基于权衡因子和多维空间度量的高鲁棒性图像分割算法

doi:10.11996/JG.j.2095-302X.2024030482

图学学报 ›› 2024, Vol. 45 ›› Issue (3): 482-494.DOI: 10.11996/JG.j.2095-302X.2024030482

• 图像处理与计算机视觉 • 上一篇下一篇

基于权衡因子和多维空间度量的高鲁棒性图像分割算法

刘以¹(), 邱军海², 张嘉星¹, 张小峰¹^,³^,⁴(), 王桦¹^,⁴, 张彩明⁵

1.鲁东大学信息与电气工程学院，山东烟台 264025
2.烟台工程职业技术学院，山东烟台 264006
3.烟台理工学院信息工程学院，山东烟台 264003
4.山东省高等学校青少年行为大数据智能分析文科实验室，山东烟台 264025
5.山东大学软件学院，山东济南 250014

收稿日期:2023-09-06 接受日期:2023-11-13 出版日期:2024-06-30 发布日期:2024-06-11
通讯作者:张小峰(1978-)，男，教授，博士。主要研究方向为图形图像处理、计算机视觉等。E-mail：iamzxf@126.com
第一作者:刘以(1998-)，男，硕士研究生。主要研究方向为数字图像处理与模式识别。E-mail：yi_domi@163.com
基金资助:
国家自然科学基金项目(62007017);国家自然科学基金项目(U22A2033);国家自然科学基金项目(61873117);国家自然科学基金项目(62171209);国家自然科学基金项目(62176140);烟台市科技创新发展计划基础研究项目(2023JCYJ044)

A highly robust image segmentation algorithm based on trade-off factors and multidimensional spatial metrics

LIU Yi¹(), QIU Junhai², ZHANG Jiaxing¹, ZHANG Xiaofeng¹^,³^,⁴(), WANG Hua¹^,⁴, ZHANG Caiming⁵

1. School of Information and Electrical Engineering, Ludong University, Yantai Shandong 264025, China
2. Yantai Engineering & Technology College, Yantai Shandong 264006, China
3. School of Information Engineering, Yantai Institute of Technology, Yantai Shandong 264003, China
4. Humanities Laboratory of Intelligent Analysis on Big Data of Adolescent Behaviors, Universities of Shandong Province, Yantai Shandong 264025, China
5. School of Software, Shandong University, Jinan Shandong 250014, China

Received:2023-09-06 Accepted:2023-11-13 Published:2024-06-30 Online:2024-06-11
First author：LIU Yi (1998-), master student. His main research interests cover digital image processing and pattern recognition. E-mail: yi_domi@163.com
Supported by:
National Natural Science Foundation of China(62007017);National Natural Science Foundation of China(U22A2033);National Natural Science Foundation of China(61873117);National Natural Science Foundation of China(62171209);National Natural Science Foundation of China(62176140);Basic Research Project of Yantai Science and Technology Innovation Development Plan(2023JCYJ044)

摘要/Abstract

摘要：

图像分割是计算机视觉的重要研究方向。聚类算法作为一种无监督的方法，一直是图像分割的有力工具。然而，当图像存在高强度噪声和复杂结构时，聚类算法的分割效果可能不理想。针对这一问题，提出了一种高鲁棒性的图像分割算法，该算法基于权衡因子和多维空间度量。首先，引入了一个权衡因子，通过调节该因子，可以有效地降低噪声对分割结果的影响。其次，结合了低维和高维的空间度量，能够捕捉图像中的线性和非线性特征。并更好地理解图像中的复杂结构和纹理，从而提高分割的准确性和鲁棒性。最后，利用改进的模糊聚类算法实现了图像分割。为了验证该算法的性能，在合成、自然和医学图像上进行了大量的实验，结果显示，该算法在分割性能上明显优于其他算法。

关键词: 图像分割, 聚类, 无监督, 权衡因子, 多维空间度量

Abstract:

Image segmentation is an important research direction in computer vision. Clustering algorithms, serving as an unsupervised method, have always been a powerful tool for image segmentation. However, in scenarios where image possess high-intensity noise and complex structures, the segmentation effect of clustering algorithms might prove unsatisfactory. To address this problem, a highly robust image segmentation algorithm was proposed based on trade-off factors and multi-dimensional space metrics. Firstly, a trade-off factor was introduced to effectively reduce the influence of noise on the segmentation result by adjusting the factor. Secondly, the algorithm integrated both low-dimensional and high-dimensional space metrics, enabling the capture of linear and nonlinear features in the image. In this way, the algorithm facilitated a more comprehensive understanding of the complex structure and texture in the image, thereby enhancing the accuracy and robustness of segmentation. Finally, the algorithm achieved image segmentation through the application of an enhanced fuzzy clustering algorithm. To verify the performance of the algorithm, extensive experiments were conducted on synthetic, natural, and medical images, and the results demonstrated that the proposed method significantly outperformed other algorithms in terms of segmentation.

