[Insight-developers] level sets: curvature term and time step

[Paul Yushkevich]

Hi Lydia, this is a really good question!

I looked at Sethian's book and here is what I got out of it:

1. The timestep limit is defined by (pg 67)
    max_{\Omega}(F \Delta t) \le \Delta \x

2. F is defined as (pg 73)
    F = F_{prop} + F_{curv} + F_{adv} = F_0 + \vec{U}(x,y,t) \cdot 
\vec{n} - \epsilon \kappa

Sorry for the latex.

In the level set code, the max of F_0 and max of U \vec{n}are already 
computed and used for setting the timestep, if I am correct.  Seems like 
we need to compute the max of the sum of those two and - \epsilon \kappa 
to get the time step.  Here,
\epsilon = \epsilon(x,y,t) is the "Curvature Speed" times the "Curvature 
Weight".

That's my 2 cents, but I am no expert.  Perhaps we could talk after the 
T-Con this week? 

Paul

Lydia Ng wrote:

>Question for those interested in level sets:
>
>Currently the itk::LevelSetFunction class does not take the curvature
>term into account when computing the time step to meet the CFL criterion
>to ensure numerical stability.
>
>This is causing some grief with users playing around with the scaling
>parameter in each of the term in particular when they set the curvature
>scaling to be high relative to the propagation and advection terms.
>
>Can someone point me to a paper/book that talks about have to compute
>the CFL time step for the curvature term? 
>
>Alternatively, (hacking versus mathematically sound) could we just
>restrict the time step such that the change in level set value due to
>the curvature term is no larger that half a pixel? Would this have the
>desired affect?
>
>The second alternative is for me to change my filters
>ShapeDetectionLevelSetImageFilter and
>GeodesicActiveContourLevelSetImageFilter just to use a constant time
>step - making it the user's problem to ensure they choose the time step
>small enough. This is how it was before, when I got complaints from
>other users about how it was difficult to set this parameter...
>
>Cheers,
>Lydia
>_______________________________________________
>Insight-developers mailing list
>Insight-developers at itk . org
>http://www . itk . org/mailman/listinfo/insight-developers
>
>
>  
>


-- 
--------------------------------
Paul A. Yushkevich, Ph.D.
President, Cognitica Corporation

17 Flemington Rd
Chapel Hill, NC 27517
Tel: 1-919-929-7652
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