[Insight-users] Curvature in Level Set

[Sah Rayman]

Karl,

Your interpretation makes sense to me. I examed the
pixel location of some of the output curvatures, and
it does seem like the digitizing effect.

However, when I increase the curvature weight to 1
(same as propagation weight, and propagation in any
pixel is either +1 or -1), the std is almost in the
same level. The std range between different iterations
are now (0.1, 0.5). 

When I further increase curvature weight to 10, the
level set will refuse to grow. It will end up with
some circle that is a little smaller than my initial
circle (R < 60), despite that the propagation term
should make it R=80. Even in this case, the calculated
curvature is still high (0.1, 0.2).

And in fact, I first observed the effect that high
curvature weight make LS shrinking before I started
debugging my curvature values. 

I am still wondering if the reason is a bug of my
application or it is common in curvature calculation. 

Can someone post their std of curvature? 


--- Karl Krissian <karl at bwh.harvard.edu> wrote:
> Hello,
> 
> I don't think there is any problem in the curvature
> computation.
> If I understand well, the experiment you are doing
> is almost equivalent
> to computing the curvature on a binary image of a
> circle,
> which cannot lead to good results at small scales.
> 
> In practice, if you increase the curvature weight,
> your statistics
> will get much better, because level set result will
> be smoother.
> 
> Regards,
> 
> 
> Sah Rayman wrote:
> 
> >I found some "wierd behavior" of the curvature
> >calculated in SegmentationLevelSetFunction. 
> >
> >While I expect the curvature to be 0.0125
> everywhere, 
> >the actual curvature has a mean of 0.0137 (which is
> >good), but a s.t.d of 0.4. In another words, when
> the
> >tangent circle is actually of radius 80, the
> >calculation tells me the radius is 2 or 1 at some
> edge
> >points, and even concave in some other points.
> >
> >Is it true that there are errors in curvature
> >calculation in the range of my discription? Or,
> there
> >must be something wrong in my application?
> >
> >======================================
> >Here is what I do in the test.
> >
> >Full image is 256x256, ground truth is a circle
> whose
> >radius is 80 pixels, initial is a 60-pixel-radius
> >circle with a same center.
> >
> >I disabled advection, curvature term, and there are
> >only speed term. Speed is +1 inside my ground
> truth,
> >and -1 otherwise. In fact, curvature weight is 1e-6
> to
> >enable the curvature calculation.
> >
> >After 180 iterations, I observe the output of
> >ComputeMeanCurvature() for one iteration, and take
> >statistics.
> >
> >The output segmentation matches well with my ground
> >truth.
> >======================================
> >
> >
> >
> >
> >
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> >  
> >
> 
> -- 
> Karl Krissian, PhD
> Instructor in Radiology, Harvard Medical School
> Laboratory of Mathematics in Imaging, Brigham and
> Women's Hospital
> Tel:617-525-6232, Fax:617-525-6220 
> 
> 
> 


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