[Insight-users] Explaining Vesselness getting Eigen Vectors

[Kevin H. Hobbs]

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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