## 1 Introduction
Nevertheless, they are all off-line data compression algorithms and can only compress the point cloud data of a whole measured surface after data acquisition. In other words, they cannot perform online data compression during real-time measurement. Data acquisition and data compression processes are completely separate. A large amount of redundant point cloud data occupies a great deal of storage space in scanning measuring devices. Moreover, the transmission and processing of point cloud data still takes up a significant amount of time and hardware resources. This problem has attracted the attention of many scholars and engineers, and they have proposed quite a number of on-line point cloud data compression/reduction methods. [PERSON] et al. [33] adopted the chordal method to compress point cloud data, and realized the on-line data compression of point cloud data during real-time scanning measurement for the first time. [PERSON] and [PERSON] [34] presented an automatic surface sampling approach based on scanning isoparametric lines. The sampling locations are confirmed by the deviations between the alternative geometry and sampled model, and the location of each sampling line is confirmed by the curvature of the sampled surface model. [PERSON], [PERSON], and [PERSON] [35] presented a point cloud data compression method based on fuzzy logic and the geometric solution of an arc at each measured point. This is an on-line data compression method and can be used in the surface scanning measuring process of coordinate measuring machines (CMMs). [PERSON] et al. [36] proposed an on-line data compression method based on the equal-error chordal method and isochronous sampling. In order to solve the problem of massive data storage, dual-buffer and dual-thread dynamic storage is adopted. [PERSON] et al. [37] found that the essence of all the above on-line point cloud data compression methods is the chordal method, which specifies that all discrete dense point sets are connected by straight segments. Therefore, the surface reconstructed by the compressed point cloud will be full of cusp points, and so we cannot obtain a smooth interpolated surface. In view of this limitation, they presented an on-line point cloud data extraction algorithm using bi-Akima spline interpolation. Although the above methods implement on-line point cloud data compression, they can only eliminate data redundancy of the current scanning line. Nevertheless, most surface 3D scanning measuring devices adopt a layer-by-layer scanning path (e.g., contact scanning probes [38], laser triangle displacement sensors [39], linear structured light systems [40], industrial computed tomography (CT) systems [41], etc. ), and adjacent scanning lines are extremely similar in shape. The geometric feature similarity between such scanning layers is bound to result in data redundancy, which makes it possible to further compress the point cloud data during the scanning measuring process. Therefore, this study focuses on identifying and eliminating this kind of data redundancy caused by geometric feature similarity between adjacent scanning layers. After that, the massive amount of point cloud data can be further compressed during the 3D free-form surface measuring process. The contents of this paper consist of four sections. In Section 2, the innovative methodology of the on-line point cloud data compression algorithm for 3D free-form surface scanning measurement is described in detail. In Section 3, the proposed algorithm was tested in the real-time scanning measuring process and compared with existing methods. Finally, some conclusions are drawn from this paper in Section 4.