A Gaussian Filter for Plate Flatness Evaluation System with 3-D Scanner

Abstract

A LIDAR (light detection and ranging) system was applied to a plate flatness evaluation system. Plate flatness surfaces are reconstructed from many points generated by LIDAR by a smoothing spline method. We defined a smoothing spline functional with sampling measure weights. The equivalent number of parameters defined on this functional does not depend on the distributions of samples. The approximation of the equivalent number of parameters is derived when the number of samples becomes infinity. This approximation greatly reduced the calculation time needed to estimate the optimal smoothing. The smoothing spline calculation cost was so high that new algorithms (FMM: fast multi-pole method) were introduced and we developed a smoothing engine which was applied to practical problems. The engine generated clear surfaces and was robust against various dirty point clouds.