Biomedical Engineering Reference
In-Depth Information
Step 3.
The prototypes of the clusters are obtained in the form of weighted
averages of the patterns using Eq. 9.42.
Step 4.
Estimate the bias term using Eq. 9.46.
Repeat steps 2-4 till termination. The termination criterion is as follows
||
V
ne
w
−
V
old
||
<,
(9.47)
where
||·||
is the Euclidean norm,
V
is a vector of cluster centers, and
is a
small number that can be set by the user.
9.4.4.8 BCFCM Results
In this section, we describe the application of the BCFCM segmentation to syn-
thetic images corrupted with multiplicative gain, as well as digital MR phan-
toms [51] and real brain MR images. The MR phantoms simulated the appear-
ance and image characteristics of the T1 weighted images. There are many
advantages of using digital phantoms rather than real image data for validating
segmentation methods. These advantages include prior knowledge of the true
tissue types and control over image parameters such as mean intensity values,
noise, and intensity inhomogeneities. We used a high-resolution T1 weighted
phantom with in-plane resolution of 0
.
94 mm
2
, Gaussian noise with
σ
=
6
.
0, and
3D linear shading of 7% in each direction. All of the real MR images shown in
this section were obtained using a General Electric Signa 1.5 T clinical MR
imager with the same in-plane resolution as the phantom. In all the exam-
ples, we set the parameter
α
(the neighbors effect) to be 0.7,
p
=
2,
N
R
=
9
(a 3
×
3 window centered around each pixel), and
=
0
.
01. For low SNR im-
ages, we set
α
=
0
.
85. The choice of these parameters seems to give the best
results.
Figure 9.15(a) shows a synthetic test image. This image contains a two-class
pattern corrupted by a sinusoidal gain field of higher spatial frequency. The test
image is intended to represent two tissue classes, while the sinusoid represents
an intensity inhomogeneity. This image was constructed so that it would be dif-
ficult to correct using homomorphic filtering or traditional FCM approaches. As
shown in Fig. 9.15(b), FCM algorithm was unable to separate the two classes,
while the BCFCM and EM algorithms have succeeded in correcting and classi-
fying the data as shown in Fig. 9.15(c). The estimate of the multiplicative gain
