itk::Matrix< double , 3 , 3 > ComputeMatrixSquareRoot( itk::Matrix< double , 3 , 3 > matrix )
{
itk::Matrix< double , 3 , 3 > sqrMatrix;
vnl_matrix<double> M( 3, 3 );
M = matrix.GetVnlMatrix();
vnl_real_eigensystem eig( M );
vnl_matrix<vcl_complex<double> > D( 3, 3 );
vnl_matrix<vcl_complex<double> > vnl_sqrMatrix( 3, 3 );
D.fill( 0.0 );
for( int i = 0; i < 3; i++ )
{
D.put( i, i, vcl_pow( eig.D.get( i, i ), 0.5 ) );
}
vnl_sqrMatrix = eig.V * D * vnl_matrix_inverse<vcl_complex<double> >( eig.V );
vnl_matrix<double> vnl_sqrMatrix_real( 3, 3 );
vnl_sqrMatrix_real = vnl_real( vnl_sqrMatrix );
for( int i = 0; i < 3; i++ )
{
for( int j = 0; j < 3; j++ )
{
sqrMatrix[i][j] = vnl_sqrMatrix_real.get( i, j );
}
}
return sqrMatrix;
}
std::vector<float> compute_ec_features( USImageType::Pointer input_image, USImageType::Pointer inp_labeled, int number_of_rois, unsigned short thresh, int surr_dist, int inside_dist ){
std::vector< float > qfied_num;
std::vector< USImageType::PixelType > labelsList;
std::vector< double > quantified_numbers_cell;
typedef itk::ExtractImageFilter< USImageType, UShortImageType > LabelExtractType;
typedef itk::ImageRegionConstIterator< UShortImageType > ConstIteratorType;
typedef itk::ImageRegionIteratorWithIndex< USImageType > IteratorType;
typedef itk::SignedDanielssonDistanceMapImageFilter<FloatImageType, FloatImageType > DTFilter;
typedef itk::ImageRegionIteratorWithIndex< FloatImageType > IteratorTypeFloat;
typedef itk::LabelGeometryImageFilter< USImageType > GeometryFilterType;
typedef GeometryFilterType::LabelIndicesType labelindicestype;
itk::SizeValueType sz_x, sz_y, sz_z;
sz_x = input_image->GetLargestPossibleRegion().GetSize()[0];
sz_y = input_image->GetLargestPossibleRegion().GetSize()[1];
sz_z = input_image->GetLargestPossibleRegion().GetSize()[2];
if( sz_x==1 || sz_y==1 || sz_z==1 ){
LabelExtractType::Pointer deFilter = LabelExtractType::New();
USImageType::RegionType dRegion = inp_labeled->GetLargestPossibleRegion();
dRegion.SetSize(2,0);
deFilter->SetExtractionRegion(dRegion);
deFilter->SetInput( inp_labeled );
deFilter->SetDirectionCollapseToIdentity();
try{
deFilter->Update();
}
catch( itk::ExceptionObject & excep ){
std::cerr << "Exception caught !" << std::endl;
std::cerr << excep << std::endl;
}
//Dialate input first
WholeCellSeg *dialate_filter = new WholeCellSeg;
dialate_filter->set_nuc_img( deFilter->GetOutput() );
dialate_filter->set_radius( surr_dist );
dialate_filter->RunSegmentation();
UShortImageType::Pointer input_lab = dialate_filter->getSegPointer();
USImageType::Pointer input_labeled = USImageType::New();
USImageType::PointType origint;
origint[0] = 0;
origint[1] = 0;
origint[2] = 0;
input_labeled->SetOrigin( origint );
USImageType::IndexType startt;
startt[0] = 0; // first index on X
startt[1] = 0; // first index on Y
startt[2] = 0; // first index on Z
USImageType::SizeType sizet;
sizet[0] = inp_labeled->GetLargestPossibleRegion().GetSize()[0]; // size along X
sizet[1] = inp_labeled->GetLargestPossibleRegion().GetSize()[1]; // size along Y
sizet[2] = inp_labeled->GetLargestPossibleRegion().GetSize()[2]; // size along Z
USImageType::RegionType regiont;
regiont.SetSize( sizet );
regiont.SetIndex( startt );
