# HiGoReg: A Hierarchical Grouping Strategy for Point Cloud Registration
## 3 Experiments
### Real-World Data Experiment  
Under real conditions, the first experiment was implemented using the open-source dataset WHU-TLS proposed by [72]. We selected the subway station TLS data ([[https://github.com/WHU-USI3](https://github.com/WHU-USI3) DV/WHU-TLS]([https://github.com/WHU-USI3](https://github.com/WHU-USI3) DV/WHU-TLS), accessed on 20 March 2025) as the registration object, which covers a scene with dimensions of 20 m in length and 11 m in width. In this case, as displayed in Figure 7, the source and target point clouds contained 5,092,812 and 6,094,880 points, respectively. Another demonstration study was conducted using the self-collected point cloud data of a statue. For this work, a Faro Focus 3D X330 scanner (FARO Technologies Inc., Lake Mary, FL, USA) was engaged to acquire data from two different angles at a distance of about 7 m from the target. The scanner achieved excellent accuracy, with a distance accuracy of 0.4 mm and an angular resolution of 0.009\({}^{\circ}\), ensuring high fidelity of the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & \multicolumn{3}{c}{**Batch (s)**} & \multicolumn{3}{c}{**HiGoReg (s)**} & \multicolumn{3}{c}{**Improvement (\%)**} \\ \cline{2-10}  & **Min 1** & **Max 2** & **Ave 3** & **Min** & **Max** & **Ave** & **Min** & **Max** & **Ave** \\ \hline Bunny & 1.3763 & 1.4649 & 1.4151 & 0.8537 & 0.9144 & 0.8748 & 37.86 & 37.58 & 38.18 \\ Monkey & 4.7757 & 5.0573 & 4.9710 & 1.2902 & 1.4239 & 1.3517 & 72.98 & 71.84 & 72.81 \\ Dragon & 20.2370 & 21.8469 & 20.8628 & 3.5107 & 3.7435 & 3.6131 & 82.65 & 82.86 & 82.68 \\ Large-scale & 2079.8988 & 2082.2567 & 2081.1157 & 4.3026 & 4.4598 & 4.3611 & 99.79 & 99.79 & 99.79 \\ \hline \hline \end{tabular}  
* Min, 2 Max, and 3 Are represent the minimum, maximum, and average values, respectively.  
\end{table} 
Table 3: Time consumption of simulated dataset registration under their respective optimal group. Figure 6: Statistics on computing time cost of simulated large-scale dataset under equal weighting. “Running index” denotes the index of execution counts, where each execution sequentially completes the batch solving process and HiGoReg algorithm workflows under different groups, with a total of 10 executions. Figure 7: Subway station point clouds from WHU-TLS. (**a**) Source point cloud; (**b**) target point cloud. captured data. The source point cloud and target point cloud consisted of 32,546 and 27,894 points, respectively, as depicted in Figure 8.  
Before the experiment, meticulous preparations were performed: Considering the requirements of the Matlab platform for matrix dimensions, we first grid-sampled the original data; then, three points were carefully selected using the open-source CloudCompare software (version: 2.13.1, [[https://www.danielgm.net/cc/](https://www.danielgm.net/cc/)]([https://www.danielgm.net/cc/](https://www.danielgm.net/cc/)), accessed on 20 March 2024) to establish a quality initial pose for subsequent iterations. After ISS processing, the source and target point clouds in the subway station scene contained 3818 and 3943 feature points, respectively. In comparison, the statue scene yielded 344 and 367 feature points. Following the feature-matching process, the subway scene yielded 3698 and 1665 correspondences at voxel grid sizes of 0.03 m and 0.05 m, respectively. In contrast, the statue scene produced only 244 correspondences at a voxel size of 0.001 m.  
As WHU-TLS did not provide the accuracy information of the scanner, only equal weighting for the stochastic model was carried out. On the other side, as for the statue, we introduced two commonly used stochastic models, namely, identity matrix (equal weighting) and nominal accuracy weighting, to evaluate impacts on the HiGoReg registration results. After successful registration, for WHU-TLS, which supplied the ground-truth of parameters, we evaluated the parameters' precision through Equations (29) and (30) similarly.