[Insight-users] Comparison of Sethians equation and itkLevelSetFunction implementation

[Christoph Palm]

Dear all,

to understand the levelSet implementation within ITK
I went very deep into the code and find an inconsistancy
between the cited bood of Sethian and the implementation
of itkLevelSetFunction:

The following lines code refer obviously to equation (6.15)
on page 65 chapter 6 of Sethians famous bool about LevelSets:
      
for(i = 0; i< ImageDimension; i++)
{
   propagation_gradient += vnl_math_sqr(    
                           vnl_math_max(gd->m_dx_backward[i], ZERO) )
          + vnl_math_sqr( vnl_math_min(gd->m_dx_forward[i],  ZERO) );
}

To my mind, there is the square of each derivative missing and the
square root should not be used only for one term.
Therefore, the code should be like the following:

for(i = 0; i< ImageDimension; i++)
{
   propagation_gradient +=    vnl_math_max(gd->m_dx_backward[i], ZERO) 
                            * vnl_math_max(gd->m_dx_backward[i], ZERO)
                            + vnl_math_min(gd->m_dx_forward[i],  ZERO) 
                            * vnl_math_min(gd->m_dx_forward[i],  ZERO);
}
propagation_gradient = vnl_math_sqr(propagation_gradient);

(the else part in the code should be changed accordingly) 

Am I right or should I have to look closer into the code?
Comments on that are highly appreciated.

Thanks

Christoph

-- 
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Dr. Christoph Palm

Research Center Juelich
Institute of Medicine
D-52428 Juelich

Web:   www.chripa.de/AtWork
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