  Although spatial information of images usually enhance the robustness of the
Fuzzy C-Means (FCM) algorithm, it greatly increases the computational costs for
image segmentation. To achieve a sound trade-off between the segmentation
performance and the speed of clustering, we come up with a Kullback-Leibler
(KL) divergence-based FCM algorithm by incorporating a tight wavelet frame
transform and a morphological reconstruction operation. To enhance FCM's
robustness, an observed image is first filtered by using the morphological
reconstruction. A tight wavelet frame system is employed to decompose the
observed and filtered images so as to form their feature sets. Considering
these feature sets as data of clustering, an modified FCM algorithm is
proposed, which introduces a KL divergence term in the partition matrix into
its objective function. The KL divergence term aims to make membership degrees
of each image pixel closer to those of its neighbors, which brings that the
membership partition becomes more suitable and the parameter setting of FCM
becomes simplified. On the basis of the obtained partition matrix and
prototypes, the segmented feature set is reconstructed by minimizing the
inverse process of the modified objective function. To modify abnormal features
produced in the reconstruction process, each reconstructed feature is
reassigned to the closest prototype. As a result, the segmentation accuracy of
KL divergence-based FCM is further improved. What's more, the segmented image
is reconstructed by using a tight wavelet frame reconstruction operation.
Finally, supporting experiments coping with synthetic, medical and color images
are reported. Experimental results exhibit that the proposed algorithm works
well and comes with better segmentation performance than other comparative
algorithms. Moreover, the proposed algorithm requires less time than most of
the FCM-related algorithms.
