[Insight-users] Hessian Matrix

[Karthik Krishnan]

----
As Chris mentioned, the filter Hessian3DToVesselnessMeasureImageFilter is a
direct translation of the "3D Line filter using Hessian Matrix" from
http://splweb.bwh.harvard.edu:8000/pages/papers/yoshi/node3.html#SECTION00021000000000000000.

It is intended for the extraction of tubular structures (blood vessels,
bronchi..)

----

If you find the performance of the line filter unsatisfactory, you might
want to look at the following application:
  http://itk.org/HTML/Curve3DExtraction.htm

This application is partly a superset of what you'd do with the
VesselenessMeasureImage Filter. It plots the each pixel in eigen space and
then allows you to play with the region in eigen space where you'd find
tubular structures  and discard noise by decreasing the depth of the
frustum, away from the origin.

Rephrased, both the vesseleness and the above application do the same upto a
certain point :
  ie both do
Scalar Image -> Image with 3D Hessian matrix at each pixel -> Eigen Values
at each pixel .

Tubular structures are pixels with a two large (negative) eigen values and a
near zero eigen value.
 - The vesselness filter (with some filtering) picks those pixels out for
you.
 - The Curves3DExtractor application will allow you to position a frustum in
eigen space to interactively pick those out.

----

HTH
-karthik

On 1/18/07, Chris McIntosh <cmcintos.sfu at gmail.com> wrote:
>
> Hello,
>
> To my knowledge the itk::Hessian3DToVesselnessMeasureImageFilter< TPixel >
> class will compute the Hessian, which can then be input to the
> Hessian3DToVesselnessMeasureImageFilter in the ./Code/Basic filters.
>
> It appears from its header file that it defaultly sets the output image
> type
> to: "Image< SymmetricSecondRankTensor< ITK_TYPENAME
> <itkWin32Header_8h.html#a0> NumericTraits< ITK_TYPENAME
> TInputImage::PixelType>::RealType,
> ::itk::GetImageDimension<TInputImage>::ImageDimension >,
> ::itk::GetImageDimension<TInputImage>::ImageDimension >"
>
> which is what's needed for the Hessian3DToVesselenssMeasureImageFilter
>
>
> http://www.itk.org/Doxygen/html/itkHessianRecursiveGaussianImageFilter_8h-source.html
>
> http://www.itk.org/Doxygen/html/classitk_1_1Hessian3DToVesselnessMeasureImageFilter.html
>
>
> So in theory you need only do something *like* this: (note I have not
> compiled or tested this)
>
> typedef itk::HessianRecursiveGaussianImageFilter< TInputImage > hrgType;
> typedef itk::Hessian3DToVesselnessMeasureImageFilter< TypeOutputPixel>
> hvmType;
>
> hrgType::Pointer hessian = hrgType::New();
> hessian->SetInput(reader->GetOutput()); //Pipe the reader into the
> hessian filter
> hessian->SetSigma(5.0);// Will find vessels of radius 5
>
> hvmType::Poiner vesselFilter = hvmType::New();
> vesselFilter->SetInput(hessian->GetOutput()); //Set the hessian as the
> input to the vessel filter
> vesselFilter->SetAlpha1(0.5);//
> vesselFilter->SetAlpha2(2.0);//
>
> http://splweb.bwh.harvard.edu:8000/pages/papers/yoshi/node3.html#SECTION00021000000000000000
>
> writer->SetInput(vesselFilter->GetOutput());
> writer->Update();
>
> For more details check the included ITK example in:
> InsightToolkit-2.6.0-src
> /Examples/Filtering/VesselnessMeasureImageFilter.cxx
>
> HTH,
>
> Chris
>
>
> 예동해 wrote:
>
> > Hi all.
> >
> > I am trying to compute 3D hessian matrix for vessel enhancement.
> >
> > I found some functions that are supposed to be useful for my goal.
> >
> > This is Hessian3DToVesselnessMeasureImageFilter in the ./Code/Basic
> > filters.
> >
> > But, I don't know how to use it.
> >
> > Please show the way and Help me out.
> >
> > I'm looking forward to your reply.
> >
> > Thank you.
> >
> >------------------------------------------------------------------------
> >
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> >
> >
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