[Insight-users] Re: rigid 3d Registration question (still a newbie, feels like )

[Luis Ibanez]

Robert,


The recommendation for the scaling of translation parameters
versus rotation parameter is to use a factor proportional to
the diagonal length of the image.

For your case the, you have 100 pixels with 1 mm / pixel,
therefore the physical extent of your image is

        100mm  X  100mm  X 100mm

The diagonal the image bounding box is

          sqrt(3) * 100 mm

which is about

              173.2

and extra factor of 10X is usually useful, so you should
probably try a factor of


     1.0 / ( 10 x 173.2 )  =  1.0 / 1732.0

You could use this same factor for the three components
of the translation or you could estimate independent
factor for each component in the way it is done in the
VolView plugin.

Note that this factors are not expected to be computed
precisely. Their purpose is simply to bring the rotational
and translational parameters to a similar numerical scale.

By default, they are quite disproportionate since rotation
are in radians, therefore in a range about -1:1, while
translations are in millimeters, and for an image of 100mm
you probably can expect translations as large as 50mm.


The difference between Offset and Translation is relevant
only for the "Centered" transforms.  For example, for the
case of the CenteredAffineTransform the full transformation
is given by


           P' = R x ( P - C ) + ( C + T )

where

   C  is the Center of rotation
   P  is the point to be transformed
   P' is the transformed point
   T  is the translation.


This equation can be rewritten as

        P' =   R x P     +     [ C + T - R X C ]

and we call Offset the expression

      Offset = [ C + T - R X C ]

so the transformation is

       P'  =  R x P  + Offset

So, the relationship between Translation and offset is


      Offset =  [ I - R ] x C    +    T


In practice, if you are using Centered transform, you should
not care about the Offset. Instead make sure that you provide
appropriate values for the Center of Rotation and the Translation.
The Offset is computed from these two and the rotation matrix.



Note that the step length is also a critical value.
There is no magic recipe for selecting one. You probably
want to start experimenting with a small value (e.g. 0.01)
and plot the metric evaluations during the registration
process.  If you observe that the metric values are fairly
monotonic, that means that you can safely increment the
step length. Such an increment has the advantage of reducing
the time required to reach an extrema of the cost function
(the image metric in this case).   You could restart the
registration with larger values of the step length, as long
as you don't observe a noisy and/or erratic behavior on the
Metric values.

Step length issues are discussed in the course material
from the "Image Registration Techniques" course at RPI.

   http://www.cs.rpi.edu/courses/spring04/imagereg/

for example in lecture 9:

http://www.cs.rpi.edu/courses/spring04/imagereg/lecture09.ppt


Regards,



     Luis



-----------------------
Atwood, Robert C wrote:

> Dear Luis and the list:
> As a start at trying my 3d registration, I have looked into example
> ImageRegistrationExample8 and the vvITKImageRegistration plugin. I have
> found that for my test examples, the volview plugin works better, so I
> was looking into the differences in implementation. I already applied
> the 
> 
> itkNormalizedCorrelationImageToImageMetric
> 
> instead of the one originally in Example8.
> 
>  
> 
> In the following lines, the scales and StepLenght parameters are set,
> how did you decide upon these values ?  
> If I have a volume where each voxel is 1 unit and the entire volume is
> 100x100x100, is the value of optimizerScales[3] equal to 1/1000 or 1/10
> ? 
> 
> Also, I am unclear about what the difference between the 'Offset' as in
> transform->GetOffset() and the 'Translation' as in versor rigid 3d
> transform parameters [3][4][5] ?
> 
> 
> Thanks!
> Robert
> 
> 
> 
> in vvITKImageRegistration.cxx
>     316   optimizerScales[0] = 1.0;
>     317   optimizerScales[1] = 1.0;
>     318   optimizerScales[2] = 1.0;
>     319   optimizerScales[3] = 1.0/
>     320
> (10.0*info->InputVolumeSpacing[0]*info->InputVolumeDimensions[0]);
>     321   optimizerScales[4] = 1.0/
>     322
> (10.0*info->InputVolumeSpacing[1]*info->InputVolumeDimensions[1]);
>     323   optimizerScales[5] = 1.0/
>     324
> (10.0*info->InputVolumeSpacing[2]*info->InputVolumeDimensions[2]);
>     325   m_Optimizer->SetScales(optimizerScales);
>     326
>     327   m_Optimizer->SetMaximumStepLength(1.0);
>     328   m_Optimizer->SetMinimumStepLength(0.01);
>     329
> 
> 
>  In ImageRegistration8.cxx some different values are used:
> 
> 
>      332   typedef OptimizerType::ScalesType       OptimizerScalesType;
>     333   OptimizerScalesType optimizerScales(
> transform->GetNumberOfParameters()         );
>     334   const double translationScale = 1.0 / 1000.0;
>     335
>     336   optimizerScales[0] = 1.0;
>     337   optimizerScales[1] = 1.0;
>     338   optimizerScales[2] = 1.0;
>     339   optimizerScales[3] = translationScale;
>     340   optimizerScales[4] = translationScale;
>     341   optimizerScales[5] = translationScale;
>     342
>     343   optimizer->SetScales( optimizerScales );
>     344
>     345   optimizer->SetMaximumStepLength( 1.000  );
>     346   optimizer->SetMinimumStepLength( 0.001 );
>     347
> 
>