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基于多节点拓扑重叠测度高阶MRF模型的图像分割

徐胜军 周盈希 孟月波 刘光辉 史亚

徐胜军, 周盈希, 孟月波, 刘光辉, 史亚. 基于多节点拓扑重叠测度高阶MRF模型的图像分割. 自动化学报, 2022, 48(5): 1353−1369 doi: 10.16383/j.aas.c190780
引用本文: 徐胜军, 周盈希, 孟月波, 刘光辉, 史亚. 基于多节点拓扑重叠测度高阶MRF模型的图像分割. 自动化学报, 2022, 48(5): 1353−1369 doi: 10.16383/j.aas.c190780
Xu Sheng-Jun, Zhou Ying-Xi, Meng Yue-Bo, Liu Guang-Hui, Shi Ya. Image segmentation based on higher-order MRF model with multi-node topological overlap measure. Acta Automatica Sinica, 2022, 48(5): 1353−1369 doi: 10.16383/j.aas.c190780
Citation: Xu Sheng-Jun, Zhou Ying-Xi, Meng Yue-Bo, Liu Guang-Hui, Shi Ya. Image segmentation based on higher-order MRF model with multi-node topological overlap measure. Acta Automatica Sinica, 2022, 48(5): 1353−1369 doi: 10.16383/j.aas.c190780

基于多节点拓扑重叠测度高阶MRF模型的图像分割

doi: 10.16383/j.aas.c190780
基金项目: 国家自然科学基金(51678470, 61803293), 陕西省自然科学基础研究计划(2020JM-472, 2020JM-473, 2019JQ-760, 2017JM6106, 2015JM6276), 陕西省教育厅专项科研项目(18JK0477), 西安建筑科技大学基础研究基金(JC1703, JC1706)资助
详细信息
    作者简介:

    徐胜军:西安建筑科技大学信息与控制工程学院副教授. 2013年获得西安交通大学工学博士学位. 主要研究方向为图像处理, 人工智能与自动化.E-mail: duplin@sina.com

    周盈希:西安建筑科技大学信息与控制工程学院硕士研究生. 主要研究方向为图像分割, 深度学习. 本文通信作者.E-mail: 13572978250@163.com

    孟月波:西安建筑科技大学信息与控制工程学院副教授. 2014年获得西安交通大学工学博士学位. 主要研究方向为机器学习, 建筑智能化技术.E-mail: mengyuebo@163.com

    刘光辉:西安建筑科技大学信息与控制工程学院副教授. 2016年获得西安建筑科技大学工学博士学位. 主要研究方向为机器学习, 建筑智能化技术.E-mail: guanghuil@163.com

    史亚:西安建筑科技大学信息与控制工程学院讲师. 分别于2008年, 2011年, 2015年获得西安电子科技大学学士学位、硕士学位和博士学位. 主要研究方向为机器学习.E-mail: shiyaworld@163.com

Image Segmentation Based on Higher-order MRF Model With Multi-node Topological Overlap Measure

Funds: Supported by National Natural Science Foundation of China(51678470, 61803293), the Natural Science Foundation of Shaanxi Province (2020JM-472, 2020JM-473, 2019JQ-760, 2017JM6106,2015JM6276), the Special Research Project of Education Department of Shaanxi Province (18JK0477), the Basic Research Foundation of Xi'an University of Architecture and Technology (JC1703, JC1706)
More Information
    Author Bio:

    XU Sheng-Jun Associate professor at the School of Information and Control Engineering, Xi' an University of Architecture and Technolgoy. He received his Ph. D. degree of engineering from Xi' an Jiaotong University in 2013. His research interest covers image processing, artificial intelligence and automation

    ZHOU Ying-Xi Master student at the School of Information and Control Engineering, Xi' an University of Architecture and Technology. Her research interest covers image segmentation, deep learning. Corresponding author of this paper

    MENG Yue-Bo Associate professor at the School of Information and Control Engineering, Xi' an University of Architecture and Technology. She received her Ph. D. degree of engineering from Xi' an Jiaotong University in 2014. Her research interest covers machine learning, intelligent building technology

    LIU Guang-Hui Associate professor at the School of Information and Control Engineering, Xi' an University of Architecture and Technology. He received his Ph. D. degree of engineering from Xi' an University of Architecture and Technology in 2016. His research interest covers machine learning, intelligent building technology

