# A 3D Vision-Based Weld Seam Extraction Method for Arbitrarily Placed Spatial Planar Weldments
## 4 Experimental Verification
### Experiment for Plane Segmentation  
Several experiments are conducted to evaluate the performance of the plane segmentation algorithm proposed in Section 3. The standard cube serves as the experimental object for the initial comparison. Table 2 presents a detailed comparison of segmentation results between vanilla RANSAC, RANSAC without normal vector clustering (non-clustering RANSAC hereafter), and the improved RANSAC. To ensure a fair comparison, all implementations utilize identical configurations for variables such as downsampling, distance threshold, max iteration, etc. No parallel computation, such as AVX, is employed (the same goes for the following comparisons). The reported results are averaged over 20 runs. For vanilla RANSAC, the PCL implementation [25] is utilized. Figure 16: Point clouds before (**first row**) and after (**second row**) registration, with each point cloud frame rendered in a different color. Figure 15: Spatial planar weldments from a signal tower base manufacture. Analysis of Table 2 reveals that the improved RANSAC significantly outperforms vanilla RANSAC regarding segmentation accuracy, although this difference may not be readily apparent in Figure 17. Vanilla RANSAC exhibits faster execution compared to the proposed algorithm, as the surface normal estimation and Euclidean clustering utilized in the proposed algorithm are relatively time-consuming. However, compared to non-clustering RANSAC, the improved RANSAC demonstrates superior efficiency. In the subsequent experiment, an icosahedral column, serving as a relatively complex standard workpiece, is employed as the experimental object. The comparison results are depicted in Figure 18 and summarized in Table 3. In this set of experiments, both vanilla RANSAC and non-clustering RANSAC exhibit poor performance in accurately segmented planes, with numerous incorrect planes generated. With further tuning in the configuration, the latter may perform better in this experiment. However, we retain this result as, with the same configuration, the improved RANSAC efficiently identifies all the planes. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & **Vanilla RANSAC** & **Non-Clustering RANSAC** & **Improved RANSAC (Proposed)** \\ \cline{2-5}  & **Value** & **Value** & **Comparison \({}^{*}\)** & **Value** & **Comparison \({}^{*}\)** \\ \hline average error (mm) & 0.28 & 0.40 & +42.9\% & 0.072 & \(-74.3\%\) \\ standard deviation & 0.0023 & 0.0030 & +30.4\% & 0.00081 & \(-64.8\%\) \\ execution time (s) & 4.85 & 30.46 & +528\% & 16.79 & +246\% \\ correct planes & \(5/5\) & \(5/5\) & 0\% & \(5/5\) & 0\% \\ segmented & 0 & 0 & 0\% & 0 & 0\% \\ total points (downsampled) & \(140,022\) & \(140,022\) & 0\% & \(140,022\) & 0\% \\ inliers & \(139,003\) & \(134,471\) & \(-3.2\%\) & \(134,591\) & \(-3.17\%\) \\ \hline \hline \end{tabular} \({}^{*}\) The comparisons are made against Vanilla RANSAC.  
\end{table} 
Table 2: Segmentation result comparison with a standard cube. Figure 17: Segmentation comparison over a standard cube. (**a**) Vanilla RANSAC; (**b**) non-clustering RANSAC; (**c**) improved RANSAC. Figure 18: Segmentation comparison over an icosahedral column. (**a**) Vanilla RANSAC; (**b**) non-clustering RANSAC; (**c**) improved RANSAC. It is to be noted that in Tables 1-3, the total planes to be segmented (displayed as denominators in a row \"correct planes segmented\") is not equal to \"correct planes segmented\" plus \"incorrect planes segmented\". As an example, for a given point cloud with three planes to be segmented, if the segmentation mistakenly has two of the planes recognized as one plane and the left one plane recognized as three planes, the number of incorrect planes reaches four, which is bigger than the total planes to be segmented (three). Unreasonable segmentation may output more planes than needed, as actually happens to Vanilla RANSAC and non-clustering RANSAC in Tables 3 and 4. This phenomenon can be more intuitively observed in Figure 18a,b.