Digital Signal Processing Reference
In-Depth Information
Fig. 2.19
Segmentation
results with parameters of
Bream sequence by AESS
method: (
a
)
α
=
2,
β
=
1,
γ
=
1; (
b
)
α
=
2,
β
=
1,
γ
=
0
2.4
Color Object Segmentation Using Fuzzy C-Means
(FCM) with Eigen-Subspace Projection
In this section, two eigen-based FCM methods by combing both PCT and FCM con-
cepts together to achieve effective color segmentation were proposed. In Sect.
2.4.1
,
conventional FCM algorithms are briefly reviewed. In Sect.
2.4.2
, the separated
eigen-based FCM (SEFCM) algorithm with the FCM clustering mechanism is
separately applied to projections of signal and noise subspaces. Then, a coupled
eigen-based FCM (CEFCM) method by introducing an eigen-based membership
function embedded in the FCM cluster process is introduced. In Sect.
2.4.3
,thesim-
ulation results show to verify the proposed methods for any desired color objects
segmentation.
2.4.1
Fuzzy C-Means (FCM)
The fuzzy C-means (FCM) algorithm [
30
-
32
] is an iterative unsupervised clustering
algorithm that robustly adjusts representative centers of each pattern to best parti-
tion the data into several distinct classes. The clustering process is accomplished by
minimizing an objective function, which is defined by some measure similarity of
the data samples. The objective function can be expressed as follows [
30
,
31
]:
N
q
=
1
c
j
=
1
u
jq
·
dist
2
(
,
)=
(
,
)
,
J
m
U
V
;
X
x
q
v
j
(2.40)
where
N
is the number of the data,
c
is the number of clusters, and scalar
m
is
the arbitrary chosen FCM weighting exponent, which must be greater than one.
In (
2.40
),
X
=
{
x
1
,
x
2
,...,
x
N
}
denotes a set of unlabeled column vectors and
V
represents the unknown prototypes, which are known as the
cluster centers. The vectors
x
q
and
v
j
are both k-dimensional real Euclidean space
ℜ
=
{
v
1
,
v
2
,...,
v
c
}
k
. Hence, the similarity measurement
dist
can be specified as either the
Euclidean distance or the Mahalanobis distance. The fuzzy C-partition matrix
U
is
with size of
c
(
x
q
,
v
j
)
×
N
that its element can be defined as
u
j
,
q
∈
M
fcm
as,
