对类大小不敏感的图像分割模糊C均值聚类方法

赵战民; 朱占龙; 刘永军; 刘明; 郑一博

doi:doi:10.3788/LOP57.021001

激光与光电子学进展, 2020, 57 (2): 021001, 网络出版: 2020-01-03

对类大小不敏感的图像分割模糊C均值聚类方法下载： 1074次

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

赵战民 ^1,2朱占龙 ^1,2,*刘永军 ¹刘明 ^1,2郑一博 ²

作者单位

¹ 河北地质大学信息工程学院, 河北石家庄 050031

² 河北地质大学河北省光电信息与地球探测技术重点实验室, 河北石家庄 050031

图 & 表

图 1. 图像及相应的标准分割图和灰度直方图。(a)~(f) #NDT1~#NDT6;(g)~(l)标准分割图#NDT1~#NDT6;(m)~(r)灰度直方图#NDT1~#NDT6

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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图 2. #NDT1图像的分割结果。(a)添加高斯噪声(0,0.02)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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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图 3. #NDT2图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法; (e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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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图 4. #NDT3图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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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图 5. #NDT4图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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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图 6. #NDT5图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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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图 7. #NDT6图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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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表 1相关算法的参数设置

Table1. Parameter settings for different related algorithms

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

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表 2对#NDT1~#NDT6图像各算法的分割指标对比

Table2. Comparison of segmentation indices of different algorithms on #NDT1~#NDT6 images

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

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赵战民, 朱占龙, 刘永军, 刘明, 郑一博. 对类大小不敏感的图像分割模糊C均值聚类方法[J]. 激光与光电子学进展, 2020, 57(2): 021001. 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): 021001.

对类大小不敏感的图像分割模糊C均值聚类方法下载： 1074次

图 1. 图像及相应的标准分割图和灰度直方图。(a)~(f) #NDT1~#NDT6;(g)~(l)标准分割图#NDT1~#NDT6;(m)~(r)灰度直方图#NDT1~#NDT6

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

图 2. #NDT1图像的分割结果。(a)添加高斯噪声(0,0.02)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

图 3. #NDT2图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法; (e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

图 4. #NDT3图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

图 5. #NDT4图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

图 6. #NDT5图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

图 7. #NDT6图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

表 1相关算法的参数设置

Table1. Parameter settings for different related algorithms

表 2对#NDT1~#NDT6图像各算法的分割指标对比

Table2. Comparison of segmentation indices of different algorithms on #NDT1~#NDT6 images

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对类大小不敏感的图像分割模糊C均值聚类方法 下载： 1074次

图 1. 图像及相应的标准分割图和灰度直方图。(a)~(f) #NDT1~#NDT6;(g)~(l)标准分割图#NDT1~#NDT6;(m)~(r)灰度直方图#NDT1~#NDT6

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

图 2. #NDT1图像的分割结果。(a)添加高斯噪声(0,0.02)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

图 3. #NDT2图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法; (e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

图 4. #NDT3图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

图 5. #NDT4图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

图 6. #NDT5图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

图 7. #NDT6图像的分割结果。(a)添加高斯噪声(0,0.01)图像;(b) FCM_S1算法;(c) FCM_S2算法;(d) EnFCM算法;(e) FGFCM算法;(f)文献[ 20]算法;(g)文献[ 21]算法;(h) IFCM_S1算法;(i) IFCM_S2算法

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

表 1相关算法的参数设置

Table1. Parameter settings for different related algorithms

表 2对#NDT1~#NDT6图像各算法的分割指标对比

Table2. Comparison of segmentation indices of different algorithms on #NDT1~#NDT6 images

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对类大小不敏感的图像分割模糊C均值聚类方法下载： 1074次