快速自适应非局部空间加权与隶属度连接的模糊C-均值噪声图像分割算法

王小鹏; 王庆圣; 焦建军; 梁金诚

doi:10.11999/JEIT191016

快速自适应非局部空间加权与隶属度连接的模糊C-均值噪声图像分割算法

doi: 10.11999/JEIT191016

兰州交通大学电子与信息工程学院兰州 730070

基金项目: 国家自然科学基金(61761027)

详细信息

作者简介:
王小鹏：男，1969年生，博士，教授，研究方向为图像分析，信号与信息处理

王庆圣：男，1995年生，硕士生，研究方向为图像处理与模式识别

焦建军：男，1984年生，博士生，研究方向为图像分析

梁金诚：男，1997年生，硕士生，研究方向为图像处理与目标检测

通讯作者:
王小鹏　wangxp1969@sina.com

中图分类号: TN911.73; TP391.4
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出版历程
- 收稿日期: 2019-12-19
- 修回日期: 2020-11-04
- 网络出版日期: 2020-11-07
- 刊出日期: 2021-01-15

Fuzzy C-Means Clustering with Fast and Adaptive Non-local Spatial Constraint and Membership Linking for Noise Image Segmentation

School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

Funds: The National Natural Science Foundation of China (61761027)

摘要

摘要:
针对传统模糊C-均值聚类(FCM)算法难以对噪声图像进行分割的问题，该文提出一种快速自适应非局部空间加权与隶属度连接的模糊FCM抗噪图像分割算法。首先，利用一种非局部空间信息快速计算方法，将以图像所有像素为循环的原始非局部信息计算方法，改为以搜索窗口尺寸为循环，利用空间位移图像与递归高斯滤波的计算方法，克服非局部空间信息计算复杂的问题；其次，计算原始图像与非局部信息项的差值的平方，将其作为非局部信息项的自适应权重，并将差值的平方作倒数变换，作为原始图像的自适应权重；最后，将每个聚类簇中所有像素隶属度之和的对数平方加入目标函数的分母，形成隶属度连接，减少目标函数迭代次数。含噪人工与自然图像分割实验表明，该算法在分割准确度、平均交并比、归一化互信息、运行时间与迭代次数等性能方面优于其他几种FCM算法。
- 噪声图像分割 /
- 模糊C-均值聚类 /
- 非局部空间信息 /
- 自适应加权 /
- 隶属度连接
Abstract:
Considering the problem of the low anti-noise performance when Fuzzy C-Means clustering (FCM) algorithm is applied to image segmentation, a FCM clustering algorithm with fast and adaptive non-local spatial constraint and membership linking is proposed in this paper. Firstly, in order to increase the computing speed of non-local spatial term, a fast method is proposed by modifying the loop based on all pixels in an image into a loop based on search window and by utilising spatial shift image and recursive Gaussian filter. Next, the squared difference between original image and non-local spatial term is calculated as adaptive weight of non-local information term. The squared difference is reciprocally transformed as adaptive weight of the original image. Finally, the membership linking is established to reduce the iteration steps before convergence by adding the square of the sum of all the membership degrees in every cluster in logarithmic form as the denominator of the objectvie function. Experiments on noisy artificial and natural images prove that this proposed algorithm has superior performance in terms of Segmentation accuracy, mean intersection over union, normalized mutual information, running time and iteration steps.
- Noisy Image Segmentation /
- Fuzzy C-Means clustering (FCM) /
- Non-local spatial information /
- Adaptive constraint /
- Membership linking

HTML全文

图 1 5种算法对含5%混合噪声人工图像的分割结果(K=4)

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图 2 5种算法对含20%混合噪声齿轮图像的分割结果(K=2)

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图 3 5种算法对含10%混合噪声#42049的分割结果(K=2)

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图 4 5种算法对含10%混合噪声#86016的分割效果(K=2)

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图 5 5种算法对含5%混合噪声#118035的分割效果(K=3)

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表 1 5种算法对含不同混合噪声人工图像的分割结果

分割指标	SA(%)				mIoU(%)				NMI(%)				运行时间(s)				迭代次数
噪声大小(%)	5	10	15	20	5	10	15	20	5	10	15	20	5	10	15	20	5	10	15	20
FCM	55.09	43.77	31.21	28.21	52.65	48.48	35.41	30.41	25.34	14.42	9.09	7.13	0.48	0.63	0.67	0.69	18	36	32	35
FLICM	89.54	70.89	60.00	52.08	84.95	64.25	55.16	49.51	73.32	50.10	38.71	30.90	7.52	7.94	7.23	8.02	108	125	106	130
FCM-NLS	96.83	91.48	76.26	59.43	96.35	87.40	68.46	47.80	85.93	76.97	53.63	38.10	185.57	194.82	195.57	195.14	24	33	47	47
SNLS-IFCM	97.66	92.23	77.04	61.02	96.67	88.75	70.12	54.59	86.00	79.18	57.83	40.13	184.12	196.07	196.40	196.83	17	40	51	73
本文算法	98.02	97.30	95.26	90.12	97.70	95.54	92.40	86.71	92.23	89.88	84.35	74.84	1.85	1.92	2.09	2.09	10	10	16	17