input_labeled->SetRegions( regiont );
input_labeled->Allocate();
input_labeled->FillBuffer(0);
input_labeled->Update();
ConstIteratorType pix_buf1( input_lab, input_lab->GetRequestedRegion() );
IteratorType iterator2 ( input_labeled, input_labeled->GetRequestedRegion() );
iterator2.GoToBegin();
for ( pix_buf1.GoToBegin(); !pix_buf1.IsAtEnd(); ++pix_buf1 ){
iterator2.Set( pix_buf1.Get() );
++iterator2;
}
std::vector< float > quantified_numbers;
typedef itk::LabelGeometryImageFilter< USImageType > GeometryFilterType;
typedef GeometryFilterType::LabelIndicesType labelindicestype;
GeometryFilterType::Pointer geomfilt1 = GeometryFilterType::New();
geomfilt1->SetInput( input_labeled );
geomfilt1->SetCalculatePixelIndices( true );
geomfilt1->Update();
labelsList = geomfilt1->GetLabels();
bool zp=false;
for( USImageType::PixelType i=0; i < labelsList.size(); ++i ){
if( labelsList[i] == 0 ){ zp=true; continue; }
std::vector<float> quantified_numbers_cell;
for( unsigned j=0; j<number_of_rois; ++j ) quantified_numbers_cell.push_back((float)0.0);
double centroid_x = geomfilt1->GetCentroid(labelsList[i])[0];
double centroid_y = geomfilt1->GetCentroid(labelsList[i])[1];
labelindicestype indices1;
indices1 = geomfilt1->GetPixelIndices(labelsList[i]);
for( labelindicestype::iterator itPixind = indices1.begin(); itPixind!=indices1.end(); ++itPixind ){
IteratorType iterator1 ( input_image, input_image->GetRequestedRegion() );
iterator1.SetIndex( *itPixind );
if( iterator1.Get() < thresh )
continue;
double x = iterator1.GetIndex()[0];
double y = iterator1.GetIndex()[1];
double angle = atan2((centroid_y-y),fabs(centroid_x-x));
if( (centroid_x-x)>0 )
angle += M_PI_2;
else
angle = M_PI+M_PI-(angle+M_PI_2);
angle = ((number_of_rois-1)*angle)/(2*M_PI);
double angle_fraction[1];
unsigned angular_index;
if( modf( angle, angle_fraction ) > 0.5 )
angular_index = ceil( angle );
else
angular_index = floor( angle );
quantified_numbers_cell[angular_index] += iterator1.Get();
}
for( unsigned j=0; j<number_of_rois; ++j ) quantified_numbers.push_back(quantified_numbers_cell[j]);
}
unsigned qnum_sz = zp? (labelsList.size()-1) : (labelsList.size());
for( unsigned i=0; i<qnum_sz; ++i ){
unsigned counter=0;
for( unsigned j=0; j<number_of_rois; ++j ){
if( quantified_numbers[(i*number_of_rois+j)] > (255.0*surr_dist) )
++counter;
}
qfied_num.push_back(counter);
}
}
else{
GeometryFilterType::Pointer geomfilt1 = GeometryFilterType::New();
geomfilt1->SetInput( inp_labeled );
geomfilt1->SetCalculatePixelIndices( true );
geomfilt1->Update();
labelsList = geomfilt1->GetLabels();
std::cout<<std::endl<<"The size is: "<<labelsList.size();
if( labelsList.size() == 1 )
{
qfied_num.clear();
return qfied_num;
}
bool zp=false; USPixelType zero;
//Check if the background is also included
for( USPixelType i=0; i<labelsList.size(); ++i ) if( labelsList[i] == 0 ){ zp=true; zero = i; }
USImageType::SizeType sizee;
sizee[0] = inp_labeled->GetLargestPossibleRegion().GetSize()[0]; // size along X
sizee[1] = inp_labeled->GetLargestPossibleRegion().GetSize()[1]; // size along Y
sizee[2] = inp_labeled->GetLargestPossibleRegion().GetSize()[2]; // size along Z
itk::SizeValueType roi_list_size = zp ?
