[Insight-developers] Perona-Malik -> questions

[Rashindra Manniesing]

The message below was previously posted to the insight-users list, but I 
guess the developer's list is more appropriate. I hope someone can 
provide some insight on these issues, or perhaps give me the names of 
the main developers of the finite difference classes - I am considering 
extending these classes to support anisotropic diffusion.

Thanks,

Rashindra Manniesing.


I am studying the finite difference solver hierarchy, and in particular 
the classes related to the Perona&Malik implementation. Several 
questions arises:

  - in itkGradientNDAnistropicDiffusionFunction.h the function
InitializeIteration is defined for calculating m_K (modified global 
average grad magn) as  -2.0 CondPar2 * GradMagSq, but shouldn't this be 
- GradMagSq/CondPar2 ?

- in the 'functional hierarchy' (i.e. FiniteDifferenceFunction and its
derived classes) the term global is used, for example in
'globalAverageGradMag'. Just to be sure, global refers to the local roi
(from the 'finite difference hierachy') for which the pde is solved at a
particular location? If so, where and how are the sizes of the roi then
chosen?

- the gradientMagSq itself is calculated in 
itkScalarAnistropicDiffusionFunction, by a finite element scheme. But 
then instability issues might occur, in particular for certain values of 
the conductance parameter the pde behaves as the inverse heat equation! 
Has this been resolved (already) by using Gaussian derivatives?

- the term anistropic used in these classes is inappropriate, since C(x) 
- the conductance term - returns a scalar. Perhaps a better naming would 
be inhomogenous for the PM equation? And reserving the term anistropic 
for directional diffusion equations, such as EED (edge enhancing diffusion).


Thanks,
Rashindra




-- 
  Rashindra Manniesing, PhD
  Biomedical Imaging Group Rotterdam (BIGR)
  Erasmus MC - University Medical Center Rotterdam
  Departments of Medical Informatics and Radiology

  phone  +31 10 40 88001
  fax    +31 10 40 87050
  email  r.manniesing at erasmusmc.nl

  room   Ee2342
  postal P.O. Box 1738, 3000 DR Rotterdam
  visit  Dr. Molewaterplein 40/50, 3015 GE Rotterdam