Digital Signal Processing Reference
In-Depth Information
Fig. 2.20
The proposed eigen-based FCM algorithms
the eigen-analysis procedures to obtain the eigenvectors. Then, we perform the
eigen-subspace transformation of image color planes with (
2.48
). Finally, the it-
erative segmentation process with updated membership functions will be applied
on the eigen-subspaces. Although the eigenvectors are generated by the selected
color samples, we still need to adjust the eigen-subspaces to achieve more satis-
factory segmentation results. We are iterative in adjusting the eigen-subspaces with
new eigenvectors obtained from new covariance matrix. The detail algorithms of
SEFCM and CEFCM will be addressed in Sects.
2.4.2.1
and
2.4.2.2
.
2.4.2.1
Separate Eigen-Based FCM (SEFCM) Method
In this section, we have proposed the SEFCM algorithm to separately consider the
signal and noise planes. During simulation, we iteratively construct new covariance
matrices that are similar to (
2.47
) by using the eigen-subspace data
z
q
instead of
x
q
in color image. The expression of the covariance matrix can be stated as follows:
N
q
=
1
u
jq
z
q
z
q
.
1
N
C
z
j
=
(2.49)
The color objects will be extracted after the objective function reaches a mini-
mum. With the help of the eigenvalues, we can obtain the represented segmented
color objects with respective to the signal and noise subspaces. Following, with a
simple logical “AND” operation on both results, we can obtain the segmentation of
