Efficient Rock-Mass Point Cloud Registration Using $n$ -Point Complete Graphs

The surfaces of rock masses are arbitrary and complex. Moreover, the point clouds of rock-mass surfaces acquired via terrestrial laser scanning typically span large distances and have high resolutions. These characteristics cause difficulties in registration between scans. To address these difficulties, an efficient method using
$n$
-point complete graphs is proposed. To handle massive point clouds, a step-by-step strategy is adopted to reduce the number of points involved in the computation. First, the Gaussian curvature of each point of the initial data is estimated, and points with low Gaussian curvatures are filtered out such that only the interesting points are preserved. Second, these interesting points are clustered, and the centroid of each cluster is calculated. Finally, a descriptor is built from the
$n$
-point complete graph formed by each centroid and its
$n-1$
nearest neighbors. By matching the descriptors generated from two point clouds, corresponding point pairs can be obtained, thus achieving alignment. In addition, this strategy inherently incorporates denoising, outlier handling, and filtration, thereby endowing the method with strong adaptability to various conditions without incurring any additional cost. Experiments on data sets with varying degrees of outliers, noise and overlap were conducted to demonstrate the robustness of the proposed method. The results show that, with point span
$r~\approx ~1$
cm, the output root mean square error is around 0.5 cm, which is comparable with that of the Iterative Closest Point algorithm. A runtime analysis shows that the total processing time of the proposed method grows nearly linearly with increasing data size.