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表 2 5种算法对含不同混合噪声图像的分割结果

分割指标	SA(%)				mIoU(%)				NMI(%)				运行时间(s)				迭代次数
噪声大小(%)	5	10	15	20	5	10	15	20	5	10	15	20	5	10	15	20	5	10	15	20
FCM	90.58	81.82	74.57	70.88	82.60	68.88	58.82	54.41	54.99	31.42	17.80	12.32	0.18	0.20	0.15	0.18	15	16	16	18
	71.56	63.16	58.74	55.83	51.16	42.74	38.74	36.26	15.74	7.56	4.50	3.02	0.46	0.44	0.35	0.22	23	21	16	11
	61.87	57.51	54.04	51.51	40.96	36.52	34.03	32.04	8.19	3.27	2.22	1.33	0.37	0.58	0.28	0.34	18	19	14	16
	55.87	49.23	46.77	23.50	36.50	30.73	28.12	12.35	19.45	9.96	6.11	4.11	1.02	0.76	0.52	0.70	35	25	17	23
FLICM	98.83	98.11	96.68	94.41	97.68	96.27	93.52	89.36	90.80	86.44	78.90	69.03	1.60	4.52	3.66	4.29	64	79	88	109
	95.33	93.19	90.76	88.61	86.31	80.92	75.39	70.90	63.81	52.86	42.46	34.63	12.32	11.41	13.69	16.14	158	148	177	212
	92.19	92.88	85.82	84.07	78.59	78.10	65.45	61.08	52.91	46.01	28.02	19.98	13.22	9.58	23.61	22.00	157	100	300	300
	62.15	54.53	44.45	37.20	46.35	39.20	30.85	24.99	49.01	37.81	27.21	20.47	18.85	23.17	18.47	13.09	132	194	151	108
FCM-NLS	98.84	98.16	97.38	95.87	97.68	96.35	94.84	91.98	90.98	86.94	82.90	76.62	189.77	190.08	188.92	197.12	13	16	16	25
	95.30	93.53	83.52	71.62	86.26	82.39	65.37	51.49	63.69	55.42	31.17	17.26	472.53	474.82	468.91	473.51	29	29	36	30
	96.13	84.85	71.70	63.39	88.00	65.12	50.88	42.73	70.85	37.34	21.15	11.77	473.12	470.12	454.68	472.68	29	28	31	28
	85.85	79.31	72.22	61.25	67.48	60.08	52.31	41.84	62.82	55.36	44.63	36.43	478.75	473.25	479.75	480.75	35	53	49	49
SNLS-IFCM	98.92	98.05	97.31	95.50	97.83	96.14	94.70	91.29	91.43	86.40	82.50	75.51	188.42	189.15	188.50	196.30	11	12	13	18
	96.75	93.89	84.72	72.61	89.64	82.86	67.01	52.56	73.57	56.67	33.03	18.48	470.25	465.61	470.42	472.76	20	25	42	31
	96.80	86.21	71.96	63.01	89.76	65.51	51.21	42.49	79.81	41.55	21.99	12.23	470.30	468.14	452.14	467.14	23	20	28	24
	87.92	79.33	71.63	63.11	70.80	59.87	51.72	43.86	65.78	54.15	44.72	35.16	474.25	471.81	470.25	472.25	30	39	24	35
本文算法	99.23	98.26	97.40	96.89	98.12	96.55	95.19	93.90	92.07	87.70	83.54	81.32	1.75	2.06	1.90	1.80	6	6	6	8
	98.89	94.36	94.34	93.40	96.04	84.55	83.45	82.15	87.01	61.06	58.27	55.88	4.53	4.41	4.78	4.44	7	12	14	13
	98.97	97.72	97.46	91.87	96.31	92.34	91.38	78.10	87.79	78.32	75.44	53.15	4.53	5.51	4.53	4.37	7	10	7	11
	90.71	87.40	87.82	79.06	72.75	66.27	67.85	60.03	69.84	65.58	63.13	54.46	4.86	4.37	4.81	4.92	9	7	9	17

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表 3 5种算法的时间复杂度

分割算法	计算步骤$E$	计算步骤函数$E(n)$	时间复杂度
FCM	$H \times W \times K \times {\rm{iter} }$	${n^4}$	$O({n^4})$
FLICM	$H \times W \times K \times {k^2} \times {\rm{iter} }$	${n^6}$	$O({n^6})$
FCM-NLS	$H \times W \times {(2S + 1)^2} \times {(2s + 1)^2} + H \times W \times K \times {\rm{iter} }$	${n^2}{(n + 1)^4} + {n^4}$	$O({n^6})$
SNLS-IFCM	$H \times W \times {(2S + 1)^2} \times {(2s + 1)^2} + H \times W \times (K - 1) \times K \times {\rm{iter} }$	${n^2}{(n + 1)^4} + {n^4}(n - 1)$	$O({n^6})$
本文算法	$H \times W \times [{(2S + 1)^2} - 1] + (2 \times H \times W) \times K \times {\rm{iter} }$	${n^2}[{(n + 1)^2} - 1] + 2{n^4}$	$O({n^4})$

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