Image Processing Reference
In-Depth Information
7.9 Type II Fuzzy Clustering
Clustering using Type II fuzzy on medical images is discussed in this sec-
tion. There is no work based on medical image clustering using Type II fuzzy
set. Rhee and Hwang [13] suggested a clustering algorithm, but the algo-
rithm was tried on patterns.
Rhee and Hwang proposed type II fuzzy clustering of pattern set. Type
II fuzzy set is the fuzziness in a fuzzy set. In this algorithm, the member-
ship value of each pattern in the image is extended to type II fuzzy mem-
bership by assigning membership grades to Type I fuzzy membership. Any
type of membership function may be used. If the membership value of the
pattern is high, it is considered to have less uncertainty and vice versa. So,
the higher the membership value of the pattern, the more is the contribution
of the pattern to the cluster. On using type 2 membership, the contribution of
the pattern that has a low membership in Type I will have a relatively lower
membership which helps in representing the membership in a better way.
In their work, they used a triangular membership function to obtain Type
I membership. In doing so, cluster centres converge to a desirable location
than cluster centres obtained in Type I membership. The membership values
for type II membership are obtained as
au u
ik
=−
1
ik
ik
2
where a ik and u ik are the type II and Type I fuzzy membership, respectively.
The cluster centres are updated accordingly using conventional FCM taking
into account the new type II fuzzy membership as
n
ax
m
ik
ik
type2
v
=
k
=
1
ik
n
m
a
ik
k
=
1
Then the usual procedure as in FCM follows. When performing cluster-
ing in a fuzzy set, the membership assigns the availability of the pattern
in the clusters, but when applying the fuzzy membership to the pattern set,
imperfect information lies in various parameters in the fuzzy membership
assignment.
Supervised methods have been largely employed in medical image seg-
mentation, but they require conditions, which are difficult to satisfy in clini-
cal fields: (1) they require labelling a set of prototypical samples in order to
apply the process of generalization; (2) if the number of clusters is defined,
labelling of voxels in a training set belonging with certainty in different clus-
ters is not trivial, especially when it contains multimodal data; (3) users have
 
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