opencv/modules/core/src/pca.cpp

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#include "precomp.hpp"
/****************************************************************************************\
* PCA *
\****************************************************************************************/
namespace cv
{
PCA::PCA() {}
PCA::PCA(InputArray data, InputArray _mean, int flags, int maxComponents)
{
operator()(data, _mean, flags, maxComponents);
}
PCA::PCA(InputArray data, InputArray _mean, int flags, double retainedVariance)
{
operator()(data, _mean, flags, retainedVariance);
}
PCA& PCA::operator()(InputArray _data, InputArray __mean, int flags, int maxComponents)
{
Mat data = _data.getMat(), _mean = __mean.getMat();
int covar_flags = CV_COVAR_SCALE;
int i, len, in_count;
Size mean_sz;
CV_Assert( data.channels() == 1 );
if( flags & CV_PCA_DATA_AS_COL )
{
len = data.rows;
in_count = data.cols;
covar_flags |= CV_COVAR_COLS;
mean_sz = Size(1, len);
}
else
{
len = data.cols;
in_count = data.rows;
covar_flags |= CV_COVAR_ROWS;
mean_sz = Size(len, 1);
}
int count = std::min(len, in_count), out_count = count;
if( maxComponents > 0 )
out_count = std::min(count, maxComponents);
// "scrambled" way to compute PCA (when cols(A)>rows(A)):
// B = A'A; B*x=b*x; C = AA'; C*y=c*y -> AA'*y=c*y -> A'A*(A'*y)=c*(A'*y) -> c = b, x=A'*y
if( len <= in_count )
covar_flags |= CV_COVAR_NORMAL;
int ctype = std::max(CV_32F, data.depth());
mean.create( mean_sz, ctype );
Mat covar( count, count, ctype );
if( !_mean.empty() )
{
CV_Assert( _mean.size() == mean_sz );
_mean.convertTo(mean, ctype);
covar_flags |= CV_COVAR_USE_AVG;
}
calcCovarMatrix( data, covar, mean, covar_flags, ctype );
eigen( covar, eigenvalues, eigenvectors );
if( !(covar_flags & CV_COVAR_NORMAL) )
{
// CV_PCA_DATA_AS_ROW: cols(A)>rows(A). x=A'*y -> x'=y'*A
// CV_PCA_DATA_AS_COL: rows(A)>cols(A). x=A''*y -> x'=y'*A'
Mat tmp_data, tmp_mean = repeat(mean, data.rows/mean.rows, data.cols/mean.cols);
if( data.type() != ctype || tmp_mean.data == mean.data )
{
data.convertTo( tmp_data, ctype );
subtract( tmp_data, tmp_mean, tmp_data );
}
else
{
subtract( data, tmp_mean, tmp_mean );
tmp_data = tmp_mean;
}
Mat evects1(count, len, ctype);
gemm( eigenvectors, tmp_data, 1, Mat(), 0, evects1,
(flags & CV_PCA_DATA_AS_COL) ? CV_GEMM_B_T : 0);
eigenvectors = evects1;
// normalize eigenvectors
for( i = 0; i < out_count; i++ )
{
Mat vec = eigenvectors.row(i);
normalize(vec, vec);
}
}
if( count > out_count )
{
// use clone() to physically copy the data and thus deallocate the original matrices
eigenvalues = eigenvalues.rowRange(0,out_count).clone();
eigenvectors = eigenvectors.rowRange(0,out_count).clone();
}
return *this;
}
void PCA::write(FileStorage& fs ) const
{
CV_Assert( fs.isOpened() );
fs << "name" << "PCA";
fs << "vectors" << eigenvectors;
fs << "values" << eigenvalues;
fs << "mean" << mean;
}
void PCA::read(const FileNode& fs)
{
CV_Assert( !fs.empty() );
String name = (String)fs["name"];
CV_Assert( name == "PCA" );
cv::read(fs["vectors"], eigenvectors);
cv::read(fs["values"], eigenvalues);
cv::read(fs["mean"], mean);
}
template <typename T>
int computeCumulativeEnergy(const Mat& eigenvalues, double retainedVariance)
{
CV_DbgAssert( eigenvalues.type() == DataType<T>::type );
Mat g(eigenvalues.size(), DataType<T>::type);
for(int ig = 0; ig < g.rows; ig++)
{
g.at<T>(ig, 0) = 0;
for(int im = 0; im <= ig; im++)
{
g.at<T>(ig,0) += eigenvalues.at<T>(im,0);
}
}
int L;
for(L = 0; L < eigenvalues.rows; L++)
{
double energy = g.at<T>(L, 0) / g.at<T>(g.rows - 1, 0);
if(energy > retainedVariance)
break;
}
L = std::max(2, L);
return L;
}
PCA& PCA::operator()(InputArray _data, InputArray __mean, int flags, double retainedVariance)
{
Mat data = _data.getMat(), _mean = __mean.getMat();
int covar_flags = CV_COVAR_SCALE;
int i, len, in_count;
Size mean_sz;
CV_Assert( data.channels() == 1 );
if( flags & CV_PCA_DATA_AS_COL )
{
len = data.rows;
in_count = data.cols;
covar_flags |= CV_COVAR_COLS;
mean_sz = Size(1, len);
}
else
{
len = data.cols;
in_count = data.rows;
covar_flags |= CV_COVAR_ROWS;
mean_sz = Size(len, 1);
