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/*=========================================================================
Program: Insight Segmentation & Registration Toolkit
Module: $RCSfile: itkVesselEnhancingDiffusion3DImageFilter.txx,v $
Language: C++
Date: $Date: 2009/01/09 11:15:27 $
Version: $Revision: 1.2 $
=========================================================================*/
#ifndef __itkVesselEnhancingDiffusion3DImageFilter_txx
#define __itkVesselEnhancingDiffusion3DImageFilter_txx
#include "itkVesselEnhancingDiffusion3DImageFilter.h"
#include "itkCastImageFilter.h"
#include "itkConstShapedNeighborhoodIterator.h"
#include "itkHessianRecursiveGaussianImageFilter.h"
#include "itkImageRegionConstIterator.h"
#include "itkImageRegionIterator.h"
#include "itkMinimumMaximumImageFilter.h"
#include "itkNeighborhoodAlgorithm.h"
#include "itkNumericTraits.h"
#include "itkZeroFluxNeumannBoundaryCondition.h"
#include <vnl/vnl_vector.h>
#include <vnl/vnl_matrix.h>
#include <vnl/algo/vnl_symmetric_eigensystem.h>
#include<iostream>
namespace itk
{
// constructor
template <class PixelType, unsigned int Dimension>
VesselEnhancingDiffusion3DImageFilter<PixelType, Dimension>
::VesselEnhancingDiffusion3DImageFilter():
m_TimeStep(NumericTraits<Precision>::Zero),
m_Iterations(0),
m_RecalculateVesselness(0),
m_Epsilon(0.0),
m_Omega(0.0),
m_Sensitivity(0.0),
m_DarkObjectLightBackground(false)
{
this->SetNumberOfRequiredInputs(1);
}
// printself for debugging
template <class PixelType, unsigned int Dimension>
void VesselEnhancingDiffusion3DImageFilter<PixelType, Dimension>
::PrintSelf(std::ostream &os, Indent indent) const
{
Superclass::PrintSelf(os,indent);
os << indent << "TimeStep : " << m_TimeStep << std::endl;
os << indent << "Iterations : " << m_Iterations << std::endl;
os << indent << "RecalculateVesselness : " << m_RecalculateVesselness << std::endl;
os << indent << "Scales : ";
for (unsigned int i=0; i<m_Scales.size(); ++i)
os << m_Scales[i] << " ";
os << std::endl;
os << indent << "Epsilon : " << m_Epsilon << std::endl;
os << indent << "Omega : " << m_Omega << std::endl;
os << indent << "Sensitivity : " << m_Sensitivity << std::endl;
os << indent << "DarkObjectLightBackground : " << m_DarkObjectLightBackground << std::endl;
}
// singleiter
template <class PixelType, unsigned int Dimension>
void VesselEnhancingDiffusion3DImageFilter<PixelType, Dimension>
::VED3DSingleIteration(typename ImageType::Pointer ci)
{
bool rec(false);
if (
(m_CurrentIteration == 1) ||
(m_RecalculateVesselness == 0) ||
(m_CurrentIteration % m_RecalculateVesselness == 0)
)
{
rec = true;
if (m_Verbose)
{
std::cout << "v ";
std::cout.flush();
}
MaxVesselResponse (ci);
DiffusionTensor ();
}
if (m_Verbose)
{
if (!rec)
{
std::cout << ". ";
std::cout.flush();
}
}
// calculate d = nonlineardiffusion(ci)
