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Frontiers of Computer Science

ISSN 2095-2228

ISSN 2095-2236(Online)

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Front Comput Sci Chin    2011, Vol. 5 Issue (1) : 45-56    https://doi.org/10.1007/s11704-010-0393-8
RESEARCH ARTICLE
Fuzzy c-means clustering with non local spatial information for noisy image segmentation
Feng ZHAO(), Licheng JIAO, Hanqiang LIU
Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Institute of Intelligent Information Processing, Xidian University, Xi’an 710071, China
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Abstract

As an effective image segmentation method, the standard fuzzy c-means (FCM) clustering algorithm is very sensitive to noise in images. Several modified FCM algorithms, using local spatial information, can overcome this problem to some degree. However, when the noise level in the image is high, these algorithms still cannot obtain satisfactory segmentation performance. In this paper, we introduce a non local spatial constraint term into the objective function of FCM and propose a fuzzy c-means clustering algorithm with non local spatial information (FCM_NLS). FCM_NLS can deal more effectively with the image noise and preserve geometrical edges in the image. Performance evaluation experiments on synthetic and real images, especially magnetic resonance (MR) images, show that FCM_NLS is more robust than both the standard FCM and the modified FCM algorithms using local spatial information for noisy image segmentation.
Keywords image segmentation      fuzzy clustering algorithm      non local spatial information      magnetic resonance (MR) image     
Corresponding Author(s): ZHAO Feng,Email:add_zf1119@hotmail.com   
Issue Date: 05 March 2011
 Cite this article:   
Feng ZHAO,Licheng JIAO,Hanqiang LIU. Fuzzy c-means clustering with non local spatial information for noisy image segmentation[J]. Front Comput Sci Chin, 2011, 5(1): 45-56.
 URL:  
https://academic.hep.com.cn/fcs/EN/10.1007/s11704-010-0393-8
https://academic.hep.com.cn/fcs/EN/Y2011/V5/I1/45
Fig.1  CA of FCM_NLS versus the filtering degree parameter, , and the . (a) original image; (b) CA surface
Fig.1  CA of FCM_NLS versus the filtering degree parameter, , and the . (a) original image; (b) CA surface
Fig.2  CA of FCM_NLS versus the filtering degree parameter for different noisy images. (a) Gaussian noise (0, 0.006); (b) Gaussian noise (0, 0.016); (c) Gaussian noise (0, 0.026)
Fig.2  CA of FCM_NLS versus the filtering degree parameter for different noisy images. (a) Gaussian noise (0, 0.006); (b) Gaussian noise (0, 0.016); (c) Gaussian noise (0, 0.026)
Fig.3  CA of FCM_NLS for different noisy images under different search window size × and square neighborhood size ×. (a) Gaussian noise (0, 0.006); (b) Gaussian noise (0, 0.016); (c) Gaussian noise (0, 0.026)
Fig.3  CA of FCM_NLS for different noisy images under different search window size × and square neighborhood size ×. (a) Gaussian noise (0, 0.006); (b) Gaussian noise (0, 0.016); (c) Gaussian noise (0, 0.026)
Fig.4  Segmentation results on the synthetic image corrupted by Gaussian noise (0, 0.022). (a) noisy image; (b) FCM (CA= 0.8062); (c) FCM-NLS (CA= 0.9984); (d) FCM_S1 under 3×3 neighbor window (CA= 0.9905); (e) FCM_S1 under 5×5 neighbor window (CA= 0.9867); (f) FCM_S2 under 3×3 neighbor window (CA= 0.9918); (g) FCM_S2 under 5×5 neighbor window (CA= 0.9963); (h) EnFCM under 3×3 neighbor window (CA= 0.9904); (i) EnFCM under 5×5 neighbor window (CA= 0.9905); (j) FGFCM under 3×3 neighbor window (CA= 0.9909); (k) FGFCM under 5×5neighbor window (CA= 0.9910)
Fig.4  Segmentation results on the synthetic image corrupted by Gaussian noise (0, 0.022). (a) noisy image; (b) FCM (CA= 0.8062); (c) FCM-NLS (CA= 0.9984); (d) FCM_S1 under 3×3 neighbor window (CA= 0.9905); (e) FCM_S1 under 5×5 neighbor window (CA= 0.9867); (f) FCM_S2 under 3×3 neighbor window (CA= 0.9918); (g) FCM_S2 under 5×5 neighbor window (CA= 0.9963); (h) EnFCM under 3×3 neighbor window (CA= 0.9904); (i) EnFCM under 5×5 neighbor window (CA= 0.9905); (j) FGFCM under 3×3 neighbor window (CA= 0.9909); (k) FGFCM under 5×5neighbor window (CA= 0.9910)
