[vtkusers] vtkLandmarkTransform alghoritm

[Antonio]

Il 06/12/2011 23:49, David Gobbi ha scritto:
> The title of the paper advertises (states) that the method is closed 
> form (expressed as a set of equations that can be directly evaluated 
> to give the solution).
>
> Within the paper, one important step of the method is done with a 
> standard iterative (i.e. not closed-form) algorithm to find the 
> eigenvalues of a 4x4 matrix.
>
> So, the solution presented in the paper is not closed-form.  The paper 
> states that a closed-form solution for the eigenvalues of a 4x4 matrix 
> exists, but it does not use the closed-form solution. It uses an 
> iterative solution instead.
>
> It wasn't until later (maybe 2002?) that someone finally published a 
> fully closed-form solution.  But VTK uses Horn's method, not the new 
> method.  People who are just using the method (rather than 
> implementing it) probably will not care one way or the other... the 
> two methods would give nearly identical answers.
>
>  - David
>
>
> On Tue, Dec 6, 2011 at 3:17 PM, andon <antoniod987 at gmail.com 
> <mailto:antoniod987 at gmail.com>> wrote:
>
>     I've not understood what do you mean for " it isn't a closed form
>     solution as
>     advertised." and "The complete closed-form solution was developed
>     later.
>
Wonderfull and perfect description, thank you very much. I'm using the 
transfomr but i need also these "theorical" aspects because i'll 
describe the workflow of my application also from a theorical point of 
view.. Thank you very much again, your help has been very very very 
usefull for me.
Good night
Antonio
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