Abstract The interpretation of brain images is a crucial task in the practitioners’ diagnosis process. Segmentation is one of key operations to provide a decision support to physicians. There are several methods to perform segmentation. We use Hidden Markov Random Fields (HMRF) for modelling the segmentation problem. This elegant model leads to an optimization problem. Particles Swarm Optimization (PSO) method is used to achieve brain magnetic resonance image segmentation. Setting the parameters of the HMRF-PSO method is a task in itself. We conduct a study for the choice of parameters that give a good segmentation. The segmentation quality is evaluated on ground-truth images, using the Dice coefficient also called Kappa index. The results show a superiority of the HMRF-PSO method, compared to methods such as Classical Markov Random Fields (MRF) and MRF using variants of Ant Colony Optimization (ACO).

References

[1] Ahmed M., Yamany S., Mohamed N., Farag A., and Moriarty T., A Modified Fuzzy C-Means Algorithm for Bias Field Estimation and Segmentation of MRI Data, IEEE Transactions on Medical Imaging, vol. 21, no. 3, pp. 193-199, 2002. Hidden Markov Random Fields and Particle Swarm Combination for ... 467

[2] Ait-Aoudia S., Guerrout E., and Mahiou R., Medical Image Segmentation Using Particle Swarm Optimization, in Proceedings of 18th International Conference on Information Visualisatio, Paris, pp. 287-291, 2014.

[3] Backes A., Gerhardinger L., Neto J., and Bruno O., Medical Image Retrieval and Analysis by Markov Random Fields and Multi-Scale Fractal Dimension, Physics in Medicine and Biology, vol. 60, no. 3, pp. 1125-1139, 2015.

[4] Bhateja V. and Devi S., A Reconstruction Based Measure for Assessment of Mammogram Edge- Maps, in Proceeding of the International Conference on Frontiers of Intelligent Computing: Theory and Applications, India, pp. 741-746, 2013.

[5] Bhateja V., Tiwari H., and Srivastava A., A Non- Local Means Filtering Algorithm for Restoration of Rician Distributed MRI, in Proceedings of the 49th Annual Convention of the Computer Society, India, pp. 1-8, 2015.

[6] Clerc M. and Kennedy J., The Particle Swarm- Explosion, Stability, and Convergence in A Multidimensional Complex Space, IEEE Transactions on Evolutionary Computation, vol. 6, no. 1, pp. 58-73, 2002.

[7] Cocosco C., Kollokian V., Kwan R., Pike G., and Evans A., Brainweb: Online Interface to a 3D MRI Simulated Brain Database, NeuroImage, vol. 5, no. 4, pp. 425, 1997.

[8] Dempster A., Laird N., and Rubin D., Maximum Likelihood from Incomplete Data Via the EM Algorithm, Journal of the Royal Statistical Society. Series B Methodological, vol. 39, no. 1, pp. 1-38, 1977.

[9] Dice L., Measures of the Amount of Ecologic Association between Species, Ecology, vol. 26, no 3, pp. 297-302, 1945.

[10] Eberhart R. and Kennedy J., A New Optimizer Using Particle Swarm Theory, in Proceedings of the 6th IEEE International Symposium on Micro Machine and Human Science, Nagoya, pp. 39-43, 1995.

[11] Eberhart R. and Shi Y., Comparing Inertia Weights and Constriction Factors in Particle Swarm Optimization, in Proceedings of the 2000 Congress on Evolutionary Computation, La Jolla, pp. 84-88, 2000.

[12] Geman S. and Geman D., Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721-741, 1984.

[13] Gordillo N., Montseny E., and Sobrevilla P., State of the Art Survey on MRI Brain Tumor Segmentation, Magnetic Resonance Imaging, vol. 31, no. 8, pp. 1426-1438, 2013.

[14] Grau V., Mewes A., Alcaniz M., Kikinis R., and Warfield S., Improved Watershed Transform for Medical Image Segmentation Using Prior Information, IEEE Transactions on Medical Imaging, vol. 23, no. 4, pp. 447-458, 2004.

[15] Guerrout E., Mahiou R., and Ait-Aoudia S., Hidden Markov Random Fields and Swarm Particles: A Winning Combination in Image Segmentation, in Proceedings of the International Conference on Future Information Engineering, Beijing, pp. 19-24, 2014.

[16] Gupta A., Ganguly A., and Bhateja V., A Noise Robust Edge Detector for Color Images Using Hilbert Transform, in Proceedings of 3rd IEEE International on Advance Computing Conference, Ghaziabad, pp. 1207-1212, 2013.

[17] Ho S., Bullitt L., and Gerig G., Level-Set Evolution with Region Competition: Automatic 3- D Segmentation of Brain Tumors, in Proceedings of 16th International Conference on Pattern Recognition, Quebec, pp. 532-535, 2002.

[18] Kennedy J., Particle Swarm Optimization, Springer, 2010.

[19] Liu J. and Zhang H., Image Segmentation Using A Local GMM in Avariational Framework, Journal of Mathematical Imaging and Vision, vol. 46, no. 2, pp. 161-176, 2013.

