[Insight-developers] Level sets fudge factor

[Luca Antiga]

Hi all,
  I'm almost done extending sparse field level sets and a few other  
filters (like curvature flow) to correctly account for anisotropic  
spacings.

However, there's one point I don't fully understand yet.

In this revision
http://www.itk.org/cgi-bin/viewcvs.cgi/Code/BasicFilters/ 
itkSparseFieldLevelSetImageFilter.txx?root=Insight&r1=1.29&r2=1.30
the "fudge factor" was introduced in the interpolation of surface  
location,
see also itkSparseFieldLevelSetImageFilter.txx:950 (current head  
version):

       for (i = 0; i < ImageDimension; ++i)
         {// Adding sqrt imagedimension "extends the reach" of the  
interpolation
          // to surfaces that pass close to the center of cells.   
This is a
          // heuristic fudge factor that improves interpolation and  
reduces
          // "wiggling" at convergence.
                 offset[i] = (offset[i] * centerValue) * vcl_sqrt 
(ImageDimension +0.5)
                   / (norm_grad_phi_squared + MIN_NORM);
          //       offset[i] = (offset[i] * centerValue) / (sqrt 
(norm_grad_phi_squared) + MIN_NORM);
         }

Can somebody (Josh?) please give me an idea on the rationale behind  
this factor?
My problem is that anisotropic spacings work fine when I comment out  
the first version of offset[i] and use the second instead, i.e.
offset[i] = (offset[i] * centerValue) / (sqrt(norm_grad_phi_squared)  
+ MIN_NORM);
while I can't get it to work properly when the expression is  
multiplied by vcl_sqrt(ImageDimension +0.5), as in the first version.
Maybe it's a problem in my code that gets amplified by the factor,  
but I first have to intuitively understand what's it about.
Thanks a lot for you help.

Luca

--
Luca Antiga, PhD
Head, Medical Imaging Unit,
Bioengineering Department,
Mario Negri Institute
email: antiga at marionegri.it
web: http://villacamozzi.marionegri.it/~luca
mail: Villa Camozzi, 24020, Ranica (BG), Italy
phone: +39 035 4535-381