void
rich_cell::
update_eccentricity_and_radius()
{
//Step1: project the points to the x-y plane
std::vector<vnl_vector_fixed<double, 2> > points_2d;
std::vector<bool> checked(all_points_.size(), false);
for (unsigned int i = 0; i<all_points_.size(); i++) {
if (!checked[i]) {
//record the x-y position
vnl_vector_fixed<double, 2> pt(all_points_[i][0],all_points_[i][1]);
points_2d.push_back( pt );
checked[i] = true;
//scan through the list to see if other points in the remaining
//list contains the same x-y position
for (unsigned int j = i+1; j<all_points_.size(); j++) {
if (all_points_[j][0] == all_points_[i][0]
&& all_points_[j][1] == all_points_[i][1])
checked[j] = true;
}
}
}
//Step2: compute the scatter matrix
//
// compute the center
vnl_vector_fixed<double, 2> center(0.0,0.0);
for (unsigned int i = 0; i<points_2d.size(); i++) {
center += points_2d[i];
}
center /= (double)points_2d.size();
vnl_matrix<double> cov_matrix(2,2,0.0);
std::cout<<"points_2d.size = "<<points_2d.size()<<std::endl;
for (unsigned int i = 0; i<points_2d.size(); i++) {
cov_matrix += outer_product(points_2d[i]-center, points_2d[i]-center);
}
cov_matrix /= (double)points_2d.size();
//perform eigen-value decomposition to get the semi-major (a) and minor (b)
vnl_svd<double> svd_from( cov_matrix );
//eccentricity=sqrt( 1-(b^2/a^2) ). If the shape is close to
//circular, the value is 0.
//eccentricity_ =vcl_sqrt( 1- (svd_from.W(1)*svd_from.W(1))/(svd_from.W(0)*svd_from.W(0)) );
eccentricity_ =vcl_sqrt( 1- vnl_math_abs(svd_from.W(1)/svd_from.W(0)) );
float long_axis_mag = vcl_sqrt(vnl_math_abs(svd_from.W(0)));
float short_axis_mag = vcl_sqrt(vnl_math_abs(svd_from.W(1)));
average_radius_ = 0.5*(long_axis_mag + short_axis_mag);
}
double Cell::GetVesselnessValue(const GradientVectorType & grad_Dx_vector, const GradientVectorType & grad_Dy_vector, const GradientVectorType & grad_Dz_vector)
{
double Dxx = grad_Dx_vector[0];
double Dxy = grad_Dx_vector[1];
double Dxz = grad_Dx_vector[2];
double Dyx = grad_Dy_vector[0];
double Dyy = grad_Dy_vector[1];
double Dyz = grad_Dy_vector[2];
double Dzx = grad_Dz_vector[0];
double Dzy = grad_Dz_vector[1];
double Dzz = grad_Dz_vector[2];
double grad_GVF_matrix[3][3];
grad_GVF_matrix[0][0] = Dxx;
grad_GVF_matrix[0][1] = Dxy;
grad_GVF_matrix[0][2] = Dxz;
grad_GVF_matrix[1][0] = Dyx;
grad_GVF_matrix[1][1] = Dyy;
grad_GVF_matrix[1][2] = Dyz;
grad_GVF_matrix[2][0] = Dzx;
grad_GVF_matrix[2][1] = Dzy;
grad_GVF_matrix[2][2] = Dzz;
double eigenvalues[3];
double eigenvectors[3][3];
EigenAnalysis::eigen_decomposition(grad_GVF_matrix, eigenvectors, eigenvalues);
double Lambda1 = eigenvalues[0];
double Lambda2 = eigenvalues[1];
double Lambda3 = eigenvalues[2];
if ( Lambda2 >= 0.0 || Lambda3 > 0.0 )
{
return 0.0;
}
else
{
static const double FrangiAlpha = 0.5;
static const double FrangiBeta = 0.5;
static const double FrangiC = 100.0;
const double A = 2 * pow(FrangiAlpha,2);
const double B = 2 * pow(FrangiBeta,2);
const double C = 2 * pow(FrangiC,2);
const double Ra = Lambda2 / Lambda3;
const double Rb = Lambda1 / vcl_sqrt ( vnl_math_abs( Lambda2 * Lambda3 ));
