void PivotMDS::singularValueDecomposition(
Array<Array<double> >& pivDistMatrix,
Array<Array<double> >& eVecs,
Array<double>& eVals)
{
const int l = pivDistMatrix.size();
const int n = pivDistMatrix[0].size();
Array<Array<double> > K(l);
for (int i = 0; i < l; i++) {
K[i].init(l);
}
// calc C^TC
selfProduct(pivDistMatrix, K);
Array<Array<double> > tmp(DIMENSION_COUNT);
for (int i = 0; i < DIMENSION_COUNT; i++) {
tmp[i].init(l);
}
eigenValueDecomposition(K, tmp, eVals);
// C^Tx
for (int i = 0; i < DIMENSION_COUNT; i++) {
eVals[i] = sqrt(eVals[i]);
for (int j = 0; j < n; j++) { // node j
eVecs[i][j] = 0;
for (int k = 0; k < l; k++) { // pivot k
eVecs[i][j] += pivDistMatrix[k][j] * tmp[i][k];
}
}
}
for (int i = 0; i < DIMENSION_COUNT; i++) {
normalize(eVecs[i]);
}
}
void TubeDetection::calcMaxMedialness()
{
unsigned x,y,z;
unsigned int x_size;
unsigned int y_size;
unsigned int z_size;
float V[3][3];
float d[3];
FloatImageType::Pointer max_medialnessimage;
FloatImageType::IndexType index;
float scale_index[3];
HessianFilter::OutputImageType::IndexType indexi;
DuplicatorType::Pointer duplicator = DuplicatorType::New();
duplicator->SetInputImage(medialnessImages.at(medialnessImages.size() - 1));
duplicator->Update();
max_medialnessimage = duplicator->GetOutput();
allocateEigenvectorImage();
std::cout << "Starting calculating maximum of medialness." << std::endl;
x_size = medialnessImages.at(medialnessImages.size() - 1)->GetLargestPossibleRegion().GetSize(0);
y_size = medialnessImages.at(medialnessImages.size() - 1)->GetLargestPossibleRegion().GetSize(1);
z_size = medialnessImages.at(medialnessImages.size() - 1)->GetLargestPossibleRegion().GetSize(2);
float current_medialness_value;
float max_medialness_value;
int max_medialness_scale_level;
for(x = 0; x < x_size; x++)
{
index[0] = x;
if(x % 10 == 0)
std::cout << "x " << x << std::endl;
for(y = 0; y < y_size; y++)
{
index[1] = y;
for(z = 0; z < z_size; z++)
{
index[2] = z;
//This is the value we obtain from the largest resolution
max_medialness_value = max_medialnessimage->GetPixel(index);
max_medialness_scale_level = medialnessImages.size() - 1;
//Now we go through all scale levels and look for a maximum..
for(unsigned i = 0; i < this->medialnessImages.size() - 1; i++)
{
scale_index[0] = static_cast<float>(x) / powf(2,medialnessImages.size() - 1 - i);
scale_index[1] = static_cast<float>(y) / powf(2,medialnessImages.size() - 1 - i);
scale_index[2] = static_cast<float>(z) / powf(2,medialnessImages.size() - 1 - i);
current_medialness_value = NumericsHelper::trilinearInterp(medialnessImages.at(i), scale_index[0], scale_index[1], scale_index[2]);
if(current_medialness_value > max_medialness_value)
{
max_medialness_value = current_medialness_value;
max_medialness_scale_level = i;
}
}
//Now write the maximum into the image again
max_medialnessimage->SetPixel(index, max_medialness_value);
//now calculate and save the EV of that pixel:
indexi[0] = static_cast<int>(roundf(static_cast<float>(x) / powf(2,medialnessImages.size() - 1 - max_medialness_scale_level)));
indexi[1] = static_cast<int>(roundf(static_cast<float>(y) / powf(2,medialnessImages.size() - 1 - max_medialness_scale_level)));
indexi[2] = static_cast<int>(roundf(static_cast<float>(z) / powf(2,medialnessImages.size() - 1 - max_medialness_scale_level)));
eigenValueDecomposition(max_medialness_scale_level, indexi, V, d);
eigenvector[0]->SetPixel(index, V[0][0]);
eigenvector[1]->SetPixel(index, V[0][1]);
eigenvector[2]->SetPixel(index, V[0][2]);
}
}
}
this->maxMedialnessOverScales = max_medialnessimage;
std::cout << "Finished calculating maximum of medialness." << std::endl;
}
void TubeDetection::calcMedialness()
{
unsigned x,y,z;
HessianFilter::OutputImageType::IndexType index;
unsigned int x_size;
unsigned int y_size;
unsigned int z_size;
float V[3][3];
float d[3];
FloatImageType::Pointer medialnessimage;
std::cout << "Starting calculating medialness for level: ";
for(unsigned i = 0; i < this->imagePyramid.size(); i++)
{
std::cout << i << " " << std::endl;
//medialnessimage = imagePyramid.at(i)->Clone();
DuplicatorType::Pointer duplicator = DuplicatorType::New();
duplicator->SetInputImage(imagePyramid.at(i));
duplicator->Update();
medialnessimage = duplicator->GetOutput();
x_size = imagePyramid.at(i)->GetLargestPossibleRegion().GetSize(0);
y_size = imagePyramid.at(i)->GetLargestPossibleRegion().GetSize(1);
z_size = imagePyramid.at(i)->GetLargestPossibleRegion().GetSize(2);
for(x = 0; x < x_size ; x++)
{
index[0] = x;
if(x % 10 == 0)
std::cout << "x = " << x << std::endl;
for(y = 0; y < y_size; y++)
{
index[1] = y;
for(z = 0; z < z_size; z++)
{
//Indices for gradient, forward differences
index[2] = z;
eigenValueDecomposition(i, index, V, d);
float medialness = calcMedialness(i, x, y, z, d, V);
medialnessimage->SetPixel(index, medialness);
}
}
}
medialnessImages.push_back(medialnessimage);
}
std::cout << std::endl << "Finished calculation of medialness" << std::endl;
}