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中文摘要：
针对三维扫描或三维重建获取的散乱点云数据曲面重建问题，提出基于拉普拉斯规则化的高阶平滑算法。，首先，计算点云数据的包围盒并离散化得到体素空间；其次，在体素空间根据隐式曲面的梯度和点云位置、法向信息建立目标函数，并通过对目标函数的拉普拉斯规则化达到控制重建曲面光顺效果的目的；再次，根据最优化原理将重建问题转换为一个稀疏线性方程组求解问题；最后，通过步进立方体算法得到重建曲面的三角网格表示。定性和定量的实验结果表明，该方法重建曲面绘制效果和精确度优于常用的Poisson方法。
英文摘要：
This paper presented an algorithm for reconstructing implicit surface from acquired scattered point cloud with a 3D scanner or 3D reconstruction method. Firstly, it computed the bounding box for the point cloud and used a volume to partition the points into each voxel. Secondly, it established an objective function based on the implicit surface gradients, point position and normal, and added a Laplacian regularization term to the function so as to produce more smooth result. Thirdly, it trans- formed the surface reconstruction problem into solving a system of sparse equations by using optimum approximation. Finally, it extracted the triangular mesh model from the implicit surface using marching cubes algorithm. Experimental results show that this method is superior to the widely used Poisson method.
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