((itk::SizeValueType)number_of_rois*(labelsList.size()-1)*2) :
((itk::SizeValueType)number_of_rois*labelsList.size()*2);
std::vector<double> quantified_numbers_cell((roi_list_size),0.0
);
std::cout<<"Bounding boxes computed"<<std::endl;
#ifdef _OPENMP
itk::MultiThreader::SetGlobalDefaultNumberOfThreads(1);
#pragma omp parallel for
#if _OPENMP < 200805L
for( int i=0; i<labelsList.size(); ++i )
#else
for( USImageType::PixelType i=0; i<labelsList.size(); ++i )
#endif
#else
for( USImageType::PixelType i=0; i<labelsList.size(); ++i )
#endif
{
itk::SizeValueType ind;
if( zp && (zero==i) ) continue;
if( zp && (i>zero) ) ind = i-1;
else ind = i;
//Get label indices
labelindicestype indices1;
double centroid_x,centroid_y,centroid_z;
GeometryFilterType::BoundingBoxType boundbox;
#pragma omp critical
{
indices1 = geomfilt1->GetPixelIndices(labelsList[i]);
//Get Centroid
centroid_x = geomfilt1->GetCentroid(labelsList[i])[0];
centroid_y = geomfilt1->GetCentroid(labelsList[i])[1];
centroid_z = geomfilt1->GetCentroid(labelsList[i])[2];
//Create an image with bounding box + 2 * outside distance + 2
//and get distance map for the label
boundbox = geomfilt1->GetBoundingBox(labelsList[i]);
}
//Create vnl array 3xN( label indicies )
vnl_matrix<double> B(3,indices1.size());
FloatImageType::Pointer inp_lab = FloatImageType::New();
FloatImageType::PointType origint; origint[0] = 0; origint[1] = 0; origint[2] = 0;
inp_lab->SetOrigin( origint );
FloatImageType::IndexType startt;
startt[0] = 0; // first index on X
startt[1] = 0; // first index on Y
startt[2] = 0; // first index on Z
FloatImageType::SizeType sizet;
sizet[0] = boundbox[1]-boundbox[0]+2*surr_dist+2; // size along X
sizet[1] = boundbox[3]-boundbox[2]+2*surr_dist+2; // size along Y
sizet[2] = boundbox[5]-boundbox[4]+2*surr_dist+2; // size along Z
FloatImageType::RegionType regiont;
regiont.SetSize( sizet );
regiont.SetIndex( startt );
inp_lab->SetRegions( regiont );
inp_lab->Allocate();
inp_lab->FillBuffer(0.0);
inp_lab->Update();
IteratorTypeFloat iterator444 ( inp_lab, inp_lab->GetRequestedRegion() );
//Populate matrix with deviations from the centroid for principal axes and
//at the same time set up distance-transform computation
itk::SizeValueType ind1=0;
for( labelindicestype::iterator itPixind = indices1.begin(); itPixind!=indices1.end(); ++itPixind ){
IteratorType iterator3( input_image, input_image->GetRequestedRegion() );
iterator3.SetIndex( *itPixind );
B(0,(ind1)) = iterator3.GetIndex()[0]-centroid_x;
B(1,(ind1)) = iterator3.GetIndex()[1]-centroid_y;
B(2,(ind1)) = iterator3.GetIndex()[2]-centroid_z;
FloatImageType::IndexType cur_in;
cur_in[0] = iterator3.GetIndex()[0]-boundbox[0]+1+surr_dist;
cur_in[1] = iterator3.GetIndex()[1]-boundbox[2]+1+surr_dist;
cur_in[2] = iterator3.GetIndex()[2]-boundbox[4]+1+surr_dist;
iterator444.SetIndex( cur_in );
iterator444.Set( 255.0 );
++ind1;
}
//Compute distance transform for the current object
DTFilter::Pointer dt_obj= DTFilter::New() ;
