## 1 Introduction  
With the rapid development of modern industry, three-dimensional (3D) free-form surface parts are being utilized more and more widely. These involve, but are not limited to, aviation, aerospace, shipbuilding, automotive, biomedical and home appliance industries [1; 2]. Recently, the automated 3D digitization of free-form surface objects has been widely applied in many areas, such as additive manufacturing (3D printing), rapid prototyping, reverse engineering, civil buildings, medical prosthetics and clinical diagnosis [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. Scanning measurement is one of the key technologies for digitizing 3D physical models with free-form surfaces [14; 15; 16; 17]. Unfortunately, in order to obtain a high-quality profile of a measured surface, scanning measuring devices have to produce massive amounts of point cloud data with great sampling rates, and not all these points are indispensable [18; 19; 20]. Bottlenecks arise from the inefficiencies of storing, manipulating and transferring them [21]. Furthermore, the parametric modelling from these massive amount of point cloud data is a time-consuming task [22; 23; 24]. For this reason, compressing the measured point data while maintaining the required accuracy is a crucial task during the scanning measuring process [25]. Herein, the required accuracy is a threshold of distance, which is preset to a constant positive integer before the beginning of scanning measurement. The accuracy of a certain data compression algorithm is characterized by the distance from each sampled point in the initial dense point cloud data to the surface generated by the compressed point cloud. Describing a measured surface with the least point data while guaranteeing a certain data compression accuracy is always an expectation [26; 27]. Therefore, a high-quality point cloud data compression algorithm for 3D free-form surface scanning measurement is being pursued constantly [28]. Experts and scholars around the world have been paying more and more attention to this issue, and a number of point cloud data compression/reduction algorithms for free-form/irregular surface scanning measurement have been developed. [PERSON] et al. [29] proposed an algorithm for processing point cloud data obtained by laser scanning devices. This algorithm adopts a one-directional (1D) or bi-directional (2D) non-uniform grid to reduce the amount of point cloud data. [PERSON] et al. [5] presented a data compression method based on a bi-directional point cloud slicing strategy for reverse engineering. This method can preserve local details (geometric features in both two parametric directions) when performing data compression. [PERSON] and [PERSON] [30] proposed a new data compression algorithm for surface points to preserve the original surface points. The error metric is defined as the relative Hausdorff distance between two principal curvature vector sets for surface shape comparison. After comparison, the difference between the compressed data points and original data points can be obtained. Therefore, redundant points are repeatedly removed until the difference induced exceeds the specified tolerance. [PERSON], [PERSON], and [PERSON] [31] presented a progressive encoding and compression method for surfaces generated from point cloud data. At first, an octree is built whose nodes contain planes that are constructed as the least square fit of the data within that node. Then, this octree is pruned to remove redundant data while avoiding topological changes created by merging disjointed linear pieces. [PERSON] et al. [32] presented a geometric 3D point cloud lossy compression system based on plane extraction, which represents the points of each scene plane as a Delaunay triangulation and a set of points/area information. This compression system can be customized to achieve different data compression or accuracy ratios. The above methods have focused on optimizing data compression quality based on building and processing polyhedral models or numerical iterative calculations.