Acknowledgements

mentioned in the synthetic image simulation. Figure 4(c–g) show the segmented images provided by the five algorithms in a certain run while Table 2 summarizes the averages and standard deviations (μ � σ) of the performance measures. It is obvious that the proposed LMKLFCM and LDMKLFCM algorithms provide the segmented images with lesser noise or

A popular Lena image shown in Figure 5(a) has been considered as a noise-free image example. The noisy Lena image shown in Figure 5(b) has been generated by adding WGN noise with zero-mean and 0.01 variance. The parameters of the five algorithms have been adjusted to the values similar to the ones used in the previous simulations except C ¼ 2; β ¼ 1000 for the MEFCM algorithm; γ ¼ 2000 for the LMREFCM and γ ¼ 2000 and α ¼ 0:5 for the LDMREFCM algorithms. We have also executed 25 Mont Carlo Runs of each algorithm as explained above. Figure 5(c–g) shows the resulting segmented images obtained by the five algorithms. Visually investigation of the segmented images shows that the LMKLFCM and LDMKLFCM algorithms provide the images with lesser number of misclassified pixels. Table 2 shows the average and standard deviation (μ � σ) of the performance measures of the five algorithms. It is also clear that the two algorithms provide the maximum VPC and the

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

lesser number of misclassified pixels, the maximum VPC and the minimum VPE.

7.4. Lena image

50 Recent Applications in Data Clustering

minimum VPE.

8. Conclusions

(R) core (TM) i3, CPU M370 2.4 GHZ, 4 GB RAM.

The author would like to thank for funding the open access publication of this Chapter. Also, the author would like to thank Prof. H. Selim, Dr. A. AbdelFattah and Eng. G. Gendy for their contribution to this work.
