[Insight-users] Question about AnisotropicFourthOrderLevelSetImageFilter?

[Luis Ibanez]

Hi Zhao,

The evolution of LevelSets is computed at each iteration as an update
from a finite differences equation that is approximating a continuous
partial differential equation PDE.

What is special in the case of this filter is that the differential
equation contains second order derivatives and fourth order derivatives.

So, the equation looks like:

          F(x) =  A d^2 I(x) / dx^2   +  B   d^4 I(x) / d x^4


"The 4th-order level set PDE framework is proposed as an alternative to
  2nd order PDEs. By order we mean the order of differentiation of the
  level set image function required to compute derivatives for updating
  the image. For instance, the popular curvature flow uses 2nd-order
  derivatives of the level set image; hence, it is a 2nd order PDE."


This algorithm evolves the entire level set, and by this means it
implicitly evolves the surface.

You will find a detailed description of this methods in
http://www.sci.utah.edu/stories/2003/sum_geo-surf-proc.html

and the publication
http://www.sci.utah.edu/publications/tolga03/tasdizen.pdf

T. Tasdizen, R. Whitaker, P. Burchard, S. Osher. “Geometric Surface 
Processing via Normal Maps,”  In ACM Transactions on Graphics, 2003.



    Regards,


      Luis




-----------------------------------

zhao yong qiang wrote:

> Hi all,
> 
>    When I read the document of 
> AnisotropicFourthOrderLevelSetImageFilter, I am confused that what the 
> function of fourth order level set is.
> 
> Does this filter just implement the surface diffusion algorithm or 
> evolve the isosurface? Can someone tell me where the reference of this 
> filter?
> 
> Thanks in advance!
> 
>  
> 
> Regards,
>                           Zhao Yongqiang
>                           Dept. of Computer Science & Engineering
>                           Shanghai JiaoTong University
>                           Shanghai, China
>                           zhao-yq at cs.sjtu.edu.cn 
> <mailto:zhao-yq at cs.sjtu.edu.cn>
> 
>  
>