[Insight-users] Re: ITK Gradient of vector fields -> how to compute eigensystem efficiently?

[Luis Ibanez]

Hi Ghassan,


Thanks for pointing out to the equations.


Lisa: The equations that Ghassan just indicated are
implemented in the file:


    Insight/Code/BasicFilters/
        itkEigenAnalysis2DImageFilter.txx


in lines  230-259.


   Regards,


       Luis


-------------------------
Ghassan Hamarneh wrote:
> 
> Thanks Luis!
> 
> On Sat, 31 Mar 2007, Lisa Tang wrote:
> 
> 
>>>    Note that if (N==2) then there is a closed form solution to the
>>>    eigen analysis problem, and therefore you don't need to use the
>>>    SymmetricEigenAnalysis class.
> 
> 
> http://mathworld.wolfram.com/Eigenvalue.html
> See equation 7 and 8, and the paragraph below it.
> 
> The basic idea is that you have a 2x2 matrix with variables [a11 a12; a21
> a22], and then you go through the process of calculating eigenvalues and
> eigen vectors by hand on a sheet of paper, or analytically, without
> substituting values for aij.  You may try to use Maple or Mathematica to
> solve this symbolically.
> 
> /Ghassan
> 
>