Biomedical Engineering Reference
In-Depth Information
In image filtration, the initial condition for the level set equation (11.1) is
given by the image gray-level intensity
I
0
=
I
0
and usually zero
Neumann boundary conditions are used. The solution
u
(
t
,
x
) gives a family of
scaled
(filtered, smoothed) versions of
I
0
(
x
). The parameter
t
is understood as
scale
, and the process of nonlinear selective smoothing is called image multiscale
analysis [1]. In [25], the linear semi-implicit co-volume method to solve image
selective smoothing equation [2]
itself, i.e.,
u
0
∇
u
|∇
u
|
u
t
=
g
(
|∇
G
σ
∗
u
|
)
|∇
u
|∇ ·
(11.10)
has been suggested and studied. Equation (11.10) can be used for edge-
preserving smoothing in a similar way as the so-called Perona-Malik equa-
tion [1, 2, 5, 24-28, 37, 38, 41, 45], see Fig. 11.3.
The aim of segmentation is to find boundaries of a distinguished object of an
image. In generic situation these boundaries correspond to edges. However, in
Figure 11.3:
Extraction of two chromosomes in a human cell using geometrical
diffusion (11.10) [24].