// using 3x3x3 stencil, afterwards copy
// result from d back to ci
typename PrecisionImageType::Pointer d = PrecisionImageType::New();
d->SetOrigin(ci->GetOrigin());
d->SetSpacing(ci->GetSpacing());
d->SetDirection(ci->GetDirection());
d->SetRegions(ci->GetLargestPossibleRegion());
d->Allocate();
d->FillBuffer(NumericTraits<Precision>::Zero);
// shapedneighborhood iter, zeroflux boundary condition
// division into faces and inner region
typedef ZeroFluxNeumannBoundaryCondition<PrecisionImageType> BT;
typedef ConstShapedNeighborhoodIterator<PrecisionImageType,BT> NT;
typedef typename NeighborhoodAlgorithm::ImageBoundaryFacesCalculator<PrecisionImageType>
FT;
BT b;
typename NT::RadiusType r;
r.Fill(1);
// offsets
const typename NT::OffsetType oxp = {{1,0,0}};
const typename NT::OffsetType oxm = {{-1,0,0}};
const typename NT::OffsetType oyp = {{0,1,0}};
const typename NT::OffsetType oym = {{0,-1,0}};
const typename NT::OffsetType ozp = {{0,0,1}};
const typename NT::OffsetType ozm = {{0,0,-1}};
const typename NT::OffsetType oxpyp = {{1,1,0}};
const typename NT::OffsetType oxmym = {{-1,-1,0}};
const typename NT::OffsetType oxpym = {{1,-1,0}};
const typename NT::OffsetType oxmyp = {{-1,1,0}};
const typename NT::OffsetType oxpzp = {{1,0,1}};
const typename NT::OffsetType oxmzm = {{-1,0,-1}};
const typename NT::OffsetType oxpzm = {{1,0,-1}};
const typename NT::OffsetType oxmzp = {{-1,0,1}};
const typename NT::OffsetType oypzp = {{0,1,1}};
const typename NT::OffsetType oymzm = {{0,-1,-1}};
const typename NT::OffsetType oypzm = {{0,1,-1}};
const typename NT::OffsetType oymzp = {{0,-1,1}};
// fixed weights (timers)
const typename PrecisionImageType::SpacingType ispacing = ci->GetSpacing();
const Precision rxx = m_TimeStep / (2.0 * ispacing[0] * ispacing[0]);
const Precision ryy = m_TimeStep / (2.0 * ispacing[1] * ispacing[1]);
const Precision rzz = m_TimeStep / (2.0 * ispacing[2] * ispacing[2]);
const Precision rxy = m_TimeStep / (4.0 * ispacing[0] * ispacing[1]);
const Precision rxz = m_TimeStep / (4.0 * ispacing[0] * ispacing[2]);
const Precision ryz = m_TimeStep / (4.0 * ispacing[1] * ispacing[2]);
// faces
FT fc;
typename FT::FaceListType fci = fc(ci,d->GetLargestPossibleRegion(),r);
typename FT::FaceListType fxx = fc(m_Dxx,d->GetLargestPossibleRegion(),r);
typename FT::FaceListType fxy = fc(m_Dxy,d->GetLargestPossibleRegion(),r);
typename FT::FaceListType fxz = fc(m_Dxz,d->GetLargestPossibleRegion(),r);
typename FT::FaceListType fyy = fc(m_Dyy,d->GetLargestPossibleRegion(),r);
typename FT::FaceListType fyz = fc(m_Dyz,d->GetLargestPossibleRegion(),r);
typename FT::FaceListType fzz = fc(m_Dzz,d->GetLargestPossibleRegion(),r);
typename FT::FaceListType::iterator fitci,fitxx,fitxy,fitxz,fityy,fityz,fitzz;
for ( fitci = fci.begin(),
fitxx = fxx.begin(), fitxy = fxy.begin(), fitxz = fxz.begin(),
