[Insight-users] Level-set term equation !

[Luis Ibanez]

Hi Sami,

Have you read the ITK Software Guide: ?

     http://www.itk.org/ItkSoftwareGuide.pdf

in particular Section 9.3 "Level Set Segmentation",
in pdf-page 563.

This section describes the terms of the Level Set
equation implemented in ITK.


For the theoretical background used as base of the ITK implementation
of Level Sets you may want to look at:

Sethian, James A. (1999)
"Level Set Methods and Fast Marching Methods :
Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer
Vision, and Materials Science"
(2nd ed.). Cambridge University Press.
ISBN 0-521-64557-3.
http://www.amazon.com/Level-Methods-Fast-Marching-Computational/dp/0521645573/ref=sr_11_1/104-2040997-8163952?ie=UTF8&qid=1191849386&sr=11-1

and to

"Insight into Images: Principles and Practice for Segmentation,
Registration, and Image Analysis"
by Terry S. Yoo (Editor)
http://www.amazon.com/Insight-into-Images-Segmentation-Registration/dp/1568812175/ref=sr_1_1/104-2040997-8163952?ie=UTF8&s=books&qid=1191849465&sr=1-1

About the idea of using the image Laplacian as part of the
partial differential equation used to update the Level Set,
you may want to look at the classes:

http://www.itk.org/Insight/Doxygen/html/classitk_1_1LaplacianSegmentationLevelSetFunction.html
http://www.itk.org/Insight/Doxygen/html/classitk_1_1LaplacianSegmentationLevelSetImageFilter.html




For full details on how the curvature term is computed,
please look at:


   Insight/Code/Common/itkLevelSetFunction.txx

   and the method  ComputeCurvatureTerm() in lines 27-38.

   This method will invoke

      * ComputeMeanCurvature
      * ComputeMinimalCurvature

   depending on the filter settings.

   In general the curvature is computed from an estimation of
   Second derivatives based on finite differences.


     Regards,


       Luis


---------------------
sami bourouis wrote:
> Hi
>  
> I want to know exactely the level-set formulation used by ITK and 
> especially by the algorithm  itkSegmentationLevelSetFunction. On the 
> other hand, I need to know the mathematical expression of P(x) 
> (propagation or speed term) and Z(x) (curvature term) used by 
> itkSegmentationLevelSetFunction. and what is the major difference 
> between P(x) and Z(x).
>  
> I found in this expression :
>  
> \f$\phi_{t} + \alpha 
> \stackrel{\rightharpoonup}{A}(\mathbf{x})\cdot\nabla\phi +
> \beta P(\mathbf{x})\mid\nabla\phi\mid = \gamma 
> Z(\mathbf{x})\kappa\mid\nabla\phi\mid\f$
>  
>  but what is the exression of each term ?
> _Another question please:_
>  
> It is possible to integrate the laplacian filter into  the 
> ShapeDetectionLevelSetImageFilter algorithm or 
> GeodesicActiveContourLevelSetImageFilter. Because here the expression of 
> P(x) and Z(x) are simply and are equally to g(x)  (P=Z=g). So the 
> level-set equation become more easy.
>  
> Thanks a lot
>  
> sami
> 
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