[Insight-users] Metric Error Measurements

[Luis Ibanez]

Hi Rahul,

You are raising an interesting question here.

There are no estimations of uncertainty available
for Image Fegistration in ITK at this point.

However, it shouldn't be too hard to implement
such an estimation. You could probably use the
second order derivatives of the Metric with
respect to the parameters of the Transform as
an indication of uncertainty.

Since the basic ITK image registration framework
allows you to compute the metrics for a specific
set of Transform parameters, you could implemnt
a finite difference estimations of the Metric
second derivatives with respect to the transform
parameters.

However, the estimation will be computationally
intensive. You could get a considerable speed up
by computing the metric in small local regions
as you already suggested.

Note that also the Jacobian of a transformed
point coordinates with respect to the Transform
parameters will give you an estimation of the
uncertainty on the transformation itself. That
is, how confident we are that a particular
point of the fixed image is to be mapped into
its homologous point in the moving image.

Please let us know if you need any details
on how to compute the Metric second derivatives
or the Jacobian of the transformed point
coordinates.


    Regards,


        Luis



-----------------------

Rahul Chander wrote:

> Hi,
> I was wondering if there is a way in ITK to determine the amount of 
> uncertainty in registration using a particular registration scheme.  
> In other words, lets say I am using MutualInformation metric.  I get 
> some results out of the registration process in the form of a 
> registered image A.  Now in this image A, is a measurement possible 
> that indicates how successful the registration was for a given 
> pixel.  I would imagine that this error measurement could be 
> implemented differently to suite each metric.  
> 
> Such a measurement would help in the validation of the registration 
> process itself.  For example, if the error in registration is high 
> for a particular portion of the image, then we could be made aware 
> of any artifacts being introduced.  In the absence of such a 
> measurement, we would "totally" rely on a medical expert to 
> qualitatively validate a given registered image.
> 
> Any suggestions?
> Thanks.
> Rahul.