fityy = fyy.begin(), fityz = fyz.begin(), fitzz = fzz.begin();
fitci != fci.end();
++fitci, ++fitxx, ++fitxy, ++fitxz, ++fityy, ++fityz, ++fitzz)
{
// output iter
ImageRegionIterator<PrecisionImageType> dit(d,*fitci);
// input iters
NT itci (r,ci,*fitci);
NT itxx (r,m_Dxx,*fitxx);
NT itxy (r,m_Dxy,*fitxy);
NT itxz (r,m_Dxz,*fitxz);
NT ityy (r,m_Dyy,*fityy);
NT ityz (r,m_Dyz,*fityz);
NT itzz (r,m_Dzz,*fitzz);
itci.OverrideBoundaryCondition(&b);
itxx.OverrideBoundaryCondition(&b);
itxy.OverrideBoundaryCondition(&b);
itxz.OverrideBoundaryCondition(&b);
ityy.OverrideBoundaryCondition(&b);
ityz.OverrideBoundaryCondition(&b);
itzz.OverrideBoundaryCondition(&b);
// setting active offsets (yeah there must
// be some smarter way of doing this)
itci.ClearActiveList();
itxx.ClearActiveList();
itxy.ClearActiveList();
itxz.ClearActiveList();
ityy.ClearActiveList();
ityz.ClearActiveList();
itzz.ClearActiveList();
itci.ActivateOffset(oxp);
itxx.ActivateOffset(oxp);
itxy.ActivateOffset(oxp);
itxz.ActivateOffset(oxp);
ityy.ActivateOffset(oxp);
ityz.ActivateOffset(oxp);
itzz.ActivateOffset(oxp);
itci.ActivateOffset(oxm);
itxx.ActivateOffset(oxm);
itxy.ActivateOffset(oxm);
itxz.ActivateOffset(oxm);
ityy.ActivateOffset(oxm);
ityz.ActivateOffset(oxm);
itzz.ActivateOffset(oxm);
itci.ActivateOffset(oyp);
itxx.ActivateOffset(oyp);
itxy.ActivateOffset(oyp);
itxz.ActivateOffset(oyp);
ityy.ActivateOffset(oyp);
ityz.ActivateOffset(oyp);
itzz.ActivateOffset(oyp);
itci.ActivateOffset(oym);
itxx.ActivateOffset(oym);
itxy.ActivateOffset(oym);
itxz.ActivateOffset(oym);
ityy.ActivateOffset(oym);
ityz.ActivateOffset(oym);
itzz.ActivateOffset(oym);
itci.ActivateOffset(ozp);
itxx.ActivateOffset(ozp);
itxy.ActivateOffset(ozp);
itxz.ActivateOffset(ozp);
ityy.ActivateOffset(ozp);
ityz.ActivateOffset(ozp);
itzz.ActivateOffset(ozp);
itci.ActivateOffset(ozm);
itxx.ActivateOffset(ozm);
itxy.ActivateOffset(ozm);
itxz.ActivateOffset(ozm);
ityy.ActivateOffset(ozm);
ityz.ActivateOffset(ozm);
itzz.ActivateOffset(ozm);
itci.ActivateOffset(oxpyp);
itxx.ActivateOffset(oxpyp);
itxy.ActivateOffset(oxpyp);
itxz.ActivateOffset(oxpyp);
ityy.ActivateOffset(oxpyp);
ityz.ActivateOffset(oxpyp);
itzz.ActivateOffset(oxpyp);
itci.ActivateOffset(oxmym);
itxx.ActivateOffset(oxmym);
itxy.ActivateOffset(oxmym);
itxz.ActivateOffset(oxmym);
ityy.ActivateOffset(oxmym);
ityz.ActivateOffset(oxmym);
itzz.ActivateOffset(oxmym);
itci.ActivateOffset(oxpym);
itxx.ActivateOffset(oxpym);
itxy.ActivateOffset(oxpym);
itxz.ActivateOffset(oxpym);
ityy.ActivateOffset(oxpym);
ityz.ActivateOffset(oxpym);
itzz.ActivateOffset(oxpym);
itci.ActivateOffset(oxmyp);
itxx.ActivateOffset(oxmyp);
itxy.ActivateOffset(oxmyp);
itxz.ActivateOffset(oxmyp);
ityy.ActivateOffset(oxmyp);
ityz.ActivateOffset(oxmyp);
itzz.ActivateOffset(oxmyp);
itci.ActivateOffset(oxpzp);
itxx.ActivateOffset(oxpzp);
