In this paper, C-means algorithm is fuzzified and
regularized by incorporating both local data and membership
information. The local membership information is incorporated
via two membership relative entropy (MRE) functions.
These MRE functions measure the information proximity
of the membership function of each pixel to the membership
average in the immediate spatial neighborhood. Then
minimizing these MRE functions pushes the membership
function of a pixel toward its average in the pixel vicinity.
The resulting algorithm is called the Local Membership
Relative Entropy based FCM (LMREFCM). The local data
information is incorporated into the LMREFCM algorithm
by adding to the standard distance a weighted distance computed
from the locally smoothed data. The final resulting
algorithm, called the Local Data and Membership Relative
Entropy based FCM (LDMREFCM), assigns a pixel to
the cluster more likely existing in its immediate neighborhoods.
This provides noise immunity and results in clustered
images with piecewise homogeneous regions. Simulation
results of segmentation of synthetic and real-world noisy
images are presented to compare the performance of the
proposed LMREFCM and LDMREFCM algorithms with
several FCM-related algorithms