利用Delaunay细分进行噪声点云曲面重建

针对噪声点云曲面重建，提出了一种基于Delaunay细分的曲面重建算法。首先以点云法向为约束，采用抗差估计的方法拟合球面近似局部曲面；然后利用沿坐标轴的包围盒树结构（axis aligned bounding boxes tree，AABB-tree）快速搜索与线段相交的曲面包围球，以各包围球球心为初值、半径为可信区间，并行化迭代计算出线段与球面的首个交点，该交点可近似为线段与曲面交点；最后不断地插入交点进行Delaunay细分，从而网格化曲面。实验结果表明，当点云噪声较大时，该方法可以快速、稳健地重建出高质量曲面，且曲面重建精度较高。

Using Delaunay Refinement to Reconstruct Surface from Noisy Point Clouds

To reconstruct surface from noisy point clouds, a surface reconstruction algorithm based on Delaunay refinement was proposed. Firstly, the local surface was approximated by algebraic sphere, which was fitted through neighbor point coordinates and normals by robust least square algorithm. Compared with traditional sphere fitting methods, the new method is more robust to noises and outliers. Secondly, to find any segment intersect with surface for Delaunay refinement procedure, the surface bounding spheres intersected with segment were efficiently founded with AABB-tree. Then, initialized with sphere center, the first approximated segment-surface intersections within bounding spheres were parallel-computed by iterative segment-sphere intersection. Finally, the surface was meshed by Delaunay refinement, which is not ambiguous and can reconstruct surface with good aspect ratio comparing with Marching-cube algorithm. Experiments show that the new algorithm can efficiently, robustly and accurately reconstruct surface from point clouds with high noises. But its time and memory consuming will rapidly increase for precise models.