Robust function guided color encoded single fringe pattern and unwrapping method

Abstract

Fringe Projection Profilometry (Fringe Projection Profilometry，FPP), renowned for its speed, precision, and automation advantages, has found extensive applications in industries such as mechanical processing and quality inspection. A critical challenge within fringe projection techniques involves ensuring robust unwrapping while minimizing the necessary fringe images. While various unwrapping methods exist to reduce the number of projected images, there is a deficiency in efficient unwrapping methods developed under the guidance of error analysis theory. In this study, we derive a robustness function from FPP's error theory to assess the unwrapping robustness of different encoded images. Using this robustness function, we select highly robust single-color encoded fringe images and achieve unwrapping robustness with minimal training cost based on a single fringe pattern. Furthermore, this unwrapping process does not necessitate the establishment of complex training databases, as the K-nearest neighbor (K-Nearest Neighbor，KNN) algorithm learns the correspondence between image tricolor grayscale values and fringe orders from multi-frequency unwrapping method. Finally, experimental validation through a checkerboard measurement confirms that the proposed method can achieve robust unwrapping with low training costs using only one encoded fringe, thereby affirming the effectiveness of the introduced robustness function and the feasibility of the designed color encoded single fringe pattern unwrapping method.