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浙江大学学报(工学版)
浙江大学学报(工学版)  2021, Vol. 55 Issue (12): 2373-2381    DOI: 10.3785/j.issn.1008-973X.2021.12.018
电子、通信与自动控制技术     
基于点分布模型的3D模型拟合方法
徐铸业1(),赵小强1,2,3,*(),蒋红梅1,2,3
1. 兰州理工大学 电气工程与信息工程学院，甘肃 兰州 730050
2. 兰州理工大学 甘肃省工业过程先进控制重点实验室，甘肃 兰州 730050
3. 兰州理工大学 国家级电气与控制工程实验教学中心，甘肃 兰州 730050
3D model fitting method based on point distribution model
Zhu-ye XU1(),Xiao-qiang ZHAO1,2,3,*(),Hong-mei JIANG1,2,3
1. College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China
2. Key Laboratory of Gansu Advanced Control for Industrial Process, Lanzhou University of Technology, Lanzhou 730050, China
3. National Experimental Teaching Center of Electrical and Control Engineering, Lanzhou University of Technology, Lanzhou 730050, China
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摘要：

针对传统方法构建的患者病患部位的3D解剖结构模型与测试样本拟合效果较差的问题，提出基于点分布模型的3D模型拟合方法（3DMFB-PDM）. 对训练样本集进行数据处理，使模板样本与目标样本对齐，减小训练样本由于旋转及尺度变化产生的不利影响；在训练样本间建立对应关系，用正态分布表示患者的点分布模型；计算测试样本中的特征点与点分布模型中对应点间的距离，通过引入Mahalanobis距离和转换非线性方程组，使点间距最小.根据最小间距不断调整点分布模型的形状参数，使点分布模型与测试样本拟合.选取30组左侧股骨作为训练样本集实验验证3DMFB-PDM的有效性，结果表明引入附加项后的拟合误差小于未引入附加项的拟合误差. 将 3DMFB-PDM与其他3种方法进行对比，结果显示3DMFB-PDM的拟合误差最小，表明3DMFB-PDM能够有效地将患者病患部位的3D解剖结构模型与测试样本拟合.
关键词： 医学图像处理;  3D建模;  形状分析;  点分布模型;  Mahalanobis距离    
Abstract:

A 3D model fitting method based on point distribution model (3DMFB-PDM) was proposed, aiming at the problem of poor fitting between the 3D anatomical structure model of the patient’s part constructed by the traditional method and the test samples. Firstly, the data processing was performed on the training sample set to align the template sample with the target sample, and the adverse effects of training sample due to rotation and scale changes were alleviated. Then the correspondence among training samples was established, and the patient’s point distribution model with a normal distribution was represented. Finally, the distance between the feature point and the corresponding point in the point distribution model was calculated. By introducing the Mahalanobis distance and converting the nonlinear equations were to minimize the distance. Meanwhile, the shape parameters of the point distribution model were continuously adjusted according to the minimum distance, thus the point distribution model was fitted to the test samples. 30 groups of left femurs were selected as the training sample set for experimental verification to verify the effectiveness of 3DMFB-PDM. Results show that the fitting error after introducing additional terms is smaller than the fitting error without introducing additional terms. Comparing 3DMFB-PDM with the other three methods shows that the fitting error of 3DMFB-PDM is the smallest, which indicate that 3DMFB-PDM can effectively fit the 3D anatomical structure model of the patient’s part to the test samples.
Key words: medical image processing    3D modeling    shape analysis    point distribution model    Mahalanobis distance
收稿日期: 2021-01-05 出版日期: 2021-12-31
CLC:  TP 391.41  
基金资助: 国家自然科学基金资助项目 (61763029，61873116)；国防基础科研项目(JCKY2018427C002)
通讯作者: 赵小强     E-mail: 1820481286@qq.com;xqzhao@lut.cn
作者简介: 徐铸业（1992—），男，博士生, 从事医学图像处理的研究. orcid.org/0000-0002-8680-2519.E-mail： 1820481286@qq.com
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引用本文:

徐铸业,赵小强,蒋红梅. 基于点分布模型的3D模型拟合方法[J]. 浙江大学学报(工学版), 2021, 55(12): 2373-2381.

