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基于分步子空间映射的无标记膈肌运动预测算法

余航 李晨阳 余绍德 冯冬竹 许录平

余航, 李晨阳, 余绍德, 冯冬竹, 许录平. 基于分步子空间映射的无标记膈肌运动预测算法. 自动化学报, 2021, 47(x): 1−19 doi: 10.16383/j.aas.c200471
引用本文: 余航, 李晨阳, 余绍德, 冯冬竹, 许录平. 基于分步子空间映射的无标记膈肌运动预测算法. 自动化学报, 2021, 47(x): 1−19 doi: 10.16383/j.aas.c200471
Yu Hang, Li Cheng-Yang, Yu Shao-De, Feng Dong-Zhu, Xu Lu-Ping. Markerless prediction of diaphragm displacement based on two-step subspace mapping. Acta Automatica Sinica, 2021, 47(x): 1−19 doi: 10.16383/j.aas.c200471
Citation: Yu Hang, Li Cheng-Yang, Yu Shao-De, Feng Dong-Zhu, Xu Lu-Ping. Markerless prediction of diaphragm displacement based on two-step subspace mapping. Acta Automatica Sinica, 2021, 47(x): 1−19 doi: 10.16383/j.aas.c200471

基于分步子空间映射的无标记膈肌运动预测算法

doi: 10.16383/j.aas.c200471
基金项目: 国家自然科学基金(61501352)资助
详细信息
    作者简介:

    余航:副教授, 西安电子科技大学. 分别于2005年和2014年获得西安电子科技大学学士学位和工学博士学位. 主要研究方向为合成孔径雷达图像理解与解译、模式识别和计算机视觉. E-mail: yuhang9551@163.com

    李晨阳:西安电子科技大学硕士研究生. 主要研究方向为计算机视觉、图像处理、去雾算法和机器学习. E-mail: 19888900429@163.com

    余绍德:博士, 中国传媒大学. 分别于2008年和2011年获得北京师范大学学士学位和硕士学位, 2018年获得中国科学院大学工学博士学位. 主要研究方向为机器学习和图像分析. Email: yushaodemia@163.com

    冯冬竹:教授, 博士生导师, 西安电子科技大学. 于2006年获得西北工业大学博士学位. 主要研究方向为计算机视觉、飞行器制导与控制等. 中国计算机学会计算机视觉专委会委员, 陕西省自动化学会导航制导与控制委员会委员. E-mail: dongzhufengnet@163.com

    许录平:教授, 博士生导师, 西安电子科技大学. 分别于1984年、1986年和1997年获得西安电子科技大学学士学位、硕士学位和博士学位. 主要研究方向为导航技术与应用、目标检测与跟踪、精确制导与智能控制. 在本领域国际、国内期刊和会议上发表论文100余篇, 获得授权发明专利30余件, 出版专著和教材5部. 以第一完成人获得陕西省科学技术奖和陕西省教学成果奖3项. E-mail: mail2111@163.com

Markerless Prediction of Diaphragm Displacement Based on Two-Step Subspace Mapping

Funds: Supported by National Natural Science Foundation of P. R. China (61501352)
  • 摘要: 呼吸会引起体内器官和肿瘤的运动, 这会显著影响放射治疗的过程和效果. 人体内部膈肌和胸腹部外表面是当前两种与呼吸系统高度相关的结构, 本文对其进行系统研究, 提出了一种新的分步子空间映射(TSSM)算法, 通过对体外胸腹部表面的测量, 来预测体内膈肌的运动. 本文首先采用三维图像分割技术对4D CT图像进行分割, 在不使用标记物的情况下, 准确测量体内膈肌和体外胸腹部表面的位移. 为了解决跨空间的预测问题, TSSM首先构造特征子空间, 并将膈肌数据和胸腹外表面数据分别映射到各自的子空间中, 以减少数据的相关性和冗余信息; 然后通过线性岭回归优化过程, 对两个子空间进行二次映射, 从而有效地捕获跨空间数据之间的相关性. 根据训练得到的相关模型, 通过体外胸腹部外表面的运动情况, 对体内膈肌的运动情况进行准确的预测. 为了研究数据之间的非线性关系, 本文进一步将TSSM推广到了基于核的TSSM(kTSSM)算法. 实验表明, 该方法可以根据腹腔外表面的运动情况, 准确的对体内膈肌位移进行预测, 优于经典的线性模型和ANN模型. 本文给出了优化算法的解析解, 其运算速度快, 将有助于提高放射治疗中门控技术和跟踪技术的效率和精度.
  • 图  1  三维图像分割结果冠状平面展示图, 背景体素值为0, 身体区域的体素值为1, 肺部体素值为3.

