) {
return arma :: norm ( vec1 - vec2 , 2 ) ;
} else if ( dis_type == MANHATTAN ) {
return arma :: norm ( vec1 - vec2 , 1 ) ;
} else if ( dis_type == MAHALANOBIS ) {
arma :: mat tmp = ( vec1 - vec2 ) . t ( ) * cov2 . i ( ) * ( vec1 - vec2 ) ;
return sqrt ( tmp ( 0 , 0 ) ) ;
}
return - 1.0 ;
}
![X=[x_1,\dots,x_n]](http://img.e-com-net.com/image/info8/bda97fed1677431e8aeede40b3e77195.png "X=[x_1,\dots,x_n]")
；
，令![H=\frac{1}{\sqrt{n-1}}[x_1-\mu,\dots,x_n-\mu]](http://img.e-com-net.com/image/info8/5c2c0075c7a440388b741ce9d9b8eac9.png "H=\frac{1}{\sqrt{n-1}}[x_1-\mu,\dots,x_n-\mu]")
；
；
的特征值与特征向量，取前h个最大特征值所对应的特征向量，构成矩阵
；
，Y是h行400列的矩阵，也就是将数据从10000维降为h维。
，其中Q为d*t，R为t*n，
；
，对
作奇异值分解
，其中U为n*t，V为t*t，
；
，其中
；
，所以QV可将
为
，则降维矩阵
；
，y的长度为h；
，取距离最小的i作为x的类标号。