const double S = vcl_sqrt( pow(Lambda1,2) + pow(Lambda2,2) + pow(Lambda3,2));
const double vesMeasure_1 = ( 1 - vcl_exp(-1.0*(( vnl_math_sqr( Ra ) ) / ( A ))) );
const double vesMeasure_2 = vcl_exp ( -1.0 * ((vnl_math_sqr( Rb )) / ( B )));
const double vesMeasure_3 = ( 1 - vcl_exp( -1.0 * (( vnl_math_sqr( S )) / ( C ))) );
const double V_Saliency = vesMeasure_1 * vesMeasure_2 * vesMeasure_3;
return V_Saliency;
}
}
SEXP invariantSimilarityHelper(
typename itk::Image< float , ImageDimension >::Pointer image1,
typename itk::Image< float , ImageDimension >::Pointer image2,
SEXP r_thetas, SEXP r_lsits, SEXP r_WM, SEXP r_scale,
SEXP r_doreflection, SEXP r_txfn )
{
unsigned int mibins = 20;
unsigned int localSearchIterations =
Rcpp::as< unsigned int >( r_lsits ) ;
std::string whichMetric = Rcpp::as< std::string >( r_WM );
std::string txfn = Rcpp::as< std::string >( r_txfn );
bool useprincaxis = true;
typedef typename itk::ImageMaskSpatialObject<ImageDimension>::ImageType
maskimagetype;
typename maskimagetype::Pointer mask = ITK_NULLPTR;
Rcpp::NumericVector thetas( r_thetas );
Rcpp::NumericVector vector_r( r_thetas ) ;
Rcpp::IntegerVector dims( 1 );
Rcpp::IntegerVector doReflection( r_doreflection );
unsigned int vecsize = thetas.size();
dims[0]=0;
typedef float PixelType;
typedef double RealType;
RealType bestscale = Rcpp::as< RealType >( r_scale ) ;
typedef itk::Image< PixelType , ImageDimension > ImageType;
if( image1.IsNotNull() & image2.IsNotNull() )
{
typedef typename itk::ImageMomentsCalculator<ImageType> ImageCalculatorType;
typedef itk::AffineTransform<RealType, ImageDimension> AffineType0;
typedef itk::AffineTransform<RealType, ImageDimension> AffineType;
typedef typename ImageCalculatorType::MatrixType MatrixType;
typedef itk::Vector<float, ImageDimension> VectorType;
VectorType ccg1;
VectorType cpm1;
MatrixType cpa1;
VectorType ccg2;
VectorType cpm2;
MatrixType cpa2;
typename ImageCalculatorType::Pointer calculator1 =
ImageCalculatorType::New();
typename ImageCalculatorType::Pointer calculator2 =
ImageCalculatorType::New();
calculator1->SetImage( image1 );
calculator2->SetImage( image2 );
typename ImageCalculatorType::VectorType fixed_center;
fixed_center.Fill(0);
typename ImageCalculatorType::VectorType moving_center;
moving_center.Fill(0);
try
{
calculator1->Compute();
fixed_center = calculator1->GetCenterOfGravity();
ccg1 = calculator1->GetCenterOfGravity();
cpm1 = calculator1->GetPrincipalMoments();
cpa1 = calculator1->GetPrincipalAxes();
try
{
calculator2->Compute();
moving_center = calculator2->GetCenterOfGravity();
ccg2 = calculator2->GetCenterOfGravity();
cpm2 = calculator2->GetPrincipalMoments();
cpa2 = calculator2->GetPrincipalAxes();
}
catch( ... )
{
fixed_center.Fill(0);
}
}
catch( ... )
{
// Rcpp::Rcerr << " zero image1 error ";
}
if ( vnl_math_abs( bestscale - 1.0 ) < 1.e-6 )
{
RealType volelt1 = 1;
RealType volelt2 = 1;
for ( unsigned int d=0; d<ImageDimension; d++)
{
volelt1 *= image1->GetSpacing()[d];
volelt2 *= image2->GetSpacing()[d];
}
bestscale =
( calculator2->GetTotalMass() * volelt2 )/
( calculator1->GetTotalMass() * volelt1 );
RealType powlev = 1.0 / static_cast<RealType>(ImageDimension);
