Biomedical Engineering Reference
In-Depth Information
Figure 8.
A blurring example with different filters: (a) original benign tumorw; (b) using
a low-pass filter; (c) median filter; (d) anisotropic diffusion filter.
information as object boundaries and detailed structures. Second, the noise should
be reduced in the homogeneous regions efficiently. In addition, morphological
definition by sharpening discontinuities (see Gerig et al. [37]) should be enhanced.
Speckle noise in an ultrasound image must be reduced to improve image qual-
ity. Although conventional low-pass filtering and linear diffusion on an ultrasound
image can be used to reduce speckle, the edge information may be blurred, which
imposes difficulty on segmentation of a tumor. Anisotropic diffusion filtering
(see Perona and Malik [38]) can avoid the major drawbacks of the above filters
and preserve important information on the object boundary, as depicted shown in
Figure 8. It also satisfies the above-mentioned fundamental requirements. Con-
sider the following anisotropic diffusion equation:
I
t
= div (
c
(
x, y, t
)
∇
I
)
,
(12)
where div is the divergence operator,
c
(
x, y, t
) is the diffusion coefficient, and
t
is
the time parameter. The anisotropic diffusion equation uses a diffusion coefficient
