还没有亲测，先放着，因为要用这个......
Eigenvalues of Hessian Matrix are used as a criteria for line-like structure such as pulmonary vessels and fungi vessels.ITK provides a class called ：itk::SymmetricEigenAnalysis to extract eigenvalues, eigenvalues vector as well as eigenvalues matrix from a given matrix. However, the ITK itself provided no direct implementation for the computation of Hessian Matrix. Instead, the ITK package provides a HessianRecursiveGaussianImageFilter class.
Iv´an Macıa explained[1] that the direct computation of the approximation of Hessian matrix for discrete signal would only enhance the noise component. In order to overcome such disadvantage, the author introduced a new convolution operator--the Gaussian Derivative Operator.
Though the document provides detailed description of the new class, it is not a easy task for use. Based on a example provided at <http://itk-insight-users.2283740.n2.nabble.com/EigenVector-Computation-td6054230.html>, I implemented a class to extract the eigenvalues vector of each voxel of a CT image.
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#include <iostream>
#include <string>
#include "stdlib.h"
#include "itkImageRegionIterator.h"
#include "itkImageRegionConstIterator.h"
#include "itkImageRegionIteratorWithIndex.h"
#include "itkHessianRecursiveGaussianImageFilter.h"
#include "itkCastImageFilter.h"
const unsigned short dimension = 3;
typedef short VoxelType;
typedef itk::Image<VoxelType, dimension> InputImageType;
typedef double HessianVoxelType;
typedef itk::Image<HessianVoxelType, dimension> HessianInnerImageType;
typedef itk::CastImageFilter<InputImageType, HessianInnerImageType> CastFilterType;
typedef itk::HessianRecursiveGaussianImageFilter<HessianInnerImageType> HFilterType;
typedef itk::Vector<HessianVoxelType, dimension> VecVoxType;
typedef itk::Matrix<HessianVoxelType, dimension, dimension> MatVoxType;
typedef itk::Image<VecVoxType, dimension> VecEigHImageType;
typedef itk::Image<MatVoxType, dimension> MatEigHImageType;
typedef itk::ImageRegionIterator<VecEigHImageType> OutputIterType;
typedef itk::SymmetricEigenAnalysis<MatVoxType, VecVoxType, MatVoxType> EigValAnalysisType;
typedef MatEigHImageType::Pointer MatEigHImagePointerType;
typedef MatEigHImageType::RegionType MatRegionType;
typedef MatEigHImageType::PointType MatPointType;
typedef MatEigHImageType::SpacingType MatSpacingType;
typedef VecEigHImageType::Pointer VecEigHImagePointerType;
typedef itk::ImageRegionIteratorWithIndex<HFilterType::OutputImageType> HIterType;
class EigValHessian {
private:
MatRegionType region;
MatSpacingType spacing;
MatPointType origin;
CastFilterType::Pointer CastFilter;
HFilterType::Pointer HFilter;
EigValAnalysisType EigValAnalysis;
VecEigHImagePointerType VecEigHImagePointer;
public:
EigValHessian(const InputImageType::Pointer& image) {
VecVoxType EigVal;
MatVoxType EigMat,tmpMat;
for(int i=0;i<3;i++)
for(int j=0;j<3;j++)
EigMat[i][j]=0;
region=image->GetLargestPossibleRegion();
spacing=image->GetSpacing();
origin=image->GetOrigin();
CastFilter = CastFilterType::New();
HFilter = HFilterType::New();
HFilter->SetSigma(3);//3 for sigma;read the definition of the Gaussian kernel;
//EigValAnalysis = EigValAnalysisType::New();
EigValAnalysis.SetDimension(3);
CastFilter->SetInput(image);
HFilter->SetInput(CastFilter->GetOutput());
HFilter->Update();
VecEigHImagePointer=VecEigHImageType::New();
VecEigHImagePointer->SetRegions(region);
VecEigHImagePointer->SetOrigin(origin);
VecEigHImagePointer->SetSpacing(spacing);
VecEigHImagePointer->Allocate();
EigVal[0]=EigVal[1]=EigVal[2]=0;
VecEigHImagePointer->FillBuffer(EigVal);
HIterType HIter(HFilter->GetOutput(),region);
OutputIterType OutputIter(VecEigHImagePointer,region);
itk::SymmetricSecondRankTensor<double,3> Tensor;
for(HIter.GoToBegin(),OutputIter.GoToBegin();!HIter.IsAtEnd()&&!OutputIter.IsAtEnd();++HIter,++OutputIter){
Tensor=HIter.Get();
tmpMat[0][0]=Tensor[0];
tmpMat[0][1]=Tensor[1];
tmpMat[1][0]=Tensor[1];
tmpMat[0][2]=Tensor[2];
tmpMat[2][0]=Tensor[2];
tmpMat[1][1]=Tensor[3];
tmpMat[2][1]=Tensor[4];
tmpMat[1][2]=Tensor[4];
tmpMat[2][2]=Tensor[5];
EigValAnalysis.ComputeEigenValuesAndVectors(tmpMat,EigVal,EigMat);
OutputIter.Set(EigVal);
}
try{
VecEigHImagePointer->Update();
}
catch(itk::ExceptionObject &excp) {
std::cerr << "Exception thrown while computing the eigenvalues vector!" << std::endl;
std::cerr << excp << std::endl;
exit(EXIT_FAILURE);
}
}
};
[1] Iv´an Macıa, Generalized Computation of Gaussian Derivatives Using ITK, October 5, 2007. 1VICOMTech, Paseo Mikeletegi 57, San Sebastián.