bestscale = vcl_pow( bestscale , powlev );
}
unsigned int eigind1 = 1;
unsigned int eigind2 = 1;
if( ImageDimension == 3 )
{
eigind1 = 2;
}
typedef vnl_vector<RealType> EVectorType;
typedef vnl_matrix<RealType> EMatrixType;
EVectorType evec1_2ndary = cpa1.GetVnlMatrix().get_row( eigind2 );
EVectorType evec1_primary = cpa1.GetVnlMatrix().get_row( eigind1 );
EVectorType evec2_2ndary = cpa2.GetVnlMatrix().get_row( eigind2 );
EVectorType evec2_primary = cpa2.GetVnlMatrix().get_row( eigind1 );
/** Solve Wahba's problem http://en.wikipedia.org/wiki/Wahba%27s_problem */
EMatrixType B = outer_product( evec2_primary, evec1_primary );
if( ImageDimension == 3 )
{
B = outer_product( evec2_2ndary, evec1_2ndary )
+ outer_product( evec2_primary, evec1_primary );
}
vnl_svd<RealType> wahba( B );
vnl_matrix<RealType> A_solution = wahba.V() * wahba.U().transpose();
A_solution = vnl_inverse( A_solution );
RealType det = vnl_determinant( A_solution );
if( ( det < 0 ) )
{
vnl_matrix<RealType> id( A_solution );
id.set_identity();
for( unsigned int i = 0; i < ImageDimension; i++ )
{
if( A_solution( i, i ) < 0 )
{
id( i, i ) = -1.0;
}
}
A_solution = A_solution * id.transpose();
}
if ( doReflection[0] == 1 || doReflection[0] == 3 )
{
vnl_matrix<RealType> id( A_solution );
id.set_identity();
id = id - 2.0 * outer_product( evec2_primary , evec2_primary );
A_solution = A_solution * id;
}
if ( doReflection[0] > 1 )
{
vnl_matrix<RealType> id( A_solution );
id.set_identity();
id = id - 2.0 * outer_product( evec1_primary , evec1_primary );
A_solution = A_solution * id;
}
typename AffineType::Pointer affine1 = AffineType::New();
typename AffineType::OffsetType trans = affine1->GetOffset();
itk::Point<RealType, ImageDimension> trans2;
for( unsigned int i = 0; i < ImageDimension; i++ )
{
trans[i] = moving_center[i] - fixed_center[i];
trans2[i] = fixed_center[i] * ( 1 );
}
affine1->SetIdentity();
affine1->SetOffset( trans );
if( useprincaxis )
{
affine1->SetMatrix( A_solution );
}
affine1->SetCenter( trans2 );
if( ImageDimension > 3 )
{
return EXIT_SUCCESS;
}
vnl_vector<RealType> evec_tert;
if( ImageDimension == 3 )
{ // try to rotate around tertiary and secondary axis
evec_tert = vnl_cross_3d( evec1_primary, evec1_2ndary );
}
if( ImageDimension == 2 )
{ // try to rotate around tertiary and secondary axis
evec_tert = evec1_2ndary;
evec1_2ndary = evec1_primary;
}
itk::Vector<RealType, ImageDimension> axis2;
itk::Vector<RealType, ImageDimension> axis1;
for( unsigned int d = 0; d < ImageDimension; d++ )
{
axis1[d] = evec_tert[d];
axis2[d] = evec1_2ndary[d];
}
typename AffineType::Pointer simmer = AffineType::New();
simmer->SetIdentity();
simmer->SetCenter( trans2 );
simmer->SetOffset( trans );
typename AffineType0::Pointer affinesearch = AffineType0::New();
affinesearch->SetIdentity();
affinesearch->SetCenter( trans2 );
typedef itk::MultiStartOptimizerv4 OptimizerType;
typename OptimizerType::MetricValuesListType metricvalues;
typename OptimizerType::Pointer mstartOptimizer = OptimizerType::New();
typedef itk::CorrelationImageToImageMetricv4
<ImageType, ImageType, ImageType> GCMetricType;