itxy.ActivateOffset(oxpzp);
itxz.ActivateOffset(oxpzp);
ityy.ActivateOffset(oxpzp);
ityz.ActivateOffset(oxpzp);
itzz.ActivateOffset(oxpzp);
itci.ActivateOffset(oxmzm);
itxx.ActivateOffset(oxmzm);
itxy.ActivateOffset(oxmzm);
itxz.ActivateOffset(oxmzm);
ityy.ActivateOffset(oxmzm);
ityz.ActivateOffset(oxmzm);
itzz.ActivateOffset(oxmzm);
itci.ActivateOffset(oxpzm);
itxx.ActivateOffset(oxpzm);
itxy.ActivateOffset(oxpzm);
itxz.ActivateOffset(oxpzm);
ityy.ActivateOffset(oxpzm);
ityz.ActivateOffset(oxpzm);
itzz.ActivateOffset(oxpzm);
itci.ActivateOffset(oxmzp);
itxx.ActivateOffset(oxmzp);
itxy.ActivateOffset(oxmzp);
itxz.ActivateOffset(oxmzp);
ityy.ActivateOffset(oxmzp);
ityz.ActivateOffset(oxmzp);
itzz.ActivateOffset(oxmzp);
itci.ActivateOffset(oypzp);
itxx.ActivateOffset(oypzp);
itxy.ActivateOffset(oypzp);
itxz.ActivateOffset(oypzp);
ityy.ActivateOffset(oypzp);
ityz.ActivateOffset(oypzp);
itzz.ActivateOffset(oypzp);
itci.ActivateOffset(oymzm);
itxx.ActivateOffset(oymzm);
itxy.ActivateOffset(oymzm);
itxz.ActivateOffset(oymzm);
ityy.ActivateOffset(oymzm);
ityz.ActivateOffset(oymzm);
itzz.ActivateOffset(oymzm);
itci.ActivateOffset(oypzm);
itxx.ActivateOffset(oypzm);
itxy.ActivateOffset(oypzm);
itxz.ActivateOffset(oypzm);
ityy.ActivateOffset(oypzm);
ityz.ActivateOffset(oypzm);
itzz.ActivateOffset(oypzm);
itci.ActivateOffset(oymzp);
itxx.ActivateOffset(oymzp);
itxy.ActivateOffset(oymzp);
itxz.ActivateOffset(oymzp);
ityy.ActivateOffset(oymzp);
ityz.ActivateOffset(oymzp);
itzz.ActivateOffset(oymzp);
// run for each face diffusion
for (itci.GoToBegin(), dit.GoToBegin(),
itxx.GoToBegin(),itxy.GoToBegin(), itxz.GoToBegin(),
ityy.GoToBegin(),ityz.GoToBegin(), itzz.GoToBegin();
!itci.IsAtEnd();
++itci, ++dit, ++itxx, ++itxy, ++itxz, ++ityy, ++ityz, ++itzz)
{
// weights
const Precision xp = itxx.GetPixel(oxp) + itxx.GetCenterPixel();
const Precision xm = itxx.GetPixel(oxm) + itxx.GetCenterPixel();
const Precision yp = ityy.GetPixel(oyp) + ityy.GetCenterPixel();
const Precision ym = ityy.GetPixel(oym) + ityy.GetCenterPixel();
const Precision zp = itzz.GetPixel(ozp) + itzz.GetCenterPixel();
const Precision zm = itzz.GetPixel(ozm) + itzz.GetCenterPixel();
const Precision xpyp = itxy.GetPixel(oxpyp) + itxy.GetCenterPixel();
const Precision xmym = itxy.GetPixel(oxmym) + itxy.GetCenterPixel();
const Precision xpym = - itxy.GetPixel(oxpym) - itxy.GetCenterPixel();
const Precision xmyp = - itxy.GetPixel(oxmyp) - itxy.GetCenterPixel();
const Precision xpzp = itxz.GetPixel(oxpzp) + itxz.GetCenterPixel();
const Precision xmzm = itxz.GetPixel(oxmzm) + itxz.GetCenterPixel();
const Precision xpzm = - itxz.GetPixel(oxpzm) - itxz.GetCenterPixel();
const Precision xmzp = - itxz.GetPixel(oxmzp) - itxz.GetCenterPixel();
const Precision ypzp = ityz.GetPixel(oypzp) + ityz.GetCenterPixel();
const Precision ymzm = ityz.GetPixel(oymzm) + ityz.GetCenterPixel();
