A review of point set registration: from fundamental algorithms to geometric quality inspection of aviation complex parts

Point set registration (PSR) is a key component of computer vision and pattern recognition tasks, with the goal of assigning correspondence and recovering the transformation that maps one point set to another, to achieve optimal alignment. The geometric quality inspection of aviation complex parts is mainly based on the digitization of the object, and realizes the effective evaluation of geometric quality by analyzing the digital information that characterizes the shape of object, which is of great significance for the high performance and reliability service of aircraft. However, PSR is the mathematical foundation for solving the point cloud alignment problems in the geometric quality inspection of aviation complex parts, the association between the two has not been systematically discussed, which leads to unfavorable research results. Therefore, this paper first gives a mathematical description of PSR. Secondly, the representative fundamental algorithms for PSR are introduced, mainly include: distance-based PSR algorithms, Kernel correlation-based PSR algorithm, mixture model-based PSR algorithms, global-local structure preservation-based PSR algorithms, feature-based PSR algorithms and learning-based PSR algorithms. Besides, the ideas, basic steps, and limitations of these are revealed. Thirdly, the works on point cloud alignment problems in geometric quality inspection of aviation complex parts and the PSR algorithms used are reviewed, i.e. the application of PSR. Finally, the development direction of PSR and the challenges faced in the geometric quality inspection of aviation complex parts are discussed.