Key words: image segmentation, clustering, unsupervised, trade-off factor, multidimensional spatial metric

中图分类号:

TP391

刘以, 邱军海, 张嘉星, 张小峰, 王桦, 张彩明. 基于权衡因子和多维空间度量的高鲁棒性图像分割算法[J]. 图学学报, 2024, 45(3): 482-494.

LIU Yi, QIU Junhai, ZHANG Jiaxing, ZHANG Xiaofeng, WANG Hua, ZHANG Caiming. A highly robust image segmentation algorithm based on trade-off factors and multidimensional spatial metrics[J]. Journal of Graphics, 2024, 45(3): 482-494.

图/表 15

图1 基于权衡因子和多维空间度量的算法框架

Fig. 1 Algorithmic framework based on trade-off factors and multidimensional spatial metric

图2 像素相关性模型

Fig. 2 Pixel correlation model

图3 被混合噪声污染的图像A点的权衡因子

Fig. 3 The trade-off factors at point A of the image contaminated by mixed noise

表1 各类算法中涉及的相关参数

Table 1 Relevant parameters involved in each type of algorithm

算法	参数	窗口大小
FCM	-	-
FCMS1	α=2	3×3
FCMS2	α=2	3×3
ENFCM	α=2	3×3
FGFCM	λ_s=3，λ_g=3	3×3
FLICM	-	3×3
LMKLFCM	β=3	3×3
KWFLICM	-	5×5
FRFCM	se=3	5×5
FCM_SICM	σ_d=5，σ_r=2	-
Proposed	β=0.7，γ₁=0.8	5×5

Fig. 4 Segmentation results of the first synthetic image ((a) Original image; (b) Noisy image corrupted by salt & pepper noise of 50% density; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKLFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) Ours)

图5 不同强度噪声下的第一幅合成图像的不同评价指标

Fig. 5 Different evaluation indicators under different intensity noise of the first synthetic image ((a) SA; (b) Sen; (c) Jaccard; (d) Mpa; (e) PSNR)

图6 天鹅的分割结果((a)原始图像；(b)被40%高斯噪声破坏的图像；(c) FCM；(d) FCMS1；(e) FCMS2；(f) EnFCM；(g) FGFCM；(h) FLICM；(i) LMKLFCM；(j) KWFLICM；(k) FRFCM；(l) FCM_SICM；(m)本文算法)

Fig. 6 Segmentation results of the swan ((a) Original image; (b) Noisy image corrupted by Gaussian noise of 40% variance; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKLFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) Ours)

图7 教堂的分割结果((a)原始图像；(b)被40%椒盐噪声破坏的图像；(c) FCM；(d) FCMS1；(e) FCMS2；(f) EnFCM；(g) FGFCM；(h) FLICM；(i) LMKLFCM；(j) KWFLICM；(k) FRFCM；(l) FCM_SICM；(m)本文算法)

Fig. 7 Segmentation results of the church ((a) Original image; (b) Noisy image corrupted by salt & pepper noise of 40% density; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKLFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) Ours)

图8 飞机的分割结果((a)原始图像；(b)被混合噪声破坏的图像；(c) FCM；(d) FCMS1；(e) FCMS2；(f) EnFCM；(g) FGFCM；(h) FLICM；(i) LMKLFCM；(j) KWFLICM；(k) FRFCM；(l) FCM_SICM；(m)本文算法)

Fig. 8 Segmentation results of the airplane ((a) Original image; (b) Noisy image corrupted by mixed noise; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKLFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) Ours)