typedef itk::MattesMutualInformationImageToImageMetricv4
<ImageType, ImageType, ImageType> MetricType;
typename MetricType::ParametersType newparams( affine1->GetParameters() );
typename GCMetricType::Pointer gcmetric = GCMetricType::New();
gcmetric->SetFixedImage( image1 );
gcmetric->SetVirtualDomainFromImage( image1 );
gcmetric->SetMovingImage( image2 );
gcmetric->SetMovingTransform( simmer );
gcmetric->SetParameters( newparams );
typename MetricType::Pointer mimetric = MetricType::New();
mimetric->SetNumberOfHistogramBins( mibins );
mimetric->SetFixedImage( image1 );
mimetric->SetMovingImage( image2 );
mimetric->SetMovingTransform( simmer );
mimetric->SetParameters( newparams );
if( mask.IsNotNull() )
{
typename itk::ImageMaskSpatialObject<ImageDimension>::Pointer so =
itk::ImageMaskSpatialObject<ImageDimension>::New();
so->SetImage( const_cast<maskimagetype *>( mask.GetPointer() ) );
mimetric->SetFixedImageMask( so );
gcmetric->SetFixedImageMask( so );
}
typedef itk::ConjugateGradientLineSearchOptimizerv4 LocalOptimizerType;
typename LocalOptimizerType::Pointer localoptimizer =
LocalOptimizerType::New();
RealType localoptimizerlearningrate = 0.1;
localoptimizer->SetLearningRate( localoptimizerlearningrate );
localoptimizer->SetMaximumStepSizeInPhysicalUnits(
localoptimizerlearningrate );
localoptimizer->SetNumberOfIterations( localSearchIterations );
localoptimizer->SetLowerLimit( 0 );
localoptimizer->SetUpperLimit( 2 );
localoptimizer->SetEpsilon( 0.1 );
localoptimizer->SetMaximumLineSearchIterations( 50 );
localoptimizer->SetDoEstimateLearningRateOnce( true );
localoptimizer->SetMinimumConvergenceValue( 1.e-6 );
localoptimizer->SetConvergenceWindowSize( 5 );
if( true )
{
typedef typename MetricType::FixedSampledPointSetType PointSetType;
typedef typename PointSetType::PointType PointType;
typename PointSetType::Pointer pset(PointSetType::New());
unsigned int ind=0;
unsigned int ct=0;
itk::ImageRegionIteratorWithIndex<ImageType> It(image1,
image1->GetLargestPossibleRegion() );
for( It.GoToBegin(); !It.IsAtEnd(); ++It )
{
// take every N^th point
if ( ct % 10 == 0 )
{
PointType pt;
image1->TransformIndexToPhysicalPoint( It.GetIndex(), pt);
pset->SetPoint(ind, pt);
ind++;
}
ct++;
}
mimetric->SetFixedSampledPointSet( pset );
mimetric->SetUseFixedSampledPointSet( true );
gcmetric->SetFixedSampledPointSet( pset );
gcmetric->SetUseFixedSampledPointSet( true );
}
if ( whichMetric.compare("MI") == 0 ) {
mimetric->Initialize();
typedef itk::RegistrationParameterScalesFromPhysicalShift<MetricType>
RegistrationParameterScalesFromPhysicalShiftType;
typename RegistrationParameterScalesFromPhysicalShiftType::Pointer
shiftScaleEstimator =
RegistrationParameterScalesFromPhysicalShiftType::New();
shiftScaleEstimator->SetMetric( mimetric );
shiftScaleEstimator->SetTransformForward( true );
typename RegistrationParameterScalesFromPhysicalShiftType::ScalesType
movingScales( simmer->GetNumberOfParameters() );
shiftScaleEstimator->EstimateScales( movingScales );
mstartOptimizer->SetScales( movingScales );
mstartOptimizer->SetMetric( mimetric );
localoptimizer->SetMetric( mimetric );