    SHI Ya Lecturer at the School of Information and Control Engineering, Xi' an University of Architecture and Technology. She received her bachelor, master, and Ph. D. degrees from Xidian University in 2008, 2011, 2015. Her main research interest is machine learning

  • 摘要: 针对低阶马尔科夫随机场(Markov random field, MRF)模型难以有效表达自然图像中复杂的先验知识而造成误分割问题, 提出一种基于多节点拓扑重叠测度高阶MRF模型(Higher-order MRF model with multi-node topological overlap measure, MTOM-HMRF)的图像分割方法. 首先, 为描述图像局部区域内多像素蕴含的复杂空间拓扑结构信息, 利用多节点拓扑重叠测度建立图像局部区域的高阶先验模型; 其次, 利用较大的局部区域包含更多的标签节点信息能力, 基于Pairwise MRF模型建立基于局部区域的部分二阶Potts先验模型, 提高分割模型的抗噪能力; 再次, 为有效描述观察图像场与其标签场的似然特征分布, 研究利用局部区域内邻接像素的Hamming距离引入图像局部空间相关性, 建立局部空间一致性约束的高斯混合分布; 最后, 基于MRF框架建立用于图像分割的多节点拓扑重叠测度高阶MRF模型, 采用Gibbs采样算法对提出模型进行优化. 实验结果表明, 提出模型不仅能有效抵抗图像强噪声和复杂的纹理突变干扰, 鲁棒性更好, 而且具有更准确的图像分割结果.
  • 图  1  部分二阶MRF模型

    Fig.  1  Part 2-order MRF model

    图  2  $\left| {{w_s}} \right| = {\rm{3}}$时中心像素${x_s}$与其上、下、左、右邻接像素拓扑结构示意图

    Fig.  2  When $\left| {{w_s}} \right| = {\rm{3}}$, the topological structure diagram of the center pixel and its upper, lower, left and right adjacent pixels

    图  3  T_image原图

    Fig.  3  T_image original image

    图  4  合成图像加高斯白噪声分割结果对比

    Fig.  4  Comparison of segmentation results of synthetic image with white Gaussian noise

    图  5  合成图像加椒盐噪声分割结果对比

    Fig.  5  Comparison of segmentation results of synthetic image with salt and pepper noise

    6  自然图像分割结果对比

    6  Comparison of segmentation results of natural images

    图  7  BSDS500数据集PRI分布对比

    Fig.  7  Comparison of PRI distribution of BSDS500 data sets

    图  8  BSDS500数据集CCR分布对比

    Fig.  8  Comparison of CCR distribution of BSDS500 data sets

    表  1  人工合成加噪图像在不同模型下的分割结果对比

    Table  1  Synthetic image segmentation results of different models

    ImageModelNumber of iterationsRunning time (s)CCR (均值 ± 标准差)
    高斯白噪声方差 300Pairwise MRF4612.4960.9119 ± 0.0020
    Robust ${{\cal{P}}^n}$ MRF9413.0140.9483 ± 0.0019
    不带 MTOM 项的提出模型16217.3740.9793 ± 0.0012
    提出模型13310.4860.9977 ± 0.0002
    高斯白噪声方差 900Pairwise MRF4512.3150.8854 ± 0.0039
    Robust ${{\cal{P}}^n}$ MRF8311.5880.9297 ± 0.0034
    不带 MTOM 项的提出模型14911.8530.9902 ± 0.0005
    提出模型1209.5210.9942 ± 0.0006
    椒盐噪声 0.02Pairwise MRF4411.9170.8859 ± 0.0034
    Robust ${{\cal{P}}^n}$ MRF8011.8730.9386 ± 0.0019
    不带 MTOM 项的提出模型14410.0170.9883 ± 0.0004
    提出模型16312.9470.9978 ± 0.0001
    椒盐噪声 0.05Pairwise MRF4311.5230.7463 ± 0.0025
    Robust ${{\cal{P}}^n}$ MRF7711.9550.9017 ± 0.0036
    不带 MTOM 项的提出模型948.9250.9784 ± 0.0008
    提出模型16012.6050.9976 ± 0.0001
    椒盐噪声 0.10Pairwise MRF4110.9970.5465 ± 0.0027
    Robust ${{\cal{P}}^n}$ MRF7811.2900.7915 ± 0.0047
    不带 MTOM 项的提出模型767.5560.9440 ± 0.0012
    提出模型15512.2480.9962 ± 0.0003
    下载: 导出CSV

