Abstract This paper, presents a new image segmentation method based on Wavelets, Particle Swarm Optimization (PSO) and outlier rejection caused by the membership function of the Kernel Fuzzy Local Information C-Means (KFLICM) algorithm combined with level set is proposed. The segmentation of Magnetic Resonance (MR) images plays an important role in the computer-aided diagnosis and clinical research, but the traditional approach which is the Fuzzy C-Means (FCM) clustering algorithm is sensitive to the outlier and does not integrate the spatial information in its membership function. Thus the algorithm is very sensitive to noise and in-homogeneities in the image, moreover, it depends on cluster centers initialization. A novel approach, named improved IKFLICMOR is presented to improve the outlier rejection and reduce the noise sensitivity of conventional FCM clustering algorithm. To get the first image segmentation, the traditional FCM is applied to low-resolution image after wavelet decomposition. In general, the FCM algorithm chooses the initial cluster centers randomly, but the use of PSO algorithm gives us a good result for these centers. Our algorithm is also completed by adding into the standard FCM algorithm the spatial neighborhood information. These a priori are used in the cost function to be optimized. The resulting fuzzy clustering is used as the initial level set function. The results confirm the effectiveness of the IKFLICMOR associated with level set for MR image segmentation.

References

[1] Bezdek J., Mathematical Models for Systematic and Taxonomy, in Proceedings of 8th International Conference on Numerical Taxonomy, San Franscisco, pp. 143-166, 1975.

[2] Bezdek J., Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, 1981.

[3] Brain Web: Simulated Brain Database, McConnell Brain Imaging Centre, Montreal Neurological Institute McGill, Last Visited, 2014.

[4] Canny J., A Computational Approach to Edge Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-8 no. 6, pp. 679-698, 1986.

[5] Chen S. and Zhang D., Robust Image Segmentation Using FCM with Spatial Constraints Based on New Kernel-Induced Distance Measure, IEEE Transactions on Systems, Man, and Cybernetics, vol. 34, no. 4, pp. 1907-1916, 2004.

[6] Chuang K., Tzeng H., Chen S., Wu J., and Chen T., Fuzzy C-means Clustering with Spatial Information for Image Segmentation, Computerized Medical Imaging and Graphics, vol. 30, no. 1, pp. 9-15, 2006.

[7] Clarke L., Velthuizen R., Camacho M., Heine J., Vaidyanathan M., Hall L., Thatcher R., and Silbiger M., MRI Segmentation: Methods and Applications, Magnetic Resonance Imaging, vol. 13, no. 3, pp. 343-368, 1995.

[8] Dave R., Characterization and Detection of Noise in Clustering, Pattern Recognition Letters, vol. 12, no. 11, pp. 657-664, 1991.

[9] Dunn J., A Fuzzy Relative of the ISODATA Process and its use in Detecting Compact Well- Separated Clusters, Journal of Cybernetics, vol. 3, no. 3, pp. 32-57, 1973.

[10] Elnakib A., Gimel farb G., Suri J., and El-Baz A., Medical Image Segmentation: a Brief Survey: Multi Modality State-of-the-Art Medical Image Segmentation and Registration Methodologies, Springer, pp. 1-39, 2011.

[11] Kalti K. and Mahjoub M., Image Segmentation by Gaussian Mixture Models and Modified FCM Algorithm, The International Arab Journal of Information Technologie, vol. 11, no. 1, pp. 11- 18, 2014.

[12] Kennedy J. and Eberhart R., Particle Swarm Optimization, in Proceedings of the 6th International Symposium on Micro Machine and Human Science, Nagoya, pp. 1-9, 1995.

[13] Krinidis S. and Chatzis V., A Robust Fuzzy Local Information C-means Clustering Algorithm, IEEE Transactions on Image Processing, vol. 19, no. 5, pp. 1328-1337, 2010.

[14] Li B., Chui C., Chang S., and Ong S., Integrating Spatial Fuzzy Clustering with Level Set Methods for Automated Medical Image Segmentation, Computers in Biology and Medicine, vol. 41, no. 1, pp. 1-10, 2011.

[15] Li C., Goldgof D., and Hall L., Knowledge- Based Classification and Tissue Labeling of MR Images of Human Brain, IEEE Transactions on Medical Imaging, vol. 12, no. 4, pp. 740-750, 1993.

[16] Maji P. and Paul S., Rough-Fuzzy Clustering for Grouping Functionally Similar Genes from Microarray Data, IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 2, pp. 286-299, 2013.

[17] Pham D. and Prince J., Adaptive Fuzzy Segmentation of Magnetic Resonance Images, IEEE Transactions on Medical Imaging, vol. 18, no. 9, pp. 737-752, 1999.

[18] Pham D., Xu C., and Prince J., Current Methods in Medical Image Segmentation, Annual Review of Biomedical Engineering, vol. 2, no. 1, pp. 315- 337, 2000.

[19] Pham D., Spatial Models for Fuzzy Clustering, Computer Vision and Image Understanding, vol. 84, no. 2, pp. 285-297, 2001.

[20] Pohle R. and Toennies K., Segmentation of Medical Images Using Adaptive Region Growing, in Proceedings of SPIE-The International Society for Optical Engineering, San Diego, 2001.

[21] Prasad M., Divakar T., Rao B., and Raju N., Unsupervised Image Thresholding using Fuzzy 692 The International Arab Journal of Information Technology, Vol. 15, No. 4, July 2018 Measures, International Journal of Computer Applications, vol. 27, no. 2, pp. 32-41, 2011.

[22] Shi Z., Liu Y., and Li Q., Medical Image Segmentation Based on FCM and Wavelets, in Proceedings of Intelligence Science and Big Data Engineering, Beijing, pp. 279-286, 2013.

[23] Siddiqui F., Isa N., and Yahya A., Outlier Rejection Fuzzy C-means Algorithm for Image Segmentation, Turkish Journal of Electrical Engineering and Computer Sciences, vol. 21, no. 6, pp. 1801-1819, 2013.

[24] Suzuki H. and Toriwaki J., Automatic Segmentation of Head MRI Images by Knowledge Guided Thresholding, Computerized Medical Imaging and Graphics, vol. 15, no. 4, pp. 233-240, 1991.

[25] Trelea I., The Particle Swarm Optimization Algorithm: Convergence Analysis and Parameter Selection, Information Processing Letters, vol. 85, no. 6, pp. 317-325, 2003.

[26] Xie X. and Beni G., A Validity Measure for Fuzzy Clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 8, pp. 841-847, 1991.

[27] Zanaty E. and Aljahdalia S., Improved Fuzzy Algorithms for Automatic Magnetic Resonance Image Segmentation, The International Arab Journal of Information Technologie, vol. 7, no. 3, pp. 271-279, 2010.

[28] Zhang D. and Chen S., A Novel Kernelized Fuzzy C-means Algorithm with Application in Medical Image Segmentation, Artificial Intelligence in Medicine, vol. 32, no. 1, pp. 37- 50, 2004. Abdenour Mekhmoukh Received his engineering degree in electronics in 2004 from University of Bejaia, Algeria, Magister in Automatics and signal processing in 2008 and Doctorate in 2016. He is currently a senior lecturer in the Electrical Engineering department in the University of Bejaia, Algeria. His research interests include signal, image processing. Karim Mokrani Received his engineering degree in electronics in 1982 from University of Algers, Algeria, an MSEE and Ph.D. degrees in electrical engineering in 1985 and 1988 respectively from Southern Methodist University, Dallas, USA. He is currently professor in the Electrical Engineering department in the University of Bejaia, Algeria. His research interests include signal, image processing and digital video processing.