    Fig.  1  Segmentation images on the axial plane, where the background voxels is set to 0, the voxels of body area to 1, and the voxels of lungs to 3

    图  2  三维图像分割结果, 及其对应的肺部区域和身体区域

    Fig.  2  A 3D segmentation result and the corresponding separated 3D lungs and body

    图  3  肺部面积沿左右方向的曲线

    Fig.  3  The curve of lung area along the left/right direction

    图  4  胸腹部表面, (a)初始胸腹部表面, (b)胸腹部掩膜, (c)最终胸腹部表面

    Fig.  4  The thoracoabdominal surface. (a) is the initial thoracoabdominal surface obtained from 3D body mask, (b) is the produced thoracoabdominal mask, and (c) is the final thoracoabdominal surface.

    图  5  TSSM算法的流程图

    Fig.  5  The flowchart of the propose TSSM

    图  6  膈肌和胸腹部表面的位移. 每一种颜色的曲线对应一个患者的数据.

    Fig.  6  The displacement of diaphragm and thoracoabdominal surface, where each color corresponds to a specific patient’s data.

    图  7  归一化后的膈肌和胸腹部表面的位移. 每一种颜色的曲线对应一个患者的数据.

    Fig.  7  The displacement of diaphragm and thoracoabdominal surface after normalization, where each color corresponds to a specific patient’s data.

    图  8  三个方向的预测结果. 该结果对应于100次运行MSE的中位数值.

    Fig.  8  Prediction results corresponding the median MSE value in three directions after 100 independent runs.

    图  9  三个方向各相位预测误差的统计箱图

    Fig.  9  Boxplot of the prediction performance on every phase in three directions

    图  10  主方向的预测结果. 该结果对应于100次运行MSE的中位数值.

    Fig.  10  Prediction results corresponding the median MSE value in the principal direction after 100 independent runs.

    图  11  主方向各相位预测误差的统计箱图

    Fig.  11  Boxplot of the prediction performance on every phase in the principal direction

    图  12  噪声对三个方向预测结果的影响

    Fig.  12  Influence of noise on the prediction in three directions

    图  13  噪声对主方向预测的影响

    Fig.  13  Influence of noise on the prediction in principal direction

    图  14  PCA中的阈值ε对TSSM预测模型的影响

    Fig.  14  The influence of ε in PCA on the prediction performance of TSSM

    表  1  预测结果在三个方向上的统计结果

    Table  1  Statistic results of the prediction results in three directions

    OLS模型[1]ANNTSSM(线性)kTSSM(多项式)kTSSM(高斯)
    没有噪音MSE0.45 (0.23)0.30 (0.16)0.20 (0.09)0.18 (0.08)0.20 (0.10)
    R20.70 (0.14)0.81 (0.07)0.87 (0.05)0.88 (0.04)0.88 (0.04)
    MAPE232.11 (156.44)159.60 (112.37)150.82 (83.98)116.57 (71.28)130.69 (87.26)
    噪音($\sigma =0.1$)MSE0.46 (0.22)0.29 (0.15)0.22 (0.10)0.19 (0.09)0.22 (0.09)
    R20.70 (0.15)0.8207 (0.07)0.86 (0.05)0.88 (0.04)0.86 (0.05)
    MAPE276.86 (551.10)214.82 (257.92)157.28 (117.30)137.25 (92.36)170.47 (204.00)
    噪音($\sigma =0.2$)MSE0.54 (0.24)0.39 (0.18)0.25 (0.11)0.23 (0.10)0.24 (0.10)
    R20.69 (0.13)0.76 (0.10)0.84 (0.05)0.86 (0.04)0.85 (0.06)
    MAPE277.42 (348.60)211.14 (196.70)172.08 (171.03)131.98 (78.23)166.12 (156.08)
    噪音($\sigma =0.3$)MSE0.65 (0.25)0.42 (0.21)0.30 (0.11)0.28 (0.11)0.29 (0.12)
    R20.59 (0.20)0.75 (0.11)0.82 (0.05)0.82 (0.06)0.82 (0.06)
    MAPE426.45 (1371.37)211.37 (228.00)242.75 (274.21)157.12 (94.87)179.81 (115.10)
    噪音($\sigma =0.4$)MSE0.80 (0.28)0.52 (0.33)0.37 (0.13)0.33 (0.13)0.38 (0.13)
    R20.53 (0.21)0.69 (0.19)0.79 (0.07)0.80 (0.06)0.78 (0.07)
    MAPE592.47 (1687.33)262.36 (405.00)198.89 (112.67)174.14 (116.58)185.34 (133.87)
    噪音($\sigma =0.5$)MSE0.98 (0.33)0.65 (0.29)0.46 (0.16)0.41 (0.15)0.45 (0.17)
    R20.47 (0.22)0.64 (0.15)0.75 (0.08)0.76 (0.08)0.76 (0.09)
    MAPE365.33 (399.98)254.35 (291.97)234.93 (185.28)194.18 (150.11)214.82 (260.37)
    下载: 导出CSV