dt_obj->SetInput( inp_lab );
dt_obj->SquaredDistanceOff();
dt_obj->InsideIsPositiveOff();
try{
dt_obj->Update() ;
} catch( itk::ExceptionObject & err ){
std::cerr << "Error in Distance Transform: " << err << std::endl;
}
FloatImageType::Pointer dist_im = dt_obj->GetOutput();
//Use KLT to compute pricipal axes
vnl_matrix<double> B_transp((int)indices1.size(),3);
B_transp = B.transpose();
vnl_matrix<double> COV(3,3);
COV = B * B_transp;
double norm = 1.0/(double)indices1.size();
COV = COV * norm;
//Eigen decomposition
vnl_real_eigensystem Eyegun( COV );
vnl_matrix<vcl_complex<double> > EVals = Eyegun.D;
double Eval1 = vnl_real(EVals)(0,0); double Eval2 = vnl_real(EVals)(1,1); double Eval3 = vnl_real(EVals)(2,2);
vnl_double_3x3 EVectMat = Eyegun.Vreal;
double V1[3],V2[3],EP_norm[3];
if( Eval1 >= Eval3 && Eval2 >= Eval3 ){
if( Eval1 >= Eval2 ){
V1[0] = EVectMat(0,0); V1[1] = EVectMat(1,0); V1[2] = EVectMat(2,0);
V2[0] = EVectMat(0,1); V2[1] = EVectMat(1,1); V2[2] = EVectMat(2,1);
} else {
V2[0] = EVectMat(0,0); V2[1] = EVectMat(1,0); V2[2] = EVectMat(2,0);
V1[0] = EVectMat(0,1); V1[1] = EVectMat(1,1); V1[2] = EVectMat(2,1);
}
} else if( Eval1 >= Eval2 && Eval3 >= Eval2 ) {
if( Eval1 >= Eval3 ){
V1[0] = EVectMat(0,0); V1[1] = EVectMat(1,0); V1[2] = EVectMat(2,0);
V2[0] = EVectMat(0,2); V2[1] = EVectMat(1,2); V2[2] = EVectMat(2,2);
} else {
V2[0] = EVectMat(0,0); V2[1] = EVectMat(1,0); V2[2] = EVectMat(2,0);
V1[0] = EVectMat(0,2); V1[1] = EVectMat(1,2); V1[2] = EVectMat(2,2);
}
} else {
if( Eval2 >= Eval3 ){
V1[0] = EVectMat(0,1); V1[1] = EVectMat(1,1); V1[2] = EVectMat(2,1);
V2[0] = EVectMat(0,2); V2[1] = EVectMat(1,2); V2[2] = EVectMat(2,2);
} else {
V2[0] = EVectMat(0,1); V2[1] = EVectMat(1,1); V2[2] = EVectMat(2,1);
V1[0] = EVectMat(0,2); V1[1] = EVectMat(1,2); V1[2] = EVectMat(2,2);
}
}
double n_sum = sqrt( V1[0]*V1[0]+V1[1]*V1[1]+V1[2]*V1[2] );
V1[0] /= n_sum; V1[1] /= n_sum; V1[2] /= n_sum;
n_sum = sqrt( V2[0]*V2[0]+V2[1]*V2[1]+V2[2]*V2[2] );
V2[0] /= n_sum; V2[1] /= n_sum; V2[2] /= n_sum;
//Get the normal to the plane formed by the biggest two EVs
EP_norm[0] = V1[1]*V2[2]-V1[2]*V2[1];
EP_norm[1] = V1[2]*V2[0]-V1[0]*V2[2];
EP_norm[2] = V1[0]*V2[1]-V1[1]*V2[0];
//Reassign V2 so that it is orthogonal to both EP_norm and V1
V2[0] = V1[1]*EP_norm[2]-V1[2]*EP_norm[1];
V2[1] = V1[2]*EP_norm[0]-V1[0]*EP_norm[2];
V2[2] = V1[0]*EP_norm[1]-V1[1]*EP_norm[0];
//Now we have the point normal form; EP_norm is the normal and
//centroid_x, centroid_y, centroid_z is the point
//The equation to the plane is EP_norm[0](x-centroid_x)+EP_norm[1](y-centroid_y)+EP_norm[2](z-centroid_z)=0
double dee = (centroid_x*EP_norm[0]+centroid_y*EP_norm[1]+centroid_z*EP_norm[2])*(-1.00);
//Iterate through and assign values to each region
typedef itk::ImageRegionConstIterator< FloatImageType > ConstIteratorTypeFloat;
ConstIteratorTypeFloat pix_buf2( dist_im, dist_im->GetRequestedRegion() );
IteratorType iterator44( input_image, input_image->GetRequestedRegion() );
