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 compu-ted 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 optimi-zing 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
Key words
point cloud/method of sections/MAT/distance functions/Eikonal equation/sparse optimization/gradient
维普
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