    表  2  主方向预测结果的统计结果

    Table  2  Statistic results of the prediction results in principal direction

    OLS模型[1]ANNTSSM(线性)kTSSM(多项式)kTSSM(高斯)
    没有噪音MSE0.47 (0.28)0.27 (0.18)0.14 (0.07)0.13 (0.06)0.15 (0.06)
    R20.73 (0.20)0.86 (0.08)0.93 (0.03)0.93 (0.03)0.92 (0.03)
    MAPE91.07 (38.34)63.62 (23.72)47.85 (15.31)45.17 (14.94)46.47 (14.39)
    噪音($\sigma =0.1$)MSE0.40 (0.26)0.25 (0.18)0.15 (0.07)0.14 (0.06)0.15 (0.07)
    R20.78 (0.16)0.86 (0.08)0.92 (0.04)0.92 (0.03)0.91 (0.03)
    MAPE143.90 (173.93)100.38 (136.34)116.46 (198.17)68.29 (66.63)107.08 (145.85)
    噪音($\sigma =0.2$)MSE0.43 (0.23)0.29 (0.12)0.18 (0.07)0.17 (0.06)0.18 (0.07)
    R20.76 (0.14)0.84 (0.07)0.90 (0.04)0.91 (0.04)0.90 (0.04)
    MAPE188.52 (476.86)138.61 (386.48)133.32 (129.00)79.96 (53.09)82.96 (79.07)
    噪音($\sigma =0.3$)MSE0.61 (0.33)0.38 (0.18)0.23 (0.10)0.20 (0.08)0.24 (0.09)
    R20.64 (0.20)0.79 (0.11)0.87 (0.06)0.87 (0.06)0.88 (0.05)
    MAPE192.18 (223.53)136.84 (116.74)134.21 (151.02)86.07 (64.90)101.09 (88.78)
    噪音($\sigma =0.4$)MSE0.70 (0.31)0.45 (0.36)0.30 (0.12)0.26 (0.09)0.29 (0.11)
    R20.65 (0.17)0.77 (0.21)0.83 (0.07)0.87 (0.06)0.85 (0.07)
    MAPE221.12 (417.10)175.31 (342.96)142.09 (168.43)94.42 (64.70)109.11 (116.15)
    噪音($\sigma =0.5$)MSE1.01 (0.50)0.52 (0.28)0.39 (0.13)0.32 (0.13)0.36 (0.14)
    R20.47 (0.35)0.75 (0.15)0.80 (0.09)0.84 (0.07)0.81 (0.09)
    MAPE173.44 (98.15)193.44 (455.90)146.14 (212.00)102.30 (130.34)94.49)
    下载: 导出CSV

    表  3  Parameter setting of TSSM和kTSSM for optimal results

    模型TSSM(线性)kTSSM(多项式)kTSSM(高斯)
    参数λλdcλσkernel
    三个方向的预测没有噪音1100690.10.2
    噪音($\sigma =0.1$)110003.590.10.2
    噪音($\sigma =0.2$)11002.590.10.1
    噪音($\sigma =0.3$)110.540.10.1
    噪音($\sigma =0.4$)1101.570.10.1
    噪音($\sigma =0.5$)1101410.1
    主方向的预测没有噪音0.11150.10.2
    噪音($\sigma =0.1$)0.10.1170.10.2
    噪音($\sigma =0.2$)10.10.540.10.2
    噪音($\sigma =0.3$)110.530.10.1
    噪音($\sigma =0.4$)11140.10.2
    噪音($\sigma =0.5$)10.10.570.10.1
    下载: 导出CSV
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  • 收稿日期:  2020-06-28
  • 录用日期:  2020-10-19
  • 网络出版日期:  2021-01-06

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