针对离散点云数据快速重构曲面的问题,提出一种基于紧支径向基函数(CSRBF)的2层隐式函数插值算法.首先在插值前设定一个中心减少阈值,以减少CSRBF的中心点,简化基于CSRBF的线性系统;然后在粗层上通过插值对点云模型进行逼近;再在细层上拟合曲面并对粗、细层曲面求和;最后引入一个正则化参数,将由CSRBF组成的矩阵正则化,处理携带噪声的三维点云模型.实验结果表明,该算法不仅能够简捷地处理含有噪声的三维点云数据,而且能够实现曲面快速重构,最终得到逼真、平滑的曲面模型.%For fast surface reconstruction from given scattered point clouds, this paper presents a two-level implicit function interpolation algorithm based on compactly supported radial basis function (CSRBF). Firstly, a threshold for center reduction is set before interpolation, so the center points of CSRBF are reduced and the linear system based on CSRBF is simplified. Secondly, the point cloud model is approximated by interpolating in the coarse scale. Then, the surface is fitted in the fine scale and it sums up the coarse surface and the fine surface. Finally, a regularization parameter is introduced to regularize the CSRBF matrix to deal with the noise of 3D point cloud models. Experimental results show that this algorithm can not only easily process the 3D scattered datasets with noise, but also achieve rapid surface reconstruction. The final surface models are smooth and realistic.
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