Fast and robust fuzzy \(c\)-means clustering algorithms incorporating local information for image segmentation.

*(English)*Zbl 1118.68133Summary: Fuzzy \(c\)-means (FCM) algorithms with spatial constraints (FCM_S) have been proven effective for image segmentation. However, they still have the following disadvantages: (1) although the introduction of local spatial information to the corresponding objective functions enhances their insensitiveness to noise to some extent, they still lack enough robustness to noise and outliers, especially in absence of prior knowledge of the noise; (2) in their objective functions, there exists a crucial parameter \(\alpha\) used to balance between robustness to noise and effectiveness of preserving the details of the image, it is selected generally through experience; and (3) the time of segmenting an image is dependent on the image size, and hence the larger the size of the image, the more the segmentation time. In this paper, by incorporating local spatial and gray information together, a novel fast and robust FCM framework for image segmentation, i.e., fast generalized fuzzy \(c\)-means (FGFCM) clustering algorithms, is proposed. FGFCM can mitigate the disadvantages of FCM_S and at the same time enhances the clustering performance. Furthermore, FGFCM not only includes many existing algorithms, such as fast FCM and enhanced FCM as its special cases, but also can derive other new algorithms such as FGFCM_S1 and FGFCM_S2 proposed in the rest of this paper. The major characteristics of FGFCM are: (1) to use a new factor \(S_{ij}\) as a local (both spatial and gray) similarity measure aiming to guarantee both noise-immunity and detail-preserving for image, and meanwhile remove the empirically-adjusted parameter \(\alpha\); (2) fast clustering or segmenting image, the segmenting time is only dependent on the number of the gray-levels \(q\) rather than the size \(N\) (\(\gg q\)) of the image, and consequently its computational complexity is reduced from O(\(NcI_1\)) to O(\(qcI_2\)), where c is the number of the clusters, \(I_1\) and \(I_2\) (\(< I_1\), generally) are the numbers of iterations, respectively, in the standard FCM and our proposed fast segmentation method. The experiments on the synthetic and real-world images show that FGFCM algorithm is effective and efficient.

##### Keywords:

fuzzy \(c\)-means clustering (FCM); enhanced fuzzy \(c\)-means clustering; image segmentation; robustness; spatial constraints; gray constraints; fast clustering##### Software:

Image Processing Toolbox
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\textit{W. Cai} et al., Pattern Recognition 40, No. 3, 825--838 (2007; Zbl 1118.68133)

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##### References:

[1] | Bezdek, J.C.; Hall, L.O.; Clarke, L.P., Review of MR image segmentation techniques using pattern recognition, Med. phys., 20, 1033-1048, (1993) |

[2] | Pham, D.L.; Xu, C.Y.; Prince, J.L., A survey of current methods in medical image segmentation, Annu. rev. biomed. eng., 2, 315-337, (2000) |

[3] | Wells, W.M.; LGrimson, W.E.; Kikinis, R.; Arrdrige, S.R., Adaptive segmentation of MRI data, IEEE trans. med. imag., 15, 429-442, (1996) |

[4] | Bezdek, J.C., Pattern recognition with fuzzy objective function algorithms, (1981), Plenum New York · Zbl 0503.68069 |

[5] | Udupa, J.K.; Samarasekera, S., Fuzzy connectedness and object definition: theory, algorithm and applications in image segmentation, Graph. models image process., 58, 3, 246-261, (1996) |

[6] | Yamany, S.M.; Farag, A.A.; Hsu, S., A fuzzy hyperspectral classifier for automatic target recognition (ATR) systems, Pattern recognition lett., 20, 1431-1438, (1999) |

[7] | Yang, M.S.; Hu Karen, Y.J.; Lin, C.R.; Lin, C.C., Segmentation techniques for tissue differentiation in MRI of ophthalmology using fuzzy clustering algorithms, Magnetic resonance imaging, 20, 2, 173-179, (2002) |

[8] | Karmakar, G.C.; Dooley, L.S., A generic fuzzy rule based image segmentation algorithm, Pattern recognition lett., 23, 10, 1215-1227, (2002) · Zbl 1016.68102 |

[9] | Pham, D.L.; Prince, J.L., An adaptive fuzzy c-means algorithm for image segmentation in the presence of intensity inhomogeneities, Pattern recognition lett., 20, 57-68, (1999) · Zbl 0920.68148 |

[10] | Tolias, Y.A.; Panas, S.M., On applying spatial constraints in fuzzy image clustering using a fuzzy rule-based system, IEEE signal process. lett., 5, 245-247, (1998) |

