Fuzzy C-Means Clustering Algorithm for Image Segmentation Insensitive to Cluster Size

Zhao Zhanmin; Zhu Zhanlong; Liu Yongjun; Liu Ming; Zheng Yibo

doi:10.3788/LOP57.021001

Journals >Laser & Optoelectronics Progress >Volume 57 >Issue 2 >Page 21001 > Article

Laser & Optoelectronics Progress
Vol. 57, Issue 2, 21001 (2020)

Fuzzy C-Means Clustering Algorithm for Image Segmentation Insensitive to Cluster Size

Zhao Zhanmin^1、2, Zhu Zhanlong^1、2、*, Liu Yongjun¹, Liu Ming^1、2, and Zheng Yibo²

Author Affiliations

¹School of Information Engineering, Heibei GEO University, Shijiazhuang, Hebei 0 50031, China

²Hebei Key Laboratory of Optoelectronic Information and Geo-Detection Technology, Heibei GEO University, Shijiazhuang, Hebei 0 50031, China

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DOI: 10.3788/LOP57.021001 Cite this Article Set citation alerts

Zhao Zhanmin, Zhu Zhanlong, Liu Yongjun, Liu Ming, Zheng Yibo. Fuzzy C-Means Clustering Algorithm for Image Segmentation Insensitive to Cluster Size[J]. Laser & Optoelectronics Progress, 2020, 57(2): 21001 Copy Citation Text

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Images, corresponding standard segmentation images, and gray-level histograms. (a)--(f) #NDT1--#NDT 6; (g)--(l) standard segmentation images #NDT1--#NDT 6; (m)--(r) gray-level histograms #NDT1--#NDT 6

Fig. 1. Images, corresponding standard segmentation images, and gray-level histograms. (a)--(f) #NDT1--#NDT 6; (g)--(l) standard segmentation images #NDT1--#NDT 6; (m)--(r) gray-level histograms #NDT1--#NDT 6

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Segmentation results of different algorithms on #NDT1 image. (a) Image with Gaussian noise (0, 0.02); (b) FCM_S1 algorithm; (c) FCM_S2 algorithm; (d) EnFCM algorithm; (e) FGFCM algorithm; (f) algorithm in Ref. [20]; (g) algorithm in Ref. [21]; (h) IFCM_S1 algorithm; (i) IFCM_S2 algorithm

Fig. 2. Segmentation results of different algorithms on #NDT1 image. (a) Image with Gaussian noise (0, 0.02); (b) FCM_S1 algorithm; (c) FCM_S2 algorithm; (d) EnFCM algorithm; (e) FGFCM algorithm; (f) algorithm in Ref. [20]; (g) algorithm in Ref. [21]; (h) IFCM_S1 algorithm; (i) IFCM_S2 algorithm

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Fig. 3. Segmentation results of different algorithms on #NDT2 image. (a) Image with Gaussian noise (0, 0.01); (b) FCM_S1 algorithm; (c) FCM_S2 algorithm; (d) EnFCM algorithm; (e) FGFCM algorithm; (f) algorithm in Ref. [20]; (g) algorithm in Ref. [21]; (h) IFCM_S1 algorithm; (i) IFCM_S2 algorithm

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Fig. 4. Segmentation results of different algorithms on #NDT3 image. (a) Image with Gaussian noise (0, 0.01); (b) FCM_S1 algorithm; (c) FCM_S2 algorithm; (d) EnFCM algorithm; (e) FGFCM algorithm; (f) algorithm in Ref. [20]; (g) algorithm in Ref. [21]; (h) IFCM_S1 algorithm; (i) IFCM_S2 algorithm

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Fig. 5. Segmentation results of different algorithms on #NDT4 image. (a) Image with Gaussian noise (0, 0.01); (b) FCM_S1 algorithm; (c) FCM_S2 algorithm; (d) EnFCM algorithm; (e) FGFCM algorithm; (f) algorithm in Ref. [20]; (g) algorithm in Ref. [21]; (h) IFCM_S1 algorithm; (i) IFCM_S2 algorithm

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Fig. 6. Segmentation results of different algorithms on #NDT5 image. (a) Image with Gaussian noise (0, 0.01); (b) FCM_S1 algorithm; (c) FCM_S2 algorithm; (d) EnFCM algorithm; (e) FGFCM algorithm; (f) algorithm in Ref. [20]; (g) algorithm in Ref. [21]; (h) IFCM_S1 algorithm; (i) IFCM_S2 algorithm

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Fig. 7. Segmentation results of different algorithms on #NDT6 image. (a) Image with Gaussian noise (0, 0.01); (b) FCM_S1 algorithm; (c) FCM_S2 algorithm; (d) EnFCM algorithm; (e) FGFCM algorithm; (f) algorithm in Ref. [20]; (g) algorithm in Ref. [21]; (h) IFCM_S1 algorithm; (i) IFCM_S2 algorithm

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Algorithm	Appearance	Parameter setting
Algorithm	Appearance	m	α	λ_s	λ_g	T	ε	Local window
FCM_S1	Ref. [13]	2	4			300	10^-4	3×3
FCM_S2	Ref. [13]	2	4			300	10^-4	3×3
EnFCM	Ref. [14]	2	4			300	10^-4	3×3
FGFCM	Ref. [15]	2		3	3	300	10^-4	3×3
Method in Ref. [20]	Ref. [20]	2				300	10^-4
Method in Ref. [21]	Ref. [21]	2				300	10^-4
IFCM_S1	This paper	2	4			300	10^-4	3×3
IFCM_S2	This paper	2	4			300	10^-4	3×3

