[Insight-users] Curvature Flow Image Filter - How is it working?

[Dan Mueller]

Hi Mel,

Here are some results from my googling:

"Curvature flow filtering is an anisotropic diffusion method used for
smoothing images while preserving edges. It effectively spreads the
curvature along a contour, thereby rounding corners and reducing the
Euclidean length of contours. The diffusion in a curvature flow filter
runs parallel to the image contours. Diffusion perpendicular to the
contours is omitted in order to preserve edges."
http://reference.wolfram.com/mathematica/ref/CurvatureFlowFilter.html

"The diffusion in a curvature flow filter runs parallel to the image
contours. Diffusion perpendicular to the contours is omitted in order
to preserve edges."
http://cvinhais.homeip.net/itk/Lectures/Lecture4_Filtering_5_Smoothing.pdf

"Level Set Methods offer an appealing approach to noise removal. In
particular, they exploit the fact that curves moving under their
curvature smooth out and disappear.  The idea is to view the pixel
values as a topographic map; the intensity (somewhere between white
and black) at each pixel is the height of the surface at that point.
Suppose we then let each contour undergo motion by curvature. Then
very small contours, corresponding to spikes of noise, will disappear
quickly. Better yet, the boundaries will remain sharp, since they will
not blur under this motion, and instead only move according to their
curvature."
http://math.berkeley.edu/~sethian/2006/Applications/ImageProcessing/noiseremoval.html

You might also be interested in the text book by James Sethian here:
http://math.berkeley.edu/~sethian/2006/Publications/Book/2006/book_1999.html

HTH

Cheers, Dan

On 4 July 2012 19:24, Melanie Uks <meluks2010 at googlemail.com> wrote:
> Hi,
>
> I tried to understand how the Curvature Flow Image Filter is working. I am
> using it for my image. I tested a few filters integrated in itk and this one
> gives the best results for my data. Now I want to understand the principle.
> The description here
> http://www.itk.org/Doxygen/html/classitk_1_1CurvatureFlowImageFilter.html is
> to complex for me and I couldn't find anything else (less complex) on the
> internet. Can anybody help me?
>
> Thanks a lot!
> Cheers,
> mel