}
CV_Assert( retainedVariance > 0 && retainedVariance <= 1 );
int count = std::min(len, in_count);
// "scrambled" way to compute PCA (when cols(A)>rows(A)):
// B = A'A; B*x=b*x; C = AA'; C*y=c*y -> AA'*y=c*y -> A'A*(A'*y)=c*(A'*y) -> c = b, x=A'*y
if( len <= in_count )
covar_flags |= CV_COVAR_NORMAL;
int ctype = std::max(CV_32F, data.depth());
mean.create( mean_sz, ctype );
Mat covar( count, count, ctype );
if( !_mean.empty() )
{
CV_Assert( _mean.size() == mean_sz );
_mean.convertTo(mean, ctype);
}
calcCovarMatrix( data, covar, mean, covar_flags, ctype );
eigen( covar, eigenvalues, eigenvectors );
if( !(covar_flags & CV_COVAR_NORMAL) )
{
// CV_PCA_DATA_AS_ROW: cols(A)>rows(A). x=A'*y -> x'=y'*A
// CV_PCA_DATA_AS_COL: rows(A)>cols(A). x=A''*y -> x'=y'*A'
Mat tmp_data, tmp_mean = repeat(mean, data.rows/mean.rows, data.cols/mean.cols);
if( data.type() != ctype || tmp_mean.data == mean.data )
{
data.convertTo( tmp_data, ctype );
subtract( tmp_data, tmp_mean, tmp_data );
}
else
{
subtract( data, tmp_mean, tmp_mean );
tmp_data = tmp_mean;
}
Mat evects1(count, len, ctype);
gemm( eigenvectors, tmp_data, 1, Mat(), 0, evects1,
(flags & CV_PCA_DATA_AS_COL) ? CV_GEMM_B_T : 0);
eigenvectors = evects1;
// normalize all eigenvectors
for( i = 0; i < eigenvectors.rows; i++ )
{
Mat vec = eigenvectors.row(i);
normalize(vec, vec);
}
}
// compute the cumulative energy content for each eigenvector
int L;
if (ctype == CV_32F)
L = computeCumulativeEnergy<float>(eigenvalues, retainedVariance);
else
L = computeCumulativeEnergy<double>(eigenvalues, retainedVariance);
// use clone() to physically copy the data and thus deallocate the original matrices
eigenvalues = eigenvalues.rowRange(0,L).clone();
eigenvectors = eigenvectors.rowRange(0,L).clone();
return *this;
}
void PCA::project(InputArray _data, OutputArray result) const
{
Mat data = _data.getMat();
CV_Assert( !mean.empty() && !eigenvectors.empty() &&
((mean.rows == 1 && mean.cols == data.cols) || (mean.cols == 1 && mean.rows == data.rows)));
Mat tmp_data, tmp_mean = repeat(mean, data.rows/mean.rows, data.cols/mean.cols);
int ctype = mean.type();
if( data.type() != ctype || tmp_mean.data == mean.data )
{
data.convertTo( tmp_data, ctype );
subtract( tmp_data, tmp_mean, tmp_data );
}
else
{
subtract( data, tmp_mean, tmp_mean );
tmp_data = tmp_mean;
}
if( mean.rows == 1 )
gemm( tmp_data, eigenvectors, 1, Mat(), 0, result, GEMM_2_T );
else
gemm( eigenvectors, tmp_data, 1, Mat(), 0, result, 0 );
}
Mat PCA::project(InputArray data) const
{
Mat result;
project(data, result);
return result;
}
void PCA::backProject(InputArray _data, OutputArray result) const
{
Mat data = _data.getMat();
CV_Assert( !mean.empty() && !eigenvectors.empty() &&
((mean.rows == 1 && eigenvectors.rows == data.cols) ||
(mean.cols == 1 && eigenvectors.rows == data.rows)));
Mat tmp_data, tmp_mean;
data.convertTo(tmp_data, mean.type());
if( mean.rows == 1 )
{
tmp_mean = repeat(mean, data.rows, 1);
gemm( tmp_data, eigenvectors, 1, tmp_mean, 1, result, 0 );
}
else
{
tmp_mean = repeat(mean, 1, data.cols);
gemm( eigenvectors, tmp_data, 1, tmp_mean, 1, result, GEMM_1_T );
}
}
Mat PCA::backProject(InputArray data) const
{
Mat result;
backProject(data, result);
return result;
}
}
void cv::PCACompute(InputArray data, InputOutputArray mean,
OutputArray eigenvectors, int maxComponents)
{
PCA pca;
pca(data, mean, 0, maxComponents);
pca.mean.copyTo(mean);
pca.eigenvectors.copyTo(eigenvectors);
}
void cv::PCACompute(InputArray data, InputOutputArray mean,
OutputArray eigenvectors, double retainedVariance)
{
PCA pca;
pca(data, mean, 0, retainedVariance);
pca.mean.copyTo(mean);
pca.eigenvectors.copyTo(eigenvectors);
}
void cv::PCAProject(InputArray data, InputArray mean,
InputArray eigenvectors, OutputArray result)
{
PCA pca;
pca.mean = mean.getMat();
pca.eigenvectors = eigenvectors.getMat();
pca.project(data, result);
}
void cv::PCABackProject(InputArray data, InputArray mean,
InputArray eigenvectors, OutputArray result)
{
PCA pca;
pca.mean = mean.getMat();
pca.eigenvectors = eigenvectors.getMat();
pca.backProject(data, result);
}