    表  2  自然图像在不同方法下的评价指标比较

    Table  2  Comparison of evaluation indexes of natural image on different models

    ImageEvaluation indexPairwise MRF (均值 ± 标准差)Robust ${{\cal{P}}^n}$ MRF (均值 ± 标准差)MTOM-HMRF (均值 ± 标准差)
    3 096PRI0.9159 ± 0.00080.9398 ± 0.00240.9456 ± 0.0004
    CCR0.9283 ± 0.00050.9431 ± 0.00030.9820 ± 0.0007
    135 069PRI0.9635 ± 0.00030.9640 ± 0.00020.9652 ± 0.0004
    CCR0.9646 ± 0.00020.9649 ± 0.00010.9943 ± 0.0000
    196 073PRI0.8598 ± 0.00190.8818 ± 0.00260.9522 ± 0.0005
    CCR0.9064 ± 0.00140.9186 ± 0.00160.9905 ± 0.0005
    62 096PRI0.9331 ± 0.00060.9333 ± 0.00040.9451 ± 0.0006
    CCR0.8970 ± 0.00060.8978 ± 0.00060.9611 ± 0.0003
    167 062PRI0.9529 ± 0.00090.9542 ± 0.00070.9705 ± 0.0001
    CCR0.9448 ± 0.00090.9464 ± 0.00070.9938 ± 0.0005
    238 011PRI0.8631 ± 0.00010.8709 ± 0.00000.8711 ± 0.0001
    CCR0.8428 ± 0.00420.8429 ± 0.00000.9697 ± 0.0000
    253 036PRI0.9571 ± 0.00040.9574 ± 0.00020.9600 ± 0.0005
    CCR0.9257 ± 0.00040.9286 ± 0.00080.9703 ± 0.0002
    241 004PRI0.8758 ± 0.00020.8767 ± 0.00010.8801 ± 0.0005
    CCR0.8182 ± 0.00030.8212 ± 0.00030.9236 ± 0.0002
    8 068PRI0.9093 ± 0.00060.9100 ± 0.00040.9182 ± 0.0007
    CCR0.9153 ± 0.00060.9154 ± 0.00050.9790 ± 0.0002
    24 063PRI0.9043 ± 0.00030.9040 ± 0.00020.9076 ± 0.0035
    CCR0.8910 ± 0.00390.8906 ± 0.00030.9572 ± 0.0003
    55 067PRI0.9205 ± 0.00020.9545 ± 0.00010.9552 ± 0.0002
    CCR0.8657 ± 0.00040.9072 ± 0.00020.9748 ± 0.0001
    189 080PRI0.9009 ± 0.00020.9003 ± 0.00030.9066 ± 0.0014
    CCR0.9181 ± 0.00030.9174 ± 0.00020.9727 ± 0.0003
    198 087PRI0.8200 ± 0.00040.8188 ± 0.00050.8249 ± 0.0009
    CCR0.8515 ± 0.00040.8493 ± 0.00030.9280 ± 0.0004
    311 068PRI0.8688 ± 0.00170.6542 ± 0.00140.9265 ± 0.0016
    CCR0.8819 ± 0.00120.7264 ± 0.00130.9743 ± 0.0004
    15 088PRI0.8944 ± 0.00070.8948 ± 0.00070.9170 ± 0.0015
    CCR0.9095 ± 0.00060.9096 ± 0.00060.9676 ± 0.0005
    BSDS500数据集PRI0.68640.69620.7794
    CCR0.64780.65840.7452
    下载: 导出CSV

    表  3  自然图像在不同方法下的效率比较

    Table  3  Comparison of the efficiency of natural image on different models

    ImagePairwise MRFRobust ${{\cal{P}}^n}$ MRFMTOM-HMRF
    Number of iterationsRunning time (s)Number of iterationsRunning time (s)Number of iterationsRunning time (s)
    3 0964413.3568426.0841129.578
    135 0693310.1926018.44014012.045
    196 0734714.1848726.47213411.559
    62 0964417.1308333.51613915.443
    167 0624015.5588833.23910912.082
    238 01193.4667422.96410111.919
    253 0364216.1447429.42117119.248
    241 0044621.2758032.99319725.981
    8 0684313.4058927.50915419.192
    24 0637329.4017429.42119732.271
    55 0673819.1173417.51714631.874
    189 0803812.4767222.26618923.924
    198 0874112.9277925.23917723.081
    311 0684418.1388836.11115326.101
    15 0884212.8818727.31911615.346
    下载: 导出CSV
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  • 收稿日期:  2019-11-12
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