Study of the characteristic of the penalty function in point cloud data's smoothing based on anisotropic heat conduction principle

Abstract

It is necessary to smooth the point cloud data in reverse engineering or freeform surface inspection. 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 penalty function to smooth the point cloud is no answer. The paper proposes a method to decide the penalty function based on the fuzzy mathematics' relevant function concept. The four special functions, such as rectangular distribution, drop hemi- distribution, drop hemi-normal distribution and drop hemi-Cauchy distribution, have been analyzed. Each penalty function has been used to smooth the point cloud by experiment, the result show that drop hemi-Cauchy function and drop hemi-normal function are fit to be the penalty function. The conclusion is gotten that the variant has a no-linear relationship with the result of penalty function. Some cases are used to validate the characteristics of penalty function. There is a new way to handle the point cloud during the preprocessing of reverse engineering or complex surface inspection.