const Precision ypzm = - ityz.GetPixel(oypzm) - ityz.GetCenterPixel();
const Precision ymzp = - ityz.GetPixel(oymzp) - ityz.GetCenterPixel();
// evolution
const Precision cv = itci.GetCenterPixel();
dit.Value() = cv +
+ rxx * ( xp * (itci.GetPixel(oxp) - cv)
+ xm * (itci.GetPixel(oxm) - cv) )
+ ryy * ( yp * (itci.GetPixel(oyp) - cv)
+ ym * (itci.GetPixel(oym) - cv) )
+ rzz * ( zp * (itci.GetPixel(ozp) - cv)
+ zm * (itci.GetPixel(ozm) - cv) )
+ rxy * ( xpyp * (itci.GetPixel(oxpyp) - cv)
+ xmym * (itci.GetPixel(oxmym) - cv)
+ xpym * (itci.GetPixel(oxpym) - cv)
+ xmyp * (itci.GetPixel(oxmyp) - cv) )
+ rxz * ( xpzp * (itci.GetPixel(oxpzp) - cv)
+ xmzm * (itci.GetPixel(oxmzm) - cv)
+ xpzm * (itci.GetPixel(oxpzm) - cv)
+ xmzp * (itci.GetPixel(oxmzp) - cv) )
+ ryz * ( ypzp * (itci.GetPixel(oypzp) - cv)
+ ymzm * (itci.GetPixel(oymzm) - cv)
+ ypzm * (itci.GetPixel(oypzm) - cv)
+ ymzp * (itci.GetPixel(oymzp) - cv) );
}
}
// copying
ImageRegionConstIterator<PrecisionImageType> iti (d,d->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> ito (ci,ci->GetLargestPossibleRegion());
for (iti.GoToBegin(), ito.GoToBegin(); !iti.IsAtEnd(); ++iti,++ito)
{
ito.Value() = iti.Value();
}
return;
}
// maxvesselresponse
template <class PixelType, unsigned int Dimension>
void VesselEnhancingDiffusion3DImageFilter<PixelType, Dimension>
::MaxVesselResponse(const typename ImageType::Pointer im)
{
// alloc memory for hessian/tensor
m_Dxx = PrecisionImageType::New();
m_Dxx->SetOrigin(im->GetOrigin());
m_Dxx->SetSpacing(im->GetSpacing());
m_Dxx->SetDirection(im->GetDirection());
m_Dxx->SetRegions(im->GetLargestPossibleRegion());
m_Dxx->Allocate();
m_Dxx->FillBuffer(NumericTraits<Precision>::One);
m_Dxy = PrecisionImageType::New();
m_Dxy->SetOrigin(im->GetOrigin());
m_Dxy->SetSpacing(im->GetSpacing());
m_Dxy->SetDirection(im->GetDirection());
m_Dxy->SetRegions(im->GetLargestPossibleRegion());
m_Dxy->Allocate();
m_Dxy->FillBuffer(NumericTraits<Precision>::Zero);
m_Dxz = PrecisionImageType::New();
m_Dxz->SetOrigin(im->GetOrigin());
m_Dxz->SetSpacing(im->GetSpacing());
m_Dxz->SetDirection(im->GetDirection());
m_Dxz->SetRegions(im->GetLargestPossibleRegion());
m_Dxz->Allocate();
m_Dxz->FillBuffer(NumericTraits<Precision>::Zero);
m_Dyy = PrecisionImageType::New();
m_Dyy->SetOrigin(im->GetOrigin());
m_Dyy->SetSpacing(im->GetSpacing());
m_Dyy->SetDirection(im->GetDirection());
m_Dyy->SetRegions(im->GetLargestPossibleRegion());
m_Dyy->Allocate();
m_Dyy->FillBuffer(NumericTraits<Precision>::One);
m_Dyz = PrecisionImageType::New();
m_Dyz->SetOrigin(im->GetOrigin());
m_Dyz->SetSpacing(im->GetSpacing());
m_Dyz->SetDirection(im->GetDirection());
m_Dyz->SetRegions(im->GetLargestPossibleRegion());
m_Dyz->Allocate();
m_Dyz->FillBuffer(NumericTraits<Precision>::Zero);
m_Dzz = PrecisionImageType::New();