Table 1. Parameter settings for different related algorithms

Image	Noiselevel	Index	FCM_S1	FCM_S2	EnFCM	FGFCM	Method inRef. [20]	Method inRef. [21]	IFCM_S1	IFCM_S2
#NDT1	Unadded noise	SA	0.9466	0.9467	0.9473	0.9459	0.9854	0.9877	0.9918	0.9916
	Unadded noise	ARI	0.8931	0.8933	0.8945	0.8918	0.9708	0.9753	0.9836	0.9832
	GaussianNoise(0,0.02)	SA	0.8516	0.8149	0.8721	0.8876	0.8781	0.7768	0.9765	0.9692
	GaussianNoise(0,0.02)	ARI	0.7032	0.6298	0.7443	0.7751	0.7561	0.5537	0.9530	0.9383
	Salt & peppernoise(0.1)	SA	0.8440	0.9137	0.8532	0.9344	0.9510	0.8512	0.9717	0.9859
	Salt & peppernoise(0.1)	ARI	0.6881	0.8275	0.7063	0.8688	0.9020	0.7024	0.9434	0.9718
#NDT2	Unadded noise	SA	0.8338	0.8616	0.8333	0.8556	0.9777	0.9621	0.9225	0.9554
	Unadded noise	ARI	0.6676	0.7233	0.6667	0.7112	0.9554	0.9242	0.8449	0.9109
	GaussianNoise(0,0.01)	SA	0.7571	0.7395	0.7712	0.7730	0.8342	0.7709	0.9104	0.9291
	GaussianNoise(0,0.01)	ARI	0.5143	0.4790	0.5423	0.5459	0.6684	0.5419	0.8209	0.8583
	Salt & peppernoise(0.1)	SA	0.7170	0.8556	0.7257	0.8228	0.9795	0.9875	0.9113	0.9543
	Salt & peppernoise(0.1)	ARI	0.4340	0.7112	0.4514	0.6457	0.9590	0.9750	0.8226	0.9086
#NDT3	Unadded noise	SA	0.5113	0.5826	0.5086	0.6226	0.9916	0.9916	0.9887	0.9916
	Unadded noise	ARI	0.0227	0.1653	0.0173	0.2451	0.9831	0.9831	0.9773	0.9833
	GaussianNoise(0,0.01)	SA	0.5835	0.6131	0.5934	0.6496	0.9609	0.7603	0.9844	0.9856
	GaussianNoise(0,0.01)	ARI	0.1670	0.2261	0.1869	0.2992	0.9217	0.5206	0.9689	0.9713
	Salt & peppernoise(0.1)	SA	0.5996	0.5831	0.6360	0.6185	0.8983	0.8982	0.9837	0.9895
	Salt & peppernoise(0.1)	ARI	0.1991	0.1662	0.2720	0.2371	0.7965	0.7964	0.9674	0.9790
#NDT4	Unadded noise	SA	0.9210	0.9666	0.9234	0.9672	0.9760	0.9798	0.9638	0.9850
	Unadded noise	ARI	0.8419	0.9332	0.8467	0.9344	0.9520	0.9596	0.9275	0.9696
	GaussianNoise(0,0.01)	SA	0.8109	0.8103	0.8321	0.8633	0.8657	0.8337	0.9544	0.9606
	GaussianNoise(0,0.01)	ARI	0.6218	0.6206	0.6643	0.7267	0.7315	0.6675	0.9088	0.9212
	Salt & peppernoise(0.1)	SA	0.8203	0.9208	0.7923	0.9284	0.9540	0.9538	0.9356	0.9770
	Salt & peppernoise(0.1)	ARI	0.6407	0.8415	0.5846	0.8567	0.9080	0.9076	0.8713	0.9540
#NDT5	Unadded noise	SA	0.9009	0.9290	0.9011	0.9296	0.9633	0.9593	0.9313	0.9580
	Unadded noise	ARI	0.8017	0.8580	0.8023	0.8591	0.9266	0.9186	0.8626	0.9160
	GaussianNoise(0,0.01)	SA	0.8620	0.8717	0.8614	0.8977	0.8516	0.8316	0.9291	0.9274
	GaussianNoise(0,0.01)	ARI	0.7240	0.7434	0.7229	0.7954	0.7031	0.6631	0.8583	0.8549
	Salt & peppernoise(0.1)	SA	0.8156	0.8981	0.8117	0.9103	0.9060	0.9047	0.9011	0.9384
	Salt & peppernoise(0.1)	ARI	0.6311	0.7963	0.6234	0.8206	0.8120	0.8094	0.8022	0.8769
Image	Noiselevel	Index	FCM_S1	FCM_S2	EnFCM	FGFCM	Method inRef. [20]	Method inRef. [21]	IFCM_S1	IFCM_S2
#NDT6	Unadded noise	SA	0.9477	0.9427	0.9485	0.9472	0.9692	0.9636	0.9783	0.9739
	Unadded noise	ARI	0.8954	0.8854	0.8971	0.8945	0.9384	0.9273	0.9566	0.9478
	GaussianNoise(0,0.01)	SA	0.9217	0.9181	0.9243	0.9333	0.8605	0.8455	0.9679	0.9662
	GaussianNoise(0,0.01)	ARI	0.8434	0.8362	0.8487	0.8666	0.7211	0.6910	0.9358	0.9323
	Salt & peppernoise(0.1)	SA	0.8894	0.9281	0.8902	0.9371	0.8980	0.8911	0.9475	0.9562
	Salt & peppernoise(0.1)	ARI	0.7787	0.8563	0.7805	0.8743	0.7960	0.7822	0.8949	0.9125

Table 2. Comparison of segmentation indices of different algorithms on #NDT1~#NDT6 images

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