Space-filling scan paths and Gaussian process-aided adaptive sampling for efficient surface measurements

A method combining space-filling scan paths and adaptive sampling is proposed for surface measurements. Scan paths including a fractal Hilbert curve and a spiral pattern are mainly investigated. The adaptive sampling is based on iterative Gaussian process (GP) inference. Sampling positions are intelligently suggested along the scan path and the final sampled data are trained in a GP-model to reconstruct the entire topography. Simulations and experiments on different surfaces demonstrated the capability of the proposed method. When the special scan paths are employed alone, the required data amount is reduced to about 10%-13% of the uniform sampling and the relative error of surface reconstruction is within 10%. If the GP-aided adaptive sampling is further integrated, the data amount can be reduced to approximately 3%-4%. In addition, time-consumption in scanning is significantly eliminated. Compared with the raster scan, the integration of special scan paths and GP-aided adaptive sampling has several prominent advantages such as eliminating data amount, preserving surface reconstruction accuracy, maintaining a single-pass scan and saving time-cost. The measurement method has a potential application in situations where the efficiency is of critical importance.