m_Dzz->SetOrigin(im->GetOrigin());
m_Dzz->SetSpacing(im->GetSpacing());
m_Dzz->SetDirection(im->GetDirection());
m_Dzz->SetRegions(im->GetLargestPossibleRegion());
m_Dzz->Allocate();
m_Dzz->FillBuffer(NumericTraits<Precision>::One);
// create temp vesselness image to store maxvessel
typename PrecisionImageType::Pointer vi = PrecisionImageType::New();
vi->SetOrigin(im->GetOrigin());
vi->SetSpacing(im->GetSpacing());
vi->SetDirection(im->GetDirection());
vi->SetRegions(im->GetLargestPossibleRegion());
vi->Allocate();
vi->FillBuffer(NumericTraits<Precision>::Zero);
for (unsigned int i=0; i< m_Scales.size(); ++i)
{
typedef HessianRecursiveGaussianImageFilter<PrecisionImageType> HessianType;
typename HessianType::Pointer hessian = HessianType::New();
hessian->SetInput(im);
hessian->SetNormalizeAcrossScale(true);
hessian->SetSigma(m_Scales[i]);
hessian->Update();
ImageRegionIterator<PrecisionImageType> itxx (m_Dxx, m_Dxx->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> itxy (m_Dxy, m_Dxy->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> itxz (m_Dxz, m_Dxz->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> ityy (m_Dyy, m_Dyy->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> ityz (m_Dyz, m_Dyz->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> itzz (m_Dzz, m_Dzz->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> vit(vi, vi->GetLargestPossibleRegion());
ImageRegionConstIterator<typename HessianType::OutputImageType> hit
(hessian->GetOutput(), hessian->GetOutput()->GetLargestPossibleRegion());
for (itxx.GoToBegin(), itxy.GoToBegin(), itxz.GoToBegin(),
ityy.GoToBegin(), ityz.GoToBegin(), itzz.GoToBegin(),
vit.GoToBegin(), hit.GoToBegin(); !vit.IsAtEnd();
++itxx, ++itxy, ++itxz, ++ityy, ++ityz, ++itzz, ++hit, ++vit)
{
vnl_matrix<Precision> H(3,3);
H(0,0) = hit.Value()(0,0);
H(0,1) = H(1,0) = hit.Value()(0,1);
H(0,2) = H(2,0) = hit.Value()(0,2);
H(1,1) = hit.Value()(1,1);
H(1,2) = H(2,1) = hit.Value()(1,2);
H(2,2) = hit.Value()(2,2);
vnl_symmetric_eigensystem<Precision> ES(H);
vnl_vector<Precision> ev(3);
ev[0] = ES.get_eigenvalue(0);
ev[1] = ES.get_eigenvalue(1);
ev[2] = ES.get_eigenvalue(2);
if ( vcl_abs(ev[0]) > vcl_abs(ev[1]) ) std::swap(ev[0], ev[1]);
if ( vcl_abs(ev[1]) > vcl_abs(ev[2]) ) std::swap(ev[1], ev[2]);
if ( vcl_abs(ev[0]) > vcl_abs(ev[1]) ) std::swap(ev[0], ev[1]);
const Precision vesselness = VesselnessFunction3D(ev[0],ev[1],ev[2]);
if ( vesselness > 0 && vesselness > vit.Value() )
{
vit.Value() = vesselness;
itxx.Value() = hit.Value()(0,0);
itxy.Value() = hit.Value()(0,1);
itxz.Value() = hit.Value()(0,2);
ityy.Value() = hit.Value()(1,1);
ityz.Value() = hit.Value()(1,2);
itzz.Value() = hit.Value()(2,2);
}
}
}
return;
}
// vesselnessfunction
template <class PixelType, unsigned int Dimension>
typename VesselEnhancingDiffusion3DImageFilter<PixelType, Dimension>::Precision
