[Insight-users] Time step values for 2D and 3D images?

[Luis Ibanez]

Hi Neha,

The concept of "Time Step" in the context of the
CurvatureFlow filter (and the anisotropic diffusion
filters) is explained in the SoftwareGuide

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

on Section 6.5.2, pdf-page 173 to 179.


Those filters are solving a diffusion equation
using the image intensities as the values of
a scalar field. The diffusion equation is solved
numerically by using an iterative method that applies
a finite differences approximation at each iteration.

Since the diffusion equation is modelling a physical
phenomenon that occurs over time, the discretization
of the contiuous equation necessarily implies to
discretize the time.  The "Time Step" parameter
is the unit of time discretization that you use for
solving the diffusion equation in iterations.

As with any other numerical solution of differential
equations, the smaller the time step, the better the
approximation will be, but the longer you have to
wait for the result because the process will require
more iterations.  Using a too large time step, on
the other hand, will result in numerical instability
of the discrete approximation.

In the SoftwareGuide you will find recommended values
for the time step to be used in 3D and 2D images.
In general you are safe with values around 0.01.


Regards,


    Luis


--------------
Neha D wrote:
> Hi Luis,
>  
> SetTimeStep() is the function used for smoothing filter such as 
> CurvatureFlow Filter.
>  
> Thanks,
> Neha
> 
> */Luis Ibanez <luis . ibanez at kitware . com>/* wrote:
> 
> 
>     Hi Neha,
> 
>     You question is quite ambiguous...
>     Where did you see the term "time step" ?
> 
>     The ITK image itself doesn't have a notion of time.
> 
>     You probably found this in the Anisotropic diffusion
>     filters or in the Level set solver.
> 
>     For the anisotropic diffusion filters you will find
>     explanations of what the time step means in the
>     SoftwareGuide
> 
>     http://www . itk . org/ItkSoftwareGuide . pdf
> 
>     Section 6.5.2, pdf-page 173, paper-page 199.
> 
> 
>     Regards,
> 
> 
>     Luis
> 
> 
> 
>     -------------------
>     Neha D wrote:
>      > Hi,
>      >
>      > What does the "timestep" value for 2D a single image indicate?
>      >
>      > what does this value indicate for 3D images? Is this a time
>     beween two
>      > image data sets ?
>      >
>      > thanks,
>      >
>      > neha
>      >
>      >
> 
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