Zhu-ye XU,Xiao-qiang ZHAO,Hong-mei JIANG. 3D model fitting method based on point distribution model. Journal of ZheJiang University (Engineering Science), 2021, 55(12): 2373-2381.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2021.12.018    或    https://www.zjujournals.com/eng/CN/Y2021/V55/I12/2373

图 1  3DMFB-PDM的建模与拟合流程图
图 2  30组左侧股骨的3D模型
ID 年龄 性别 W/kg H/cm F/n V
001 25 男 61 175 102 080 51 042
002 29 男 72 180 98 744 49 370
003 32 男 70 167 87 876 43 940
004 26 男 66 165 109 528 54 752
005 26 男 63 170 112 800 56 410
006 29 男 80 180 106 268 53 130
007 30 男 83 176 156 348 78 176
008 35 男 79 175 117 744 58 876
009 32 男 75 170 97 116 48 560
010 32 男 80 168 76 204 38 110
011 27 男 62 166 114 452 57 224
012 26 男 60 181 99 548 49 770
013 30 男 80 182 95 536 47 760
014 33 男 83 178 99 512 49 746
015 30 男 85 179 92 184 46 084
016 42 女 65 159 95 432 47 708
017 40 女 62 158 88 288 44 140
018 41 女 62 162 56 244 28 120
019 36 女 60 163 80 476 40 236
020 34 女 61 172 93 272 46 640
021 26 女 58 173 91 248 45 600
022 24 女 56 170 107 988 53 988
023 31 女 56 160 110 216 54 922
024 30 女 57 161 88 268 44 114
025 25 女 45 167 8 840 4 432
026 26 女 40 168 87 296 43 648
027 28 女 46 166 123 404 61 698
028 30 女 61 159 86 020 43 024
029 38 女 65 158 102 688 51 344
030 40 女 60 163 89 912 44 960
表 1  30组左侧股骨图像的人体测量学信息
图 3  模板样本的可视化结果
图 4  模板样本的点云表示
图 5  训练样本的点分布模型
图 6  特征向量表征变形模型的百分比
评价指标 Max Mean RMS
mm
ED 14.357 2.433 3.328
（ED+MD） 12.268 2.429 3.114
表 2  未引入附加项与引入附加项的误差比较
评价指标 ED （ED+MD）
Max Mean RMS Max Mean RMS
mm
样本1 15.227 3.064 4.025 13.046 3.015 3.633
样本2 14.629 2.921 3.359 12.437 2.437 3.217
样本3 13.753 2.735 3.016 12.067 2.361 3.024
样本4 15.664 2.863 3.968 12.821 2.501 3.208
表 3  点分布模型与多个测试样本的误差比较
方法 t 方法 t
s
MDL 10.146 文献[18] 2.414
SLIDE 12.269 文献[19] 9.382
文献[15] 6.025 3DMFB-PDM 2.359
表 4  不同方法构建点分布模型的时间对比
方法 Max Mean RMS
文献[15] 15.006 4.325 4.113
文献[19] 13.685 3.037 3.419
文献[18] 12.371 2.486 3.235
3DMFB-PDM 12.268 2.419 3.114
表 5  4种方法的误差比较
方法 样本2 样本3 样本4
Max Mean RMS Max Mean RMS Max Mean RMS
mm
文献[15] 13.965 3.974 4.261 14.217 4.233 4.037 14.368 4.725 4.479
文献[18] 12.174 2.316 3.216 12.537 2.518 3.168 12.265 2.241 3.092
文献[19] 13.962 3.114 3.512 13.379 2.983 3.428 13.315 3.016 3.374
3DMFB-PDM 12.037 2.165 3.191 12.366 2.401 3.037 12.117 2.235 2.894
表 6  4种方法在3个测试样本下的拟合误差
图 7  4种方法构建的点分布模型的模型性能对比
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