VesselEnhancingDiffusion3DImageFilter<PixelType,Dimension>::VesselnessFunction3D
(
const Precision l1,
const Precision l2,
const Precision l3
)
{
Precision vesselness;
if (
(m_DarkObjectLightBackground && ((l2<=0) || (l3<=0)))
||
(!m_DarkObjectLightBackground && ( (l2>=0) || (l3 >=0)))
)
{
vesselness = NumericTraits<Precision>::Zero;
}
else
{
const Precision smoothC=1E-5;
const Precision va2= 2.0*m_Alpha*m_Alpha;
const Precision vb2= 2.0*m_Beta*m_Beta;
const Precision vc2= 2.0*m_Gamma*m_Gamma;
const Precision Ra2 = (l2 * l2) / (l3 * l3);
const Precision Rb2 = (l1 * l1) / vcl_abs(l2 * l3);
const Precision S2 = (l1 * l1) + (l2 *l2) + (l3 * l3);
const Precision T = vcl_exp(-(2*smoothC*smoothC)/(vcl_abs(l2)*l3*l3));
vesselness = T * (1.0 - vcl_exp( - Ra2/va2)) *
vcl_exp(-Rb2/vb2) *
(1.0 - vcl_exp(-S2/vc2));
}
return vesselness;
}
// diffusiontensor
template <class PixelType, unsigned int Dimension>
void VesselEnhancingDiffusion3DImageFilter<PixelType, Dimension>
::DiffusionTensor()
{
ImageRegionIterator<PrecisionImageType> itxx (m_Dxx, m_Dxx->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> itxy (m_Dxy, m_Dxy->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> itxz (m_Dxz, m_Dxz->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> ityy (m_Dyy, m_Dyy->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> ityz (m_Dyz, m_Dyz->GetLargestPossibleRegion());
ImageRegionIterator<PrecisionImageType> itzz (m_Dzz, m_Dzz->GetLargestPossibleRegion());
for ( itxx.GoToBegin(), itxy.GoToBegin(), itxz.GoToBegin(),
ityy.GoToBegin(), ityz.GoToBegin(), itzz.GoToBegin();
!itxx.IsAtEnd();
++itxx, ++itxy, ++itxz, ++ityy, ++ityz, ++itzz)
{
vnl_matrix<Precision> H(3,3);
H(0,0) = itxx.Value();
H(0,1) = H(1,0) = itxy.Value();
H(0,2) = H(2,0) = itxz.Value();
H(1,1) = ityy.Value();
H(1,2) = H(2,1) = ityz.Value();
H(2,2) = itzz.Value();
vnl_symmetric_eigensystem<Precision> ES(H);
vnl_matrix<Precision> EV(3,3);
EV.set_column(0,ES.get_eigenvector(0));
EV.set_column(1,ES.get_eigenvector(1));
EV.set_column(2,ES.get_eigenvector(2));
vnl_vector<Precision> ev(3);
ev[0] = ES.get_eigenvalue(0);
ev[1] = ES.get_eigenvalue(1);
ev[2] = ES.get_eigenvalue(2);
if ( vcl_abs(ev[0]) > vcl_abs(ev[1]) ) std::swap(ev[0], ev[1]);
if ( vcl_abs(ev[1]) > vcl_abs(ev[2]) ) std::swap(ev[1], ev[2]);
if ( vcl_abs(ev[0]) > vcl_abs(ev[1]) ) std::swap(ev[0], ev[1]);
const Precision V=VesselnessFunction3D(ev[0],ev[1],ev[2]);
vnl_vector<Precision> evn(3);
// adjusting eigenvalues
// static_cast required to prevent error with gcc 4.1.2
evn[0] = 1.0 + (m_Epsilon - 1.0) * vcl_pow(V,static_cast<Precision>(1.0/m_Sensitivity));
evn[1] = 1.0 + (m_Epsilon - 1.0) * vcl_pow(V,static_cast<Precision>(1.0/m_Sensitivity));
evn[2] = 1.0 + (m_Omega - 1.0 ) * vcl_pow(V,static_cast<Precision>(1.0/m_Sensitivity));
vnl_matrix<Precision> LAM(3,3);
