颅骨点云曲面重建的Euler’s Elastica模型  

Skull Surface Reconstruction with Euler’s Elastica Model from Point Cloud Data

作　　者：牛慧勤 潘振宽 赵俊莉 周明全[2,3] Niu Huiqin;Pan Zhenkuan;Zhao Junli;Zhou Mingquan(Department of Computer Science and Technology,Qingdao University,Qingdao266071;Engineering Research Center of Virtual Reality and Applications,Ministry of Education,Beijing Normal University,Beijing100875;School of Information Science and Technology,Northwest University,Xi’an710127)

机构地区：[1]青岛大学计算机科学技术学院,青岛266071 [2]北京师范大学教育部虚拟现实应用工程研究中心,北京100875 [3]西北大学信息科学与技术学院,西安710127

出　　处：《计算机辅助设计与图形学学报》2022年第10期1515-1523,共9页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(62172247,61702293,61772294);全国统计科学研究基金(2020LY100);山东省自然科学基金(ZR2019LZH002,ZR2020QF039).

摘　　要：为从具有复杂拓扑关系的颅骨点云数据中重建精确、光滑的隐式曲面,提出了基于Euler’s Elastica的变分水平集方法.首先,将Euler’s Elastica作为正则化约束引入变分能量泛函,采用增广拉格朗日方法将变分能量泛函最小化问题转化为一系列子问题;其次,分别采用广义软阈值公式、解析公式和快速傅里叶变换求解;最后,在计算过程中采用投影算法,有效地避免了水平集函数的重新初始化过程.实验结果表明,相较于现有方法,所提基于Euler’s Elastica的变分水平集方法具有更好的收敛性和有效性,能够提高重建的精确性,避免曲面边缘的缺失.In order to reconstruct accurate smooth implicit surfaces from skull point cloud data with complex topological relations,a variational level set method based on Euler’s Elastica model is proposed.Firstly,Euler’s Elastica is introduced into the variational energy functional as a regularization constraint,and the variational energy functional minimization problem is transformed into a series of subproblems by the augmented Lagrange method.Secondly,each subproblem is solved by generalized soft threshold formula,analytical formula and fast Fourier transform respectively.Finally,the projection algorithm is used during the computation to avoid the re-initialization of the level set function effectively.The experimental results show that the proposed variational level set method based on Euler’s Elastica has better convergence and effectiveness than the existing methods,which can improve the reconstruction accuracy and avoid missing surface edges.

关 键 词：曲面重建 水平集方法 Euler’s Elastica 增广拉格朗日方法 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]