点云数据热传导平滑过程中的惩罚函数形态

针对点云数据热传导平滑处理过程中惩罚函数的形态确定问题，提出了基于模糊数学隶属度函数形态相似性的热传导惩罚函数形态确定方法.通过对降半矩形分布、降半Г分布、降半正态分布、降半哥西分布、降半梯形分布和降岭形分布的数学形态分析，得出自变量的变化与惩罚函数值成非线性反比的函数选择原则.实验验证表明，降半哥西分布和降半正态分布为最佳实用函数，从而为点云数据的平滑去噪预处理提供了一条途径.

Study on the Choice of Disciplinal Function During Point Cloud Smoothing Based on Anisotropic Heat Diffusion

The smoothing method based on the heat diffusion has a good effect to the point cloud with noise points, but how to choose a proper disciplinal function to smooth the point cloud is no answer. This paper proposed a method to decide the disciplinal function based on the fuzzy mathematics’s relevant function concept. The six special functions, such as drop semi rectangle function, drop semi Г function, drop semi normal function, drop semi Cauchy function, drop semi trapezia function and drop semi mountain function, were analyzed. The answer was gotten that the variant has a nonlinear relationship with the result of disciplinal function. Some cases were used to validate the characteristics of disciplinal function. There is a new way to handle the point cloud during the preprocessing of reverse engineering or complex surface inspection.