Biomedical Engineering Reference
In-Depth Information
9.4.3.2 Cluster Prototype Updating
Using the standard Eucledian distance and taking the derivative of
F
m
w.r.t.
v
i
and setting the result to zero, we have
N
N
u
ik
N
R
u
ik
(
x
k
−
v
i
)
+
(
x
r
−
v
i
)
=
0
.
(9.33)
k
=
1
k
=
1
y
r
∈
N
k
v
i
=
v
i
Solving for
v
i
, we have
k
=
1
u
ik
(
x
k
)
+
N
R
x
r
∈
N
k
(
x
r
)
(1
+
α
)
k
=
1
u
ik
v
i
=
.
(9.34)
9.4.4 Application: Adaptive MRI Segmentation
In this section, we describe the application of the MFCM segmentation on MRI
images having intensity inhomogeneity. Spatial intensity inhomogeneity induced
by the radio frequency (RF) coil in magnetic resonance imaging (MRI) is a major
problem in the computer analysis of MRI data [24-27]. Such inhomogeneities
have rendered conventional intensity-based classification of MR images very
difficult, even with advanced techniques such as nonparametric, multichannel
methods [28-30]. This is due to the fact that the intensity inhomogeneities ap-
pearing in MR images produce spatial changes in tissue statistics, i.e. mean and
variance. In addition, the degradation on the images obstructs the physician's
diagnoses because the physician has to ignore the inhomogeneity artifact in the
corrupted images [31].
The removal of the spatial intensity inhomogeneity from MR images is diffi-
cult because the inhomogeneities could change with different MRI acquisition
parameters from patient to patient and from slice to slice. Therefore, the correc-
tion of intensity inhomogeneities is usually required for each new image. In the
last decade, a number of algorithms have been proposed for the intensity inho-
mogeneity correction. Meyer
et al.
[32] presented an edge-based segmentation
scheme to find uniform regions in the image followed by a polynomial surface
fit to those regions. The result of their correction is, however, very dependent
on the quality of the segmentation step.
Several authors have reported methods based on the use of phantoms for
intensity calibration. Wicks
et al.
[26] proposed methods based on the signal
