Sparse sampling and reconstruction for freeform surface based on low-rank matrix completion

The coordinate measuring machine (CMM) becomes an extensive and effective method for high precision inspection of free-form surfaces due to its ability to measure complex and irregular surfaces. Sampling strategy and surface restoration method have an important influence on the efficiency and precision of CMM. In this paper, a sparse sampling strategy and surface reconstruction method for free-form surfaces based on low-rank matrix completion (LRMC) is proposed. In this method, the free-form surface is sampled randomly with uniform distribution in the cartesian coordinate system to obtain sparse sampling points, and then optimizes the scanning path to obtain the shortest path through all measurement points, and finally, the LRMC algorithm based on alternating root mean square prop was used to reconstruct the surface with high precision. The simulation and experimental results show that under the premise of ensuring accuracy, the number of sampling points is greatly reduced and the measurement efficiency is greatly improved.