Biomedical Engineering Reference
In-Depth Information
This expected local variance in Eq. ( 3.40 ) shows that the global variance can
be used to represent the coefficient of variance of a local sampled area. Intuitively,
we can perceive that the set of pixels captured by kernel during the windowing
mechanism of anisotropic diffusion represent an area with certain level of homo-
geneity. However, such set of homogeneities are not identical but reside in certain
distribution in which they have their own variance. It has been shown in ( 3.40 ) that
such variance of sample variances amounts to the global variance of the image.
This fact is critical in the context of automation in anisotropic diffusion when we
applied the diffusion function of SRAD as we are now able to adopt directly the
variance of each input image as the q 0 into the diffusion coefficient of SRAD in
Eq. ( 3.33 ). This direct adoption is critical in fulfiling criterion P2 of being high
computational efficient. This get rids of the problematic manual parameter setting
of value κ such as in Eqs. ( 3.28 ) and ( 3.29 ) and at the same time it fulfils the crite-
ria of P6 and P10.
3.3.2.2 Automated Scale Selection
After automating the diffusion strength function, the central problem of aniso-
tropic diffusion is not yet being addressed: the selection of scale. In other words,
the number of anisotropic diffusion iterations before it stop diffusing the image. It
can be viewed as a stopping criteria setting of anisotropic diffusion. This scale of
selection is of paramount importance to the diffused image; if the stopping time is
earlier than it should be, then the homogenous areas are not sufficiently smoothed;
contrarily, if the stopping time is later than it should be, then the image pertinent
details such as edges are smoothed out.
Conventionally, this scale is chosen manually by the user using trial and error
method that is subjective, time-consuming and inconsistent and thus it violates the
criteria of P7. Furthermore, it does not fulfil the P6 criterion of being automated,
p10 criterion of being adaptive and P11 criterion of being optimal. Therefore, vari-
ous automation schemes of selecting scale have been proposed: [ 15 ] proposed the
scale selection based on energy function minimization of both computational cost
and performance cost; the main weakness of this method is that the complexity
in the optimization formulation. A cross-validatory statistical approach was pro-
posed by [ 16 ]; the main weakness of this method is that the ideally-scaled image
is required to perform the scheme. The use of Markov random field in scale selec-
tion has been proposed by [ 17 ]; this method suffers the main drawback of failing
to represent tiny details during region segmentations in forming the super-pixel
Markov random field.
All the automated scale selections found in above mentioned scale selection
schemes have to compute a substantial number of extra excessive filtered images
before obtaining enough information to obtain the optimum filtered image.
Therefore, the crucial question towards this type of automated stopping time is
that how many filtered image has to be done before it is sufficient to provide
enough information to obtain the optimum filtered image. The number of filtered
Search WWH ::




Custom Search