基于拉普拉斯算子与统计形状模型的股骨三维重建方法  

Three-dimensional reconstruction of femur based on Laplace operator and statistical shape model

作　　者：张祖佩 张小刚 张亚丽 靳忠民 ZHANG Zupei;ZHANG Xiaogang;ZHANG Yali;JIN Zhongmin(School of Mechanical Engineering,Southwest Jiaotong University,Chengdu 610031,P.R.China;School of Mechanical Engineering,Xi’an Jiaotong University,Xi’an 710049,P.R.China)

机构地区：[1]西南交通大学机械工程学院,成都610031 [2]西安交通大学机械工程学院,西安710049

出　　处：《生物医学工程学杂志》2023年第6期1168-1174,共7页Journal of Biomedical Engineering

基　　金：四川省自然科学基金(2022NSFSC1940);国家自然科学基金(52005418,52035012);中央高校基本科研业务费(2682023ZTPY052)。

摘　　要：通过二维图像进行重建的三维模型,是目前术前规划、人工关节定制的普遍需求。本文提出一种统计形状模型与拉普拉斯曲面变形相结合的方法,应用于股骨图像的三维重建,以优化传统统计建模重建过程中特征不足和信息损失造成的精度问题。该方法将基于统计形状模型的重建结果用能够代表形状特征的拉普拉斯算子表示,在拉普拉斯坐标系下进行曲面结点坐标变换,建立骨骼新特征,使重建模型与二维图像充分拟合。最后选取50例股骨模型验证本方法的有效性。结果表明,引入拉普拉斯曲面变形后的方法较传统统计形状模型的精度提升了16.8%~25.9%。该方法能够以更高精度完成骨三维重建,为术前个性化假体设计及其精准定位与快速生物力学分析等研究提供模型基础。Reconstructing three-dimensional(3D)models from two-dimensional(2D)images is necessary for preoperative planning and the customization of joint prostheses.However,the traditional statistical modeling reconstruction shows a low accuracy due to limited 3D characteristics and information loss.In this study,we proposed a new method to reconstruct the 3D models of femoral images by combining a statistical shape model with Laplacian surface deformation,which greatly improved the accuracy of the reconstruction.In this method,a Laplace operator was introduced to represent the 3D model derived from the statistical shape model.By coordinate transformations in the Laplacian system,novel skeletal features were established and the model was accurately aligned with its 2D image.Finally,50 femoral models were utilized to verify the effectiveness of this method.The results indicated that the precision of the method was improved by 16.8%–25.9%compared with the traditional statistical shape model reconstruction.Therefore,the method we proposed allows a more accurate 3D bone reconstruction,which facilitates the development of personalized prosthesis design,precise positioning,and quick biomechanical analysis.

关 键 词：三维重建 统计形状模型 拉普拉斯算子 骨几何 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] R68[自动化与计算机技术—计算机科学与技术]