[11] | Tolias, Y.A.; Panas, S.M., Image segmentation by a fuzzy clustering algorithm using adaptive spatially constrained membership functions, IEEE trans. systems man cybernet. A, 28, 359-369, (1998) |

[12] | Liew, A.W.C.; Leung, S.H.; Lau, W.H., Fuzzy image clustering incorporating spatial continuity, Inst. elec. eng. vis. image signal process., 147, 185-192, (2000) |

[13] | D.L. Pham, Fuzzy clustering with spatial constraints, in: IEEE Proceedings of the International Conference Image Processing, New York, 2002, pp. II-65-II-68. |

[14] | Ahmed, M.N.; Yamany, S.M.; Mohamed, N.; Farag, A.A.; Moriarty, T., A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data, IEEE trans. med. imaging, 21, 193-199, (2002) |

[15] | Chen, S.C.; Zhang, D.Q., Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure, IEEE trans. systems man cybernet. B, 34, 4, 1907-1916, (2004) |

[16] | L. Szilágyi, Z. Benyó, S.M. Szilágyii, H.S. Adam, MR brain image segmentation using an enhanced fuzzy c-means algorithm, in: 25th Annual International Conference of IEEE EMBS, 2003, pp. 17-21. |

[17] | M.N. Ahmed, S.M. Yamany, N.A. Mohamed, A.A. Farag, T. Moriarty, Bias field estimation and adaptive segmentation of MRI data using modified fuzzy c-means algorithm, in: Proceedings of the IEEE International Conference on ComputerVision and Pattern Recognition, vol. 1, 1999, pp. 250-255. |

[18] | Leski, J., Toward a robust fuzzy clustering, Fuzzy sets systems, 137, 2, 215-233, (2003) · Zbl 1043.62058 |

[19] | Hathaway, R.J.; Bezdek, J.C., Generalized fuzzy c-means clustering strategies using L norm distance, IEEE trans. fuzzy systems, 8, 572-576, (2000) |

[20] | Jajuga, K., L norm based fuzzy clustering, Fuzzy sets systems, 39, 1, 43-50, (1991) · Zbl 0714.62052 |

[21] | Wu, K.L.; Yang, M.S., Alternative c-means clustering algorithms, Pattern recognition, 35, 2267-2278, (2002) · Zbl 1006.68876 |

[22] | K.R. Tan, S.C. Chen, Robust image denoising using kernel-induced measures, Proceedings of the 17th International Conference on Pattern Recognition, Cambridge, UK, 2004. |

[23] | Huber, P.J., Robust statistics, (1981), Wiley New York · Zbl 0536.62025 |

[24] | X. He, P. Niyogi, Locality preserving projections, Advances in Neural Information Processing Systems, vol. 16, MIT Press, Cambridge, 2003. |

[25] | Zhang, D.Q.; Chen, S.C., A novel kernelised fuzzy c-means algorithm with application in medical image segmentation, Artif. intell. med., 32, 1, 37-50, (2004) |

[26] | Yang, M.S.; Wu, K.L., A similarity-based robust clustering method, IEEE trans. pattern anal. Mach. intell., 26, 4, 434-447, (2004) |

[27] | E.E. Kuruoglu. C. Molina, S.J. Gosdill, W.J. Fitzgerald, A new analytic representation of the \(\alpha\)-stable density function, in: Proceedings of the American Statistical Society, 1997. |

[28] | Hamza, A.B.; Krim, H., Image denoising: a nonlinear robust statistical approach, IEEE trans. signal process., 49, 12, 3045-3053, (2001) |

[29] | Mathworks, Natick, MA, Image Processing Toolbox, [Online] Available:\(\langle\)http://www.mathworks.com⟩. |

[30] | C.T. Lin, C.S.G. Lee, Real-time supervised structure/parameter learning for fuzzy neural network, Proceedings of the 1992 IEEE International Conference on Fuzzy Systems, San Diego, CA, pp. 1283-1290. |

[31] | Masulli, F.; Schenone, A., A fuzzy clustering based segmentation system as support to diagnosis in medical imaging, Artif. intell. med., 16, 2, 129-147, (1999) |

[32] | R.K.S. Kwan, A.C. Evans, G.B. Pike, An extensible MRI simulator for post-processing evaluation, Visualization in Biomedical Computing, Lecture Notes in Computer Science, vol. 1131, 1996, pp. 135-140. |

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