for ( pix_buf2.GoToBegin(); !pix_buf2.IsAtEnd(); ++pix_buf2 ){
//Use pixels that are only within the defined radius from the nucleus
double current_distance = pix_buf2.Get();
if( (current_distance <= (double)surr_dist) && (current_distance>=(-1*inside_dist)) ){
USImageType::IndexType cur_in;//,cur_in_cpy;
double n_vec[3];
cur_in[0] = pix_buf2.GetIndex()[0]+boundbox[0]-1-surr_dist;
cur_in[1] = pix_buf2.GetIndex()[1]+boundbox[2]-1-surr_dist;
cur_in[2] = pix_buf2.GetIndex()[2]+boundbox[4]-1-surr_dist;
//cur_in_cpy[0] = cur_in[0]; cur_in_cpy[1] = cur_in[1]; cur_in_cpy[2] = cur_in[2];
if( cur_in[0] < 0 || cur_in[1] < 0 || cur_in[2] < 0 ) continue;
if( cur_in[0] >= sizee[0] || cur_in[1] >= sizee[1] || cur_in[2] >= sizee[2] ) continue;
iterator44.SetIndex( cur_in );
USImageType::PixelType pixel_intensity;
pixel_intensity = iterator44.Get();
if( pixel_intensity < thresh ) continue;
//The projection of the point on the plane formed by the fist two major axes
double xxx, yyy, zzz;
xxx = cur_in[0] - EP_norm[0]*((EP_norm[0]*cur_in[0]+EP_norm[1]*cur_in[1]+EP_norm[2]*cur_in[2]+dee)
/(EP_norm[0]*EP_norm[0]+EP_norm[1]*EP_norm[1]+EP_norm[2]*EP_norm[2]));
yyy = cur_in[1] - EP_norm[1]*((EP_norm[0]*cur_in[0]+EP_norm[1]*cur_in[1]+EP_norm[2]*cur_in[2]+dee)
/(EP_norm[0]*EP_norm[0]+EP_norm[1]*EP_norm[1]+EP_norm[2]*EP_norm[2]));
zzz = cur_in[2] - EP_norm[2]*((EP_norm[0]*cur_in[0]+EP_norm[1]*cur_in[1]+EP_norm[2]*cur_in[2]+dee)
/(EP_norm[0]*EP_norm[0]+EP_norm[1]*EP_norm[1]+EP_norm[2]*EP_norm[2]));
//The vector from the centroid to the projected point
n_vec[0] = centroid_x-xxx;
n_vec[1] = centroid_y-yyy;
n_vec[2] = centroid_z-zzz;
n_sum = sqrt( n_vec[0]*n_vec[0] + n_vec[1]*n_vec[1] + n_vec[2]*n_vec[2] );
n_vec[0] /= n_sum; n_vec[1] /= n_sum; n_vec[2] /= n_sum;
//n_vec is the normalized vect in the direction of the projected point
//V1 is the largest eigenvector
//Get the dot and cross product between the two
double doooot, crooos,fin_est_angle;
doooot = n_vec[0]*V1[0]+n_vec[1]*V1[1]+n_vec[2]*V1[2];
crooos = n_vec[0]*V2[0]+n_vec[1]*V2[1]+n_vec[2]*V2[2];
fin_est_angle = atan2( crooos, doooot );
USPixelType bin_num;
//Compute bin num
if( fin_est_angle<0 )
fin_est_angle += (2*M_PI);
bin_num = floor(fin_est_angle*number_of_rois/(2*M_PI));
//Check which side of the plane the point lies on
double v_norm = (cur_in[0]-centroid_x)*(cur_in[0]-centroid_x)
+(cur_in[1]-centroid_y)*(cur_in[1]-centroid_y)
+(cur_in[2]-centroid_z)*(cur_in[2]-centroid_z);
v_norm = sqrt( v_norm );
double doot = (cur_in[0]-centroid_x)*EP_norm[0]/v_norm + (cur_in[1]-centroid_y)*EP_norm[1]/v_norm + (cur_in[2]-centroid_z)*EP_norm[2]/v_norm;
if( doot<0 )
bin_num += number_of_rois;
quantified_numbers_cell.at((ind*(2*number_of_rois)+bin_num)) += pixel_intensity;
}
}
}
number_of_rois = number_of_rois*2;
if( labelsList.size() == 1 )
{
qfied_num.clear();
return qfied_num;
}
std::vector<double> quantified_numbers_cell_cpy(roi_list_size);
std::copy(quantified_numbers_cell.begin(), quantified_numbers_cell.end(), quantified_numbers_cell_cpy.begin() );