localoptimizer->SetScales( movingScales );
}
if ( whichMetric.compare("MI") != 0 ) {
gcmetric->Initialize();
typedef itk::RegistrationParameterScalesFromPhysicalShift<GCMetricType>
RegistrationParameterScalesFromPhysicalShiftType;
typename RegistrationParameterScalesFromPhysicalShiftType::Pointer
shiftScaleEstimator =
RegistrationParameterScalesFromPhysicalShiftType::New();
shiftScaleEstimator->SetMetric( gcmetric );
shiftScaleEstimator->SetTransformForward( true );
typename RegistrationParameterScalesFromPhysicalShiftType::ScalesType
movingScales( simmer->GetNumberOfParameters() );
shiftScaleEstimator->EstimateScales( movingScales );
mstartOptimizer->SetScales( movingScales );
mstartOptimizer->SetMetric( gcmetric );
localoptimizer->SetMetric( gcmetric );
localoptimizer->SetScales( movingScales );
}
typename OptimizerType::ParametersListType parametersList =
mstartOptimizer->GetParametersList();
affinesearch->SetIdentity();
affinesearch->SetCenter( trans2 );
affinesearch->SetOffset( trans );
for ( unsigned int i = 0; i < vecsize; i++ )
{
RealType ang1 = thetas[i];
RealType ang2 = 0; // FIXME should be psi
vector_r[ i ]=0;
if( ImageDimension == 3 )
{
for ( unsigned int jj = 0; jj < vecsize; jj++ )
{
ang2=thetas[jj];
affinesearch->SetIdentity();
affinesearch->SetCenter( trans2 );
affinesearch->SetOffset( trans );
if( useprincaxis )
{
affinesearch->SetMatrix( A_solution );
}
affinesearch->Rotate3D(axis1, ang1, 1);
affinesearch->Rotate3D(axis2, ang2, 1);
affinesearch->Scale( bestscale );
simmer->SetMatrix( affinesearch->GetMatrix() );
parametersList.push_back( simmer->GetParameters() );
}
}
if( ImageDimension == 2 )
{
affinesearch->SetIdentity();
affinesearch->SetCenter( trans2 );
affinesearch->SetOffset( trans );
if( useprincaxis )
{
affinesearch->SetMatrix( A_solution );
}
affinesearch->Rotate2D( ang1, 1);
affinesearch->Scale( bestscale );
simmer->SetMatrix( affinesearch->GetMatrix() );
typename AffineType::ParametersType pp =
simmer->GetParameters();
//pp[1]=ang1;
//pp[0]=bestscale;
parametersList.push_back( simmer->GetParameters() );
}
}
mstartOptimizer->SetParametersList( parametersList );
if( localSearchIterations > 0 )
{
mstartOptimizer->SetLocalOptimizer( localoptimizer );
}
mstartOptimizer->StartOptimization();
typename AffineType::Pointer bestaffine = AffineType::New();
bestaffine->SetCenter( trans2 );
bestaffine->SetParameters( mstartOptimizer->GetBestParameters() );
if ( txfn.length() > 3 )
{
typename AffineType::Pointer bestaffine = AffineType::New();
bestaffine->SetCenter( trans2 );
bestaffine->SetParameters( mstartOptimizer->GetBestParameters() );
typedef itk::TransformFileWriter TransformWriterType;
typename TransformWriterType::Pointer transformWriter =
TransformWriterType::New();
transformWriter->SetInput( bestaffine );
transformWriter->SetFileName( txfn.c_str() );
transformWriter->Update();
}
metricvalues = mstartOptimizer->GetMetricValuesList();
for ( unsigned int k = 0; k < metricvalues.size(); k++ )
{
vector_r[k] = metricvalues[k];
}
dims[0] = vecsize;
vector_r.attr( "dim" ) = vecsize;
return Rcpp::wrap( vector_r );
}
else
{
return Rcpp::wrap( vector_r );
}
}
