[Insight-users] Mean Curvature Calculation in Level Set

[Joshua Cates]

Hi Sah,

Yes you are correct.  This is a bug introduced during some refactoring of
the code right before release 1.4.  I have a fix that I will check in to 
the repository today.

thanks,

Josh.

______________________________
 Josh Cates			
 Scientific Computing and Imaging Institute
 University of Utah
 Email: cates at sci . utah . edu
 Phone: (801) 587-7697
 URL:   http://www . sci . utah . edu/~cates


On Thu, 20 Nov 2003, Sah Rayman wrote:

> Hi Josh, 
> 
> In itkLevelSetFunction.txx, Line 158-184 are:
> 
> template <class TImageType>
> typename LevelSetFunction<TImageType>::ScalarValueType
> LevelSetFunction<TImageType>::ComputeMeanCurvature(
>   const NeighborhoodType &itkNotUsed(neighborhood),
>   const FloatOffsetType &itkNotUsed(offset),
> GlobalDataStruct *gd)
> {
>   // Calculate the mean curvature
>   ScalarValueType curvature_term =
> NumericTraits<ScalarValueType>::Zero;
>   unsigned int i, j;
> 
>   
>   for (i = 0; i < ImageDimension; i++)
>     {      
>     for(j = 0; j < ImageDimension; j++)
>       {      
>       curvature_term -= gd->m_dx[i] * gd->m_dx[j] *
> gd->m_dxy[i][j];
> 
>       if(j != i)
>         {
>         curvature_term += gd->m_dxy[j][j] *
> gd->m_dx[i] * gd->m_dx[i];
>         }
>       }
>     }
>   
>   return (curvature_term / gd->m_GradMagSqr );
> }
> 
> Let's say ImageDimension==2, 
> Then before divided by gd->m_GradMagSqr:
> 
> curvature_term = 
> -dx[0]*dx[0]*dxy[0][0]
> -dx[0]*dx[1]*dxy[0][1] + dx[0]*dx[0]*dxy[1][1]
> -dx[1]*dx[0]*dxy[1][0] + dx[1]*dx[1]*dxy[0][0]
> -dx[1]*dx[1]*dxy[1][1]
> 
> According to Sethian's equation, the result should
> just be:
> 
> curvature_term = 
> -dx[0]*dx[1]*dxy[0][1] + dx[0]*dx[0]*dxy[1][1]
> -dx[1]*dx[0]*dxy[1][0] + dx[1]*dx[1]*dxy[0][0]
> 
> 
> Please confirm if that is the case for you. 
> 
> Thanks.
> Sah
> 
> --- Joshua Cates <cates at sci . utah . edu> wrote:
> > Hello Sah,
> > 
> > The default curvature calculation in the Level Set
> > function is mean
> > curvature.  I cannot find the line of code that you
> > reference.  Look in
> > the file itkLevelSetFunction.txx, method
> > ComputeMeanCurvature().  The
> > terms for the calculation come from the precomputed
> > Hessian matrix.
> > 
> > Josh.
> > 
> > ______________________________
> >  Josh Cates			
> >  Scientific Computing and Imaging Institute
> >  University of Utah
> >  Email: cates at sci . utah . edu
> >  Phone: (801) 587-7697
> >  URL:   http://www . sci . utah . edu/~cates
> > 
> > 
> > On Fri, 14 Nov 2003, Sah Rayman wrote:
> > 
> > > I am looking at function:
> > > 
> > > template <class TImageType>
> > > typename
> > LevelSetFunction<TImageType>::ScalarValueType
> > >
> > LevelSetFunction<TImageType>::ComputeMeanCurvature()
> > > 
> > > in itkLevelSetFunction.txx, line 158 (ITK 1.4)
> > > 
> > > When I compared that to Sethian's "Level Set
> > Methods
> > > and Fast Marching Methods", 2ndEd, pp. 70, Eq.
> > 6.36, I
> > > found that the C++ implementation contain some
> > extra
> > > terms in nominator:
> > > 
> > > -dx[0]*dx[0]*dxy[0][0]-dx[1]*dx[1]*dxy[1][1]-...
> > > 
> > > Can someone tell me what are these additional
> > terms
> > > for? Is the result still mean curvature? Any
> > reference
> > > for that?
> > > 
> > > 
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