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Transactions on Rough Sets IX pp 114–134Cite as

Maximum Class Separability for Rough-Fuzzy C-Means Based Brain MR Image Segmentation

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Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5390))

Abstract

Image segmentation is an indispensable process in the visualization of human tissues, particularly during clinical analysis of magnetic resonance (MR) images. In this paper, the rough-fuzzy c-means (RFCM) algorithm is presented for segmentation of brain MR images. The RFCM algorithm comprises a judicious integration of the rough sets, fuzzy sets, and c-means algorithm. While the concept of lower and upper approximations of rough sets deals with vagueness and incompleteness in class definition of brain MR images, the membership function of fuzzy sets enables efficient handling of overlapping classes. The crisp lower bound and fuzzy boundary of a class, introduced in the RFCM algorithm, enable efficient segmentation of brain MR images. One of the major issues of the RFCM based brain MR image segmentation is how to select initial prototypes of different classes or categories. The concept of discriminant analysis, based on the maximization of class separability, is used to circumvent the initialization and local minima problems of the RFCM. Some quantitative indices are introduced to extract local features of brain MR images for accurate segmentation. The effectiveness of the RFCM algorithm, along with a comparison with other related algorithms, is demonstrated on a set of brain MR images.

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References

  1. Rosenfeld, A., Kak, A.C.: 10. In: Digital Picture Processing. Academic Press, Inc., London (1982)

    Google Scholar 

  2. Suetens, P.: 6. In: Fundamentals of Medical Imaging. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  3. Lee, C., Hun, S., Ketter, T.A., Unser, M.: Unsupervised Connectivity Based Thresholding Segmentation of Midsaggital Brain MR Images. Computers in Biology and Medicine 28, 309–338 (1998)

    Article  Google Scholar 

  4. Maji, P., Kundu, M.K., Chanda, B.: Second Order Fuzzy Measure and Weighted Co-Occurrence Matrix for Segmentation of Brain MR Images. Fundamenta Informaticae, 1–15 (2008)

    Google Scholar 

  5. Manousakes, I.N., Undrill, P.E., Cameron, G.G.: Split and Merge Segmentation of Magnetic Resonance Medical Images: Performance Evaluation and Extension to Three Dimensions. Computers and Biomedical Research 31, 393–412 (1998)

    Article  Google Scholar 

  6. Singleton, H.R., Pohost, G.M.: Automatic Cardiac MR Image Segmentation Using Edge Detection by Tissue Classification in Pixel Neighborhoods. Magnetic Resonance in Medicine 37, 418–424 (1997)

    Article  Google Scholar 

  7. Pal, N.R., Pal, S.K.: A Review on Image Segmentation Techniques. Pattern Recognition 26, 1277–1294 (1993)

    Article  Google Scholar 

  8. Rajapakse, J.C., Giedd, J.N., Rapoport, J.L.: Statistical Approach to Segmentation of Single Channel Cerebral MR Images. IEEE Transactions on Medical Imaging 16, 176–186 (1997)

    Article  Google Scholar 

  9. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithm. Plenum, New York (1981)

    Book  MATH  Google Scholar 

  10. Leemput, K.V., Maes, F., Vandermeulen, D., Suetens, P.: Automated Model-Based Tissue Classification of MR Images of the Brain. IEEE Transactions on Medical Imaging 18, 897–908 (1999)

    Article  Google Scholar 

  11. Wells III, W.M., Grimson, W.E.L., Kikinis, R., Jolesz, F.A.: Adaptive Segmentation of MRI Data. IEEE Transactions on Medical Imaging 15, 429–442 (1996)

    Article  Google Scholar 

  12. Cagnoni, S., Coppini, G., Rucci, M., Caramella, D., Valli, G.: Neural Network Segmentation of Magnetic Resonance Spin Echo Images of the Brain. Journal of Biomedical Engineering 15, 355–362 (1993)

    Article  Google Scholar 

  13. Hall, L.O., Bensaid, A.M., Clarke, L.P., Velthuizen, R.P., Silbiger, M.S., Bezdek, J.C.: A Comparison of Neural Network and Fuzzy Clustering Techniques in Segmenting Magnetic Resonance Images of the Brain. IEEE Transactions on Neural Network 3, 672–682 (1992)

    Article  Google Scholar 

  14. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  15. Pawlak, Z.: Rough Sets, Theoretical Aspects of Resoning About Data. Kluwer, Dordrecht (1991)

    MATH  Google Scholar 

  16. Dubois, D., Prade, H.: Rough Fuzzy Sets and Fuzzy Rough Sets. International Journal of General Systems 17, 191–209 (1990)

    Article  MATH  Google Scholar 

  17. Maji, P., Pal, S.K.: Rough-Fuzzy C-Medoids Algorithm and Selection of Bio-Basis for Amino Acid Sequence Analysis. IEEE Transactions on Knowledge and Data Engineering 19, 859–872 (2007)

    Article  Google Scholar 

  18. Pal, S.K., Mitra, S., Mitra, P.: Rough-Fuzzy MLP: Modular Evolution, Rule Generation, and Evaluation. IEEE Transactions on Knowledge and Data Engineering 15, 14–25 (2003)

    Article  Google Scholar 

  19. Brandt, M.E., Bohan, T.P., Kramer, L.A., Fletcher, J.M.: Estimation of CSF, White and Gray Matter Volumes in Hydrocephalic Children Using Fuzzy Clustering of MR Images. Computerized Medical Imaging and Graphics 18, 25–34 (1994)

