8. Conclusions

The hard C-means algorithm has been fuzzified by incorporating into the objective function spatial local information through two KL membership divergences. The first KL membership divergence measures the information proximity between the membership of each pixel and its local membership average in the pixel neighborhood. The second one measures the information proximity between the complement membership and its local membership average in the pixel neighborhood. For regularization, the local data information has been incorporated by an additional new weighted hard C-means function in which the noisy-image is replaced by a noise-reduced one. Such incorporation of both local data and local membership information facilitates biasing the algorithm to classify each pixel in correlation with its immediate neighboring pixels. Results of segmentation of synthetic, simulated medical and real-world images have shown that the proposed local membership KL divergence-based FCM (LMKLFCM) and the local data and membership KL divergence-based entropy FCM (LDMKLFCM) algorithms outperform several widely used FCM related algorithms. Moreover, the average runtimes of all algorithms have been measured via simulation. In all runs, all algorithms start from the same randomly generated initial conditions, as mentioned in the simulation section, and stopped at the same fixed point. The LDMKLFCM, LMKLFCM, standard FCM, MEFCM, and SFCM algorithms have provided average runtime of 1.5, 1.75, 1, 0.9 and 1 sec respectively. The simulation results have been done using Matlab R2013b under windows on a processor of Intel (R) core (TM) i3, CPU M370 2.4 GHZ, 4 GB RAM.
