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<DIV><FONT face=Arial size=2>Hi there,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I think there is a small mistake in the
implementation of the CurvesLevelSetFunction or the LevelSetFunction
respectively, regarding computation of minimal curvature. Although I currently
don't use this feature, I think I might have found a litte mistake in the
implementation, and want to share it with you so it can be fixed or somebody can
correct me.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>As far as I understand the implementation of
ComputeMinimalCurvature, this function returns the principal curvature term that
has minimal *absolute* value.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I don't know, if this function is used for other
LevelSet-Filters as well, but at least in the context of CurvesLevelSetFunction
this doesn't make sense in my opinion. In this filter the regularization force
is defined on the minimal curvature and supposed to "smoothen" small tubelike
shapes only along their centerline, not it's crossection. Now, given ITK's
definitions of inside and outside, the principal curvature along the cross
section of the tube will *always* be positive. Accordingly, negative principal
curvature can only result from curvature of the centerline and should always be
used for regularization. </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Now, in most cases this might not be a problem, but
suppose a small tube with a very sharp corner, where the negative curvature on
the "inner" side of the corner has a higher amount than the curvature of the
crosssection. Then the regularization force is computed using the curvature of
the cross section and driving the surface in the wrong direction, resulting
possibly in a cut in the tube. Especially look at Figure 6 in the work (in the
version I got at <A
href="http://certis.enpc.fr/publications/papers/01mia.pdf">http://certis.enpc.fr/publications/papers/01mia.pdf</A>).
There the regularization quickly smoothens the sharp corners with negative
curvature. Has anybody tested the ITK-Filter on similar data? In their work the
authors only refer to taking "the smaller nonzero eigenvalue", which probably
can be interpreted in both ways, juding by absolute values or not.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Regards, Michael</FONT></DIV></BODY></HTML>