[20] Luo X., Kennedy D., and Cohen Z., Neuroimaging Informatics Tools and Resources Clearinghouse Resource Announcement, Neuroinformatics, vol. 7, no. 1, pp. 55-56, 2009.

[21] Makni N., Betrouni N., and Colot O., Introducing Spatial Neighbourhood in Evidential C-Means for Segmentation of Multi-Source Images: Application to Prostate Multi-Parametric MRI, Information Fusion, vol. 19, pp. 61-72, 2014.

[22] McInerney T. and Terzopoulos D., Deformable Models in Medical Image Analysis: A Survey, Medical Image Analysis, vol. 1, no. 2, pp. 91-108, 1996.

[23] Natarajan P., Krishnan N., Kenkre N., Nancy S., and Singh B., Tumor Detection Using Threshold Operation in MRI Brain Images, in Proceedings of IEEE International Conference on Computational Intelligence and Computing Research, Coimbatore, pp. 1-4, 2012.

[24] Raj A., Alankrita A., and Bhateja V., Computer Aided Detection of Brain Tumor in Magnetic Resonance Images, International Journal of Engineering and Technology, vol. 3, no. 5, pp. 523-532, 2011.

[25] Roura E., Oliver A., Cabezas M., Vilanova J., Rovira ., Torrent L., and Llad X., MARGA: Multispectral Adaptive Region Growing Algorithm for Brain Extraction on Axial MRI, Computer Methods and Programs in Biomedicine, vol. 113, no. 2, pp. 655-673, 2014.

[26] Salman N., Image Segmentation Based on Watershed and Edge Detection Techniques, The 468 The International Arab Journal of Information Technology, Vol. 15, No. 3, May 2018 International Arab Journal of Information Technology, vol. 3, no. 2, pp. 104-110, 2006.

[27] Shanthi K. and Kumar M., Skull Stripping and Automatic Segmentation of Brain MRI Using Seed Growth and Threshold Techniques, in Proceedings of International Conference on Intelligent and Advanced Systems, Kuala Lumpur, pp. 422-426, 2007.

[28] Shi Y. and Eberhart R., Empirical Study of Particle Swarm Optimization, in Proceedings of the Congress on Evolutionary Computation, Washington, pp. 1945-1950,1999.

[29] Srivastava A., Raj A., and Bhateja V., Combination of Wavelet Transform and Morphological Filtering for Enhancement of Magnetic Resonance Images, Digital Information Processing and Communications, Ostrava, pp. 460- 474, 2011.

[30] Wyatt P. and Noble J., MAP MRF Joint Segmentation and Registration of Medical Images, Medical Image Analysis, vol. 7, no. 4, pp. 539-552, 2003.

[31] Xiao Y., Fonov V., Beriault S., Gerard I., Sadikot A., Pike G., and Collins D., Patch-Based Label Fusion Segmentation of Brainstem Structures with Dual-Contrast MRI for Parkinson s Disease, International Journal of Computer Assisted Radiology and Surgery, vol. 10, no. 7, pp. 1029- 1041, 2015.

[32] Yousefi S., Azmi R., and Zahedi M., Brain Tissue Segmentation in MR Images Based on a Hybrid of MRF and Social Algorithms, Medical Image Analysis, vol. 16, no. 4, pp. 840-848, 2012.

[33] 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.

[34] Zhang T., Xia Y., and Feng D., Hidden Markov Random Field Model Based Brain MR Image Segmentation Using Clonal Selection Algorithm and Markov Chain Monte Carlo Method, Biomedical Signal Processing and Control, vol. 12, no. 1, pp. 10-18, 2014. Samy Ait-Aoudia received a DEA "Dipl me d'Etudes Approfondies" in image processing from Saint- Etienne University, France, in 1990. He holds a Ph.D. degree in computer science from the Ecole des Mines, Saint-Etienne, France, in 1994. He is currently Professor at ESI Ecole nationale Sup rieure en Informatique at Algiers. He teaches different modules at both BSc and MSc levels in computer science and software engineering. His areas of research include image processing, CAD/CAM, constraints management in solid modelling and compiling. In image processing the domains of interest are (but not limited to): Image registration, Medical Image Segmentation, Compression Methods, Biometric Authentication. Ramdane Mahiou received a DEA "Dipl me d'Etudes Approfondies" in statistical methods in operational research from Paris VI University, France, in 1984. He holds a Doctorat in statistic from the same University (Pierre and Marie Curie Paris 6, France), in 1988. He is currently Assistant Professor at ESI Ecole nationale Sup rieure en Informatique at Algiers. He teaches different modules of applied mathematics. His areas of research include parmetric and nonparametric statistical inference, operational research, method image processing, In image processing the domains of interest are (but not limited to): Image registration, Medical Image Segmentation. EL-Hachemi Guerrout received a Master degree in computer science from ESI Ecole nationale Sup rieure en Informatique, Algiers, in 2010. He is currently Teacher at ESI Ecole nationale Sup rieure en Informatique at Algiers. He teaches different modules in computer science and software engineering. His areas of research include image processing. In image processing the domains of interest are (but not limited to): Image Segmentation, Image noise removal.