[Insight-users] Parametric vs. Non-parametric image registration?

[Lodron, Gerald]

Famous nonparametric example:

Daemon registration 

B-Spline is parametric because the grid is usually much smaller and you only need to specify vectors for this grid. This transform is defenetly the parametric with most parameters and is a kind of special case. In general (not necessary) a nonparametric transformation is used for nonlinear transformations and parametric ones for linear transformations.

See wikipedia for parametric and non-parametric models!

-----Ursprüngliche Nachricht-----
Von: motes motes [mailto:mort.motes at gmail.com] 
Gesendet: Dienstag, 02. Februar 2010 10:04
An: Lodron, Gerald
Cc: insight-users at itk.org
Betreff: Re: [Insight-users] Parametric vs. Non-parametric image registration?

On Tue, Feb 2, 2010 at 9:21 AM, Lodron, Gerald <Gerald.Lodron at joanneum.at> wrote:
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>
> Parametric means that you can model the transformation via a formula which is only dependend on a few parameters, e.g.
>
> f(x,y) = (x',y') = (x,y) + (tx, ty)
>
> Here the parameters of that "translation transform" are tx and ty.
>
>
> Nonparametric means that the transformation cannot be represented by such an formular, you need an explicit deformation vector for EVERY pixel. That is for an 2D MxN image a MxNx2 deformation > field. It should be clear that a parametric transaformation is much easier to invert and smaller to save.


Ok but which well known method use a non-parametric approach? When I look in eg. the itkSoftwareguide all transforms are based on the parametric approach.

Now for the BSplineDeformationTransform a deformation vector is actually computed for each pixel (the final deformation field), though its through interpolation and from a smaller number of "prototype"
deformation vectors. But still this transform is a parametric transform.




>
>
>
> -----Ursprüngliche Nachricht-----
> Von: insight-users-bounces at itk.org 
> [mailto:insight-users-bounces at itk.org] Im Auftrag von motes motes
> Gesendet: Dienstag, 02. Februar 2010 09:14
> An: Insight Users Mailing List
> Betreff: [Insight-users] Parametric vs. Non-parametric image registration?
>
> The terms Parametric and Non-parametric Image registration are used in many articles but what is the exact difference?
>
> I know that optimizing a deformation field using eg. B-Splines is called parametric (the coefficients/parameters of the deformation vectors are optimized).
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> But what are equivalent examples of non-parametric methods?
> _____________________________________