[Insight-users] Explaining Vesselness getting Eigen Vectors

[Luis Ibanez]

Hi Kevin,

Yes,
use Open Source Software like OpenOffice for your presentation.
Way to go !!!



About the eigenvectors, you already listed the available options:

Note however that in the case:

A)  itkEigenAnalysis2DImageFilter, once you get the principal
      eigenvector, the second one is orthogonal to it.  Therefore
      you could simply plot the principal one...  and if you really
      want to show the other you can display:

                        (  Vx, Vy  )  = principal,  and
                        ( -Vy,  Vx )  = secondary one


B)  itkSymmetricEigenAnalysisImageFilter could be easily copy-pasted
     and modified, in order to build a filter that computes the eigenvectors,
     instead of the eigenvalues.

C) This is as hard as running the EigenAnalysis class in an ImageIterator
      loop and storing the output in a Vector image.


BTW: Please note that it is quite straight forward to plot this using
      Paraview:    www.paraview.org

      Ploting vector fields with paraview is discussed in the
      ITK Software Guide

             http://www.itk.org/ItkSoftwareGuide.pdf



 Good luck with your presentation,


      Luis


-----------------------------------------------------------------------------
On Mon, Oct 5, 2009 at 2:14 PM, Kevin H. Hobbs <hobbsk at ohiou.edu> wrote:
> I need to explain the vesselness filter to my bosses ( OOImpress
> presentation Friday ).
>
> The documentation for itkHessian3DToVesselnessMeasureImageFilter and the
> reference
> http://www.spl.harvard.edu/pages/spl-pre2007/pages/papers/yoshi really
> only refer to the properties of the eigenvalues for various shapes.
>
> We are left without an intuitive understanding of what the Eigen values
> and vectors mean.
>
> To help us understand what the Eigenvalues are I made a little 2D
> doodle, ran it through itkHessianRecursiveGaussianImageFilter and
> itkSymmetricEigenAnalysisImageFilter so that I could have slides of the
> lesser and greater eigenvalues.
>
> These are great! It's obvious from these images that the lesser
> eigenvalue has minima along the center of the big bright squiggly line
> in my doodle, and the greater eigenvalue has maxima along all of the
> edges.
>
> I think the last thing I need to give everybody an intuitive sense of
> what Eigen analysis does, is to get and plot both eigenvectors.
>
> As far as I can tell from the Doxygen, there is no filter that can give
> me both eigenvectors. itkEigenAnalysis2DImageFilter will give me only
> the vector for the larger eigenvalue and
> itkSymmetricEigenAnalysisImageFilter gives only the eigenvalues. Is that
> correct?
>
> Would it be easier to just iterate over the hessian image and call
> itk::SymmetricEigenAnalysis::ComputeEigenValuesAndVectors over and over
> printing x,y,ev11,ev12,ev21,ev22 for plotting with octave's quiver, or
> adapt itkSymmetricEigenAnalysisImageFilter to produce an image (or
> images) of the eigenvectors?
>
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