Biomedical Engineering Reference
In-Depth Information
Figure 11.1: Image corrupted by a structural noise (left), and result of filtering
by level set equation after two (middle) and ten (right) discrete scale steps.
11.2 Discussion on Related Mathematical
Models
The level set equation (11.1) has great significance in axiomatization of image
processing and computer vision [1]. It fulfills the so-called
morphological prin-
ciple
:If
u
is a solution then, for any nondecreasing function
ϕ
,
ϕ
(
u
) is a solution
as well. It means that level sets of a solution
u
move independently of each
other, or in other words, they diffuse only intrinsically (in tangential direction)
and there is no diffusion across level sets in the normal direction. In that sense it
provides a directional smoothing of the image along its level lines. We illustrate
the smoothing effect of the level set equation in Figs. 11.1 (removing structural
noise) and 11.2 (removing salt and pepper noise) [25].
Figure 11.2:
Initial image corrupted by salt and pepper noise (left), and result
of filtering by level set equation after two (middle) and ten (right) discrete scale
steps.