Fig.5  Segmentation results on the house image corrupted by Gaussian noise. (a) original image; (b) noisy image; (c) FCM; (d) FCM_NLS; (e) FCM_S1 under 3×3 neighbor window; (f) FCM_S1 under 5×5 neighbor window; (g) FCM_S2 under 3×3 neighbor window; (h) FCM_S2 under 5×5 neighbor window; (i) EnFCM under 3×3 neighbor window; (j) EnFCM under 5×5 neighbor window; (k) FGFCM under 3×3 neighbor window; (l) FGFCM under 5×5 neighbor window
Fig.5  Segmentation results on the house image corrupted by Gaussian noise. (a) original image; (b) noisy image; (c) FCM; (d) FCM_NLS; (e) FCM_S1 under 3×3 neighbor window; (f) FCM_S1 under 5×5 neighbor window; (g) FCM_S2 under 3×3 neighbor window; (h) FCM_S2 under 5×5 neighbor window; (i) EnFCM under 3×3 neighbor window; (j) EnFCM under 5×5 neighbor window; (k) FGFCM under 3×3 neighbor window; (l) FGFCM under 5×5 neighbor window
FCMFCM_S1FCM_S2EnFCMFGFCMFCM_NLS
3×35×53×35×53×35×53×35×5
Vpc0.76550.81650.82770.80710.82920.74240.74850.73980.74840.8592
Vpe0.44250.37540.35560.39060.35380.49920.48730.50370.48750.2974
Tab.1  Comparison of these six methods on the house image corrupted by Gaussian noise
Fig.6  Segmentation results on the MR1 image corrupted by Rician noise. (a) original image; (b) noisy image; (c) FCM; (d) FCM_NLS; (e) FCM_S1 under 3×3 neighbor window; (f) FCM_S1 under 5×5 neighbor window; (g) FCM_S2 under 3×3 neighbor window; (h) FCM_S2 under 5×5 neighbor window; (i) EnFCM under 3×3 neighbor window; (j) EnFCM under 5×5 neighbor window; (k) FGFCM under 3×3 neighbor window; (l) FGFCM under 5×5 neighbor window
Fig.6  Segmentation results on the MR1 image corrupted by Rician noise. (a) original image; (b) noisy image; (c) FCM; (d) FCM_NLS; (e) FCM_S1 under 3×3 neighbor window; (f) FCM_S1 under 5×5 neighbor window; (g) FCM_S2 under 3×3 neighbor window; (h) FCM_S2 under 5×5 neighbor window; (i) EnFCM under 3×3 neighbor window; (j) EnFCM under 5×5 neighbor window; (k) FGFCM under 3×3 neighbor window; (l) FGFCM under 5×5 neighbor window
Fig.7  Segmentation results on the MR2 image corrupted by Rician noise. (a) original image; (b) noisy image; (c) FCM; (d) FCM_NLS; (e) FCM_S1 under 3×3 neighbor window; (f) FCM_S1 under 5×5 neighbor window; (g) FCM_S2 under 3×3 neighbor window; (h) FCM_S2 under 5×5 neighbor window; (i) EnFCM under 3×3 neighbor window; (j) EnFCM under 5×5 neighbor window; (k) FGFCM under 3×3 neighbor window; (l) FGFCM under 5×5 neighbor window
Fig.7  Segmentation results on the MR2 image corrupted by Rician noise. (a) original image; (b) noisy image; (c) FCM; (d) FCM_NLS; (e) FCM_S1 under 3×3 neighbor window; (f) FCM_S1 under 5×5 neighbor window; (g) FCM_S2 under 3×3 neighbor window; (h) FCM_S2 under 5×5 neighbor window; (i) EnFCM under 3×3 neighbor window; (j) EnFCM under 5×5 neighbor window; (k) FGFCM under 3×3 neighbor window; (l) FGFCM under 5×5 neighbor window
Fig.8  Segmentation results on the MR3 image corrupted by Rician noise. (a) original image; (b) noisy image; (c) FCM; (d) FCM_NLS; (e) FCM_S1 under 3×3 neighbor window; (f) FCM_S1 under 5×5 neighbor window; (g) FCM_S2 under 3×3 neighbor window; (h) FCM_S2 under 5×5 neighbor window; (i) EnFCM under 3×3 neighbor window; (j) EnFCM under 5×5 neighbor window; (k) FGFCM under 3×3 neighbor window; (l) FGFCM under 5×5 neighbor window
Fig.8  Segmentation results on the MR3 image corrupted by Rician noise. (a) original image; (b) noisy image; (c) FCM; (d) FCM_NLS; (e) FCM_S1 under 3×3 neighbor window; (f) FCM_S1 under 5×5 neighbor window; (g) FCM_S2 under 3×3 neighbor window; (h) FCM_S2 under 5×5 neighbor window; (i) EnFCM under 3×3 neighbor window; (j) EnFCM under 5×5 neighbor window; (k) FGFCM under 3×3 neighbor window; (l) FGFCM under 5×5 neighbor window
FCMFCM_S1FCM_S2EnFCMFGFCMFCM_NLS
3×35×53×35×53×35×53×35×5
MR1Vpc0.83310.85520.84900.85480.85200.75240.76920.75480.76860.8656
Vpe0.31000.27480.28360.27580.27830.44700.41860.44320.41940.2524
MR2Vpc0.79470.82580.81840.82610.82450.70040.69170.69740.69400.8326
Vpe0.39170.34590.35750.34580.34730.57120.58570.57650.58120.3289
MR3Vpc0.82700.83450.81710.83930.82960.76260.75790.76210.76060.8431
Vpe0.34070.32590.35520.31790.33330.45740.46560.45830.45970.3066
Tab.2  Comparison of these six methods on the MR images corrupted by Rician noise
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