LAM.fill(0);
LAM(0,0) = evn[0];
LAM(1,1) = evn[1];
LAM(2,2) = evn[2];
const vnl_matrix<Precision> HN = EV * LAM * EV.transpose();
itxx.Value() = HN(0,0);
itxy.Value() = HN(0,1);
itxz.Value() = HN(0,2);
ityy.Value() = HN(1,1);
ityz.Value() = HN(1,2);
itzz.Value() = HN(2,2);
}
return;
}
// generatedata
template <class PixelType, unsigned int Dimension>
void VesselEnhancingDiffusion3DImageFilter<PixelType, Dimension>
::GenerateData()
{
if (m_Verbose)
{
std::cout << std::endl << "begin vesselenhancingdiffusion3Dimagefilter ... " << std::endl;
}
typedef MinimumMaximumImageFilter<ImageType> MinMaxType;
typename MinMaxType::Pointer minmax = MinMaxType::New();
minmax->SetInput(this->GetInput());
minmax->Update();
const typename ImageType::SpacingType ispacing = this->GetInput()->GetSpacing();
const Precision htmax = 0.5 /
( 1.0 / (ispacing[0] * ispacing[0])
+ 1.0 / (ispacing[1] * ispacing[1])
+ 1.0 / (ispacing[2] * ispacing[2])
);
if (m_TimeStep == NumericTraits<Precision>::Zero)
{
m_TimeStep = htmax;
}
if (m_TimeStep> htmax)
{
std::cerr << "the time step size is too large!" << std::endl;
this->AllocateOutputs();
return;
}
if (m_Verbose)
{
std::cout << "min/max \t" << minmax->GetMinimum() << " " << minmax->GetMaximum() << std::endl;
std::cout << "iterations/timestep \t" << m_Iterations << " " << m_TimeStep << std::endl;
std::cout << "recalc v \t" << m_RecalculateVesselness << std::endl;
std::cout << "scales \t";
for (unsigned int i=0; i<m_Scales.size(); ++i)
{
std::cout << m_Scales[i] << " ";
}
std::cout << std::endl;
std::cout << "alpha/beta/gamma \t" << m_Alpha << " " << m_Beta << " " << m_Gamma << std::endl;
std::cout << "eps/omega/sens \t" << m_Epsilon << " " << m_Omega << " " << m_Sensitivity << std::endl;
}
// cast to precision
typedef CastImageFilter<ImageType,PrecisionImageType> CT;
typename CT::Pointer cast = CT::New();
cast->SetInput(this->GetInput());
cast->Update();
typename PrecisionImageType::Pointer ci = cast->GetOutput();
if (m_Verbose)
{
std::cout << "start algorithm ... " << std::endl;
}
for (m_CurrentIteration=1; m_CurrentIteration<=m_Iterations; m_CurrentIteration++)
{
VED3DSingleIteration (ci);
}
typedef MinimumMaximumImageFilter<PrecisionImageType> MMT;
typename MMT::Pointer mm = MMT::New();
mm->SetInput(ci);
mm->Update();
if (m_Verbose)
{
std::cout << std::endl;
std::cout << "min/max \t" << mm->GetMinimum() << " " << mm->GetMaximum() << std::endl;
std::cout << "end vesselenhancingdiffusion3Dimagefilter" << std::endl;
}
// cast back to pixeltype
this->AllocateOutputs();
typedef CastImageFilter<PrecisionImageType,ImageType> CTI;
typename CTI::Pointer casti = CTI::New();
casti->SetInput(ci);
casti->GraftOutput(this->GetOutput());
casti->Update();
this->GraftOutput(casti->GetOutput());
}
} // end namespace itk
#endif
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