三维点云模型中轴变换的计算  

Computing medial axis transformation of 3D point clouds

作　　者：仲彦军[1] ZHONG Yan-jun(School of Mathematical Sciences,Xinjiang Normal University,Urumqi 830017,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017

出　　处：《计算机工程与设计》2024年第12期3695-3703,共9页Computer Engineering and Design

基　　金：自治区创新环境(人才、基地)建设专项-自然科学基金计划基金项目(2021D01A125);新疆维吾尔自治区高校科研计划基金项目(XJEDU2020Y027)。

摘　　要：为扩展当前中轴提取算法的适用范围,研究针对三维点云模型边界包含噪音、或存在数据缺失的情形下的中轴提取算法。提出截面法把一个三维问题转化成若干二维子问题的组合实现降维,基于稀疏优化技术恢复带符号三维距离场函数的尖锐特征,在检查三维距离场函数梯度模长的基础上,新增一个有效优化提取结果的判别条件,能够更加精准提取三维模型中轴,成功把适合提取平面点云中轴的算法推广到更高维。以实例验证了该方法的可行性。To develop the applicability of the current the medial axis transformation algorithm(MAT),a robust method was studied to compute the MAT of a 3D point cloud with noise and/or missing data.Dividing the high-dimensional problem became the lower dimensional problem using the method of sections.The signed 3D distance functions of the 3D point cloud were computed by solving the Eikonal equation,an approximation of the signed 3D distance function was obtained using sparse optimization technique.The medial axis of the 3D point cloud corresponded to the non-smooth ridge of the 3D distance functions,which could be extracted by checking the norm of the gradient of the 3D distance functions together with a new criterion for effectively optimizing the extraction results.A case study of setup planning was presented to verify the feasibility of the method.

关 键 词：点云 截面法 中轴变换 距离场 距离函数方程 稀疏优化 梯度 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]