    Article  Google Scholar 

  20. Li, C.L., Goldgof, D.B., Hall, L.O.: Knowledge-Based Classification and Tissue Labeling of MR Images of Human Brain. IEEE Transactions on Medical Imaging 12, 740–750 (1993)

    Article  Google Scholar 

  21. Mushrif, M.M., Ray, A.K.: Color Image Segmentation: Rough-Set Theoretic Approach. Pattern Recognition Letters 29, 483–493 (2008)

    Article  Google Scholar 

  22. Pal, S.K., Mitra, P.: Multispectral Image Segmentation Using Rough Set Initiatized EM Algorithm. IEEE Transactions on Geoscience and Remote Sensing 40, 2495–2501 (2002)

    Article  Google Scholar 

  23. Widz, S., Revett, K., Slezak, D.: A Hybrid Approach to MR Imaging Segmentation Using Unsupervised Clustering and Approximate Reducts. In: Proceedings of the 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, pp. 372–382 (2005)

    Google Scholar 

  24. Widz, S., Revett, K., Slezak, D.: A Rough Set-Based Magnetic Resonance Imaging Partial Volume Detection System. In: Proceedings of the First International Conference on Pattern Recognition and Machine Intelligence, pp. 756–761 (2005)

    Google Scholar 

  25. Widz, S., Slezak, D.: Approximation Degrees in Decision Reduct-Based MRI Segmentation. In: Proceedings of the Frontiers in the Convergence of Bioscience and Information Technologies, pp. 431–436 (2007)

    Google Scholar 

  26. Maji, P., Pal, S.K.: RFCM: A Hybrid Clustering Algorithm Using Rough and Fuzzy Sets. Fundamenta Informaticae 80, 475–496 (2007)

    MathSciNet  MATH  Google Scholar 

  27. Maji, P., Pal, S.K.: Rough Set Based Generalized Fuzzy C-Means Algorithm and Quantitative Indices. IEEE Transactions on System, Man and Cybernetics, Part B, Cybernetics 37, 1529–1540 (2007)

    Article  Google Scholar 

  28. Dunn, J.C.: A Fuzzy Relative of the ISODATA Process and its Use in Detecting Compact, Well-Separated Clusters. Journal of Cybernetics 3, 32–57 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  29. Krishnapuram, R., Keller, J.M.: A Possibilistic Approach to Clustering. IEEE Transactions on Fuzzy Systems 1, 98–110 (1993)

    Article  Google Scholar 

  30. Krishnapuram, R., Keller, J.M.: The Possibilistic C-Means Algorithm: Insights and Recommendations. IEEE Transactions on Fuzzy Systems 4, 385–393 (1996)

    Article  Google Scholar 

  31. Barni, M., Cappellini, V., Mecocci, A.: Comments on A Possibilistic Approach to Clustering. IEEE Transactions on Fuzzy Systems 4, 393–396 (1996)

    Article  Google Scholar 

  32. Pal, N.R., Pal, K., Keller, J.M., Bezdek, J.C.: A Possibilistic Fuzzy C-Means Clustering Algorithm. IEEE Transactions on Fuzzy Systems 13, 517–530 (2005)

    Article  Google Scholar 

  33. Haralick, R.M., Shanmugam, K., Dinstein, I.: Textural Features for Image Classification. IEEE Transactions on Systems, Man and Cybernetics SMC-3, 610–621 (1973)

    Article  Google Scholar 

  34. Weszka, J.S., Rosenfeld, A.: Histogram Modification for Threshold Selection. IEEE Transactions on System, Man, and Cybernetics SMC-9, 62–66 (1979)

    Article  Google Scholar 

  35. Rangayyan, R.M.: Biomedical Image Analysis. CRC Press, Boca Raton (2004)

    Book  Google Scholar 

  36. Otsu, N.: A Threshold Selection Method from Gray Level Histogram. IEEE Transactions on System, Man, and Cybernetics 9, 62–66 (1979)

    Article  Google Scholar 

  37. Banerjee, M., Mitra, S., Pal, S.K.: Rough Fuzzy MLP: Knowledge Encoding and Classification. IEEE Transactions on Neural Networks 9, 1203–1216 (1998)

    Article  Google Scholar 

  38. Lingras, P., West, C.: Interval Set Clustering of Web Users with Rough K-means. Journal of Intelligent Information Systems 23, 5–16 (2004)

    Article  MATH  Google Scholar 

  39. Bezdek, J.C., Pal, N.R.: Some New Indexes for Cluster Validity. IEEE Transactions on System, Man, and Cybernetics, Part B 28, 301–315 (1988)

    Article  Google Scholar 

  40. Pal, S.K., Ghosh, A., Sankar, B.U.: Segmentation of Remotely Sensed Images with Fuzzy Thresholding, and Quantitative Evaluation. International Journal of Remote Sensing 21, 2269–2300 (2000)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Center for Soft Computing Research, Machine Intelligence Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700 108, India

    Pradipta Maji & Sankar K. Pal

Authors
  1. Pradipta Maji
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  2. Sankar K. Pal
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Institute of Computer Science, Warsaw University of Technology, Nowowoiejska 15/19, 00-665, Warsaw, Poland

    Henryk Rybiński

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© 2008 Springer-Verlag Berlin Heidelberg

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Maji, P., Pal, S.K. (2008). Maximum Class Separability for Rough-Fuzzy C-Means Based Brain MR Image Segmentation. In: Peters, J.F., Skowron, A., Rybiński, H. (eds) Transactions on Rough Sets IX. Lecture Notes in Computer Science, vol 5390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89876-4_7

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  • DOI: https://doi.org/10.1007/978-3-540-89876-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89875-7

  • Online ISBN: 978-3-540-89876-4

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