//Run k-means
//Most of the code is adapted from mul/mbl/mbl_k_means.cxx
std::sort(quantified_numbers_cell.begin(), quantified_numbers_cell.end());
bool skipKmeans;
double Positive_thresh;
if( quantified_numbers_cell.at(0) == quantified_numbers_cell.at(quantified_numbers_cell.size()-1) )
skipKmeans = true;
if( !skipKmeans ){
std::cout<<"Starting k-means\n";
std::cout<<"First:"<<quantified_numbers_cell.at(0)<<" Last:"<<quantified_numbers_cell.at(quantified_numbers_cell.size()-1)<<std::endl;
unsigned k = 2;
//Vectors and matrices for k-means
std::vector< USImageType::PixelType > partition( roi_list_size, 0 );
std::vector< double > sums ( k, 0.0 );
std::vector< double > centers( k, 0.0 );
std::vector< USImageType::PixelType > nNearest( k, 0 );
//Use the elements that are evenly spaced to get the intial centers
for( unsigned i=0; i<k; ++i ){
double index = ((double)(i)*roi_list_size)/(k+1);
centers.at(i) = quantified_numbers_cell.at((itk::SizeValueType)index);
bool duplicated;
std::cout<<"Initializing centers\n"<<std::flush;
if(i){
if( centers.at((i-1)) == centers.at(i) ){
duplicated = true;
itk::SizeValueType ind=i+1;
while( centers.at((i-1))==quantified_numbers_cell.at(ind) )
++ind;
centers.at(i) = quantified_numbers_cell.at(ind);
sums.at(i) = quantified_numbers_cell.at(ind);
}
}
if(!duplicated)
sums.at(i) = quantified_numbers_cell.at((i+1)/(k+1));
++nNearest[i];
}
bool changed = true;
std::cout<<"Waiting for kmeans to converge\n"<<std::flush;
while(changed){
changed = false;
for(itk::SizeValueType i=0; i<roi_list_size; ++i){
unsigned bestCentre = 0;
double bestDist = fabs((centers.at(0)-quantified_numbers_cell.at(i)));
for(unsigned j=1; j<k; ++j){
double dist = fabs((centers.at(j)-quantified_numbers_cell.at(i)));
if( dist < bestDist ){
bestDist = dist; bestCentre = j;
}
}
sums[bestCentre] += quantified_numbers_cell.at(i);
++ nNearest[bestCentre];
if( bestCentre != partition.at(i) ){
changed = true;
partition.at(i) = bestCentre;
}
}
for( unsigned j=0; j<k; ++j) centers.at(j) = sums.at(j)/nNearest.at(j);
for( unsigned j=0; j<k; ++j) sums.at(j) = 0;
for( unsigned j=0; j<k; ++j) nNearest.at(j) = 0;
}
for( unsigned i=0; i<k; ++i )
std::cout<<"Center "<<i<<" "<<centers.at(i)<<"\n";
Positive_thresh = ((centers.at(0)+centers.at(1))/2) < (255.0*thresh)?
((centers.at(0)+centers.at(1))/2) : (255.0*thresh); //Arbitrary upper thresh
}
else
Positive_thresh = 255.0*thresh;
std::cout<<"Positive_thresh "<<Positive_thresh<<"\n";
std::cout<<"Done k-means\n";
itk::SizeValueType ind = 0;
for( USPixelType i=0; i<labelsList.size(); ++i ){
if( zp && (zero==i) ) continue;
int num_positive_rois = 0;
for( unsigned j=0; j<number_of_rois; ++j ){
itk::SizeValueType index_of_roi = ind*number_of_rois+j;
if( quantified_numbers_cell_cpy.at(index_of_roi)>Positive_thresh )
++num_positive_rois;
}
qfied_num.push_back(num_positive_rois);
++ind;
}
}
std::cout<<"Done surroundedness\n"<<std::flush;
return qfied_num;
}
