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

[motes motes]

On Tue, Feb 2, 2010 at 9:21 AM, Lodron, Gerald
<Gerald.Lodron at joanneum.at> wrote:
>
>
> 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).
>
> But what are equivalent examples of non-parametric methods?
> _____________________________________