表2 自然图像的Vpc和Vpe

Table 2 Vpc and Vpe on natural images

Indicators	Picture	FCM	FCMS1	FCMS2	ENFCM	FGFCM	FLICM	LMKLFCM	KWFLICM	FRFCM	FCM_SICM	Ours
V_pc	图8	0.622 8	0.724 7	0.730 0	0.817 0	0.818 2	0.872 0	0.775 3	0.691 3	0.661 6	0.791 1	0.898 3
	图9	0.830 8	0.604 9	0.732 1	0.799 0	0.825 2	0.517 5	0.725 5	0.730 6	0.756 1	0.757 5	0.911 2
	图10	0.578 5	0.571 7	0.606 0	0.772 1	0.779 2	0.501 9	0.624 2	0.483 0	0.632 9	0.633 3	0.926 6
V_pe	图8	0.961 8	0.669 4	0.655 8	0.461 5	0.456 4	0.357 4	0.549 5	0.790 3	0.865 5	0.565 2	0.317 6
	图9	0.317 6	0.979 6	0.666 4	0.528 2	0.463 0	1.174 2	0.694 7	0.717 5	0.656 6	0.635 1	0.258 6
	图10	1.052 8	1.047 4	0.954 6	0.587 2	0.556 0	1.179 3	0.919 6	1.249 7	0.926 0	0.845 2	0.252 4

图9 大脑的分割结果((a)原始图像；(b)被30%Rician噪声噪声破坏的图像；(c) Ground truth；(d) FCM；(e) FCMS1；(f) FCMS2；(g) EnFCM；(h) FGFCM；(i) FLICM；(j) LMKLFCM；(k) KWFLICM；(l) FRFCM；(m) FCM_SICM；(n)本文算法)

Fig. 9 Segmentation results of the brain ((a) Original image; (b) Noisy image corrupted by Rician noise of 30% density; (c) Ground truth (d) FCM; (e) FCMS1; (f) FCMS2; (g) EnFCM; (h) FGFCM; (i) FLICM; (j) LMKLFCM; (k) KWFLICM; (l) FRFCM; (m) FCM_SICM; (n) Ours)

图10 皮肤病的分割结果((a)原始图像；(b) Ground truth；(c) FCM；(d) FCMS1；(e) FCMS2；(f) EnFCM；(g) FGFCM；(h) FLICM；(i) LMKLFCM；(j) KWFLICM；(k) FRFCM；(l) FCM_SICM；(m)本文算法)

Fig. 10 Segmentation results of the skin ((a) Original image; (b) Ground truth; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKLFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) Ours)

表3 医学图像的SA

Table 3 SA on medical images

Picture	FCM	FCMS1	FCMS2	ENFCM	FGFCM	FLICM	LMKLFCM	KWFLICM	FRFCM	FCM_SICM	Ours
图9	0.561 2	0.642 0	0.645 1	0.695 7	0.731 9	0.723 5	0.652 9	0.796 9	0.579 2	0.773 1	0.796 1
图10	0.912 6	0.921 3	0.921 9	0.920 4	0.920 2	0.912 4	0.912 4	0.900 4	0.922 3	0.916 4	0.925 1

图11 Skyataset部分分割结果((a)被噪声污染的Skyataset_001；(b) Ground truth_001；(c)本文算法；(d)被噪声污染的Skyataset_045；(e) Ground truth_045；(f)本文算法)

Fig. 11 Partial segmentation results of Skyataset ((a) Noise-contaminated Skyataset_001; (b) Ground truth_001; (c) Results of the proposed algorithm; (d) Noise-contaminated Skyataset_045; (e) Ground truth_045; (f) Ours)

表4 相关算法在Skyataset数据集的平均结果

Table 4 Average results of the correlation algorithm on the Skyataset dataset

Indicators	FCM	FCMS1	FCMS2	ENFCM	FGFCM	FLICM	LMKLFCM	KWFLICM	FRFCM	FCM_SICM	Ours
SA	0.740 6	0.808 6	0.812 3	0.810 0	0.821 5	0.833 2	0.824 6	0.814 1	0.811 8	0.870 7	0.872 0
Sen	0.789 0	0.843 8	0.848 1	0.843 5	0.850 6	0.856 7	0.861 6	0.850 4	0.849 0	0.808 3	0.800 4
Jaccard	0.566 6	0.670 4	0.676 9	0.672 1	0.689 6	0.700 4	0.696 1	0.696 0	0.677 5	0.701 8	0.703 7
Mpa	0.789 0	0.843 8	0.848 1	0.843 5	0.850 6	0.856 7	0.861 6	0.850 4	0.849 0	0.808 3	0.800 4
PSNR	6.149 7	8.727 4	8.932 0	8.785 5	9.283 8	9.957 0	9.529 1	10.000 3	8.964 9	10.452 8	10.675 7

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基于权衡因子和多维空间度量的高鲁棒性图像分割算法

A highly robust image segmentation algorithm based on trade-off factors and multidimensional spatial metrics

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