[Insight-users] Perona&Malik diffusion - questions

[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 CondPar^2 * GradMagSq, but shouldn't this be - GradMagSq/CondPar^2 ?

- 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