# A 3D Vision-Based Weld Seam Extraction Method for Arbitrarily Placed Spatial Planar Weldments
## 4 Experimental Verification
### Experiment for Plane Segmentation
In the final comparison group, one of the spatial planar weldments is utilized for weld seam extraction as the object. Table 4 presents the data comparison of the results. The improved RANSAC successfully captures all the planes required. Conversely, vanilla RANSAC fails to segment nearly one-third of the necessary planes and produces several incorrect planes, as demonstrated in Figure 19. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & **Vanilla RANSAC** & \multicolumn{2}{c}{**Non-Clustering RANSAC**} & \multicolumn{2}{c}{**Improved RANSAC (Proposed)**} \\ \cline{2-5}  & **Value** & **Value** & **Comparison** & **Value** & **Comparison** \\ \hline average error (mm) & \(1.35\) & \(0.31\) & \(-77.0\%\) & \(0.0030\) & \(-99.8\%\) \\ standard deviation & \(0.013\) & \(0.0023\) & \(-82.3\%\) & \(0.00065\) & \(-95\%\) \\ execution time (s) & \(74.77\) & \(597.63\) & \(+699\%\) & \(578.42\) & \(+674\%\) \\ correct planes & \(15/21\) & \(16/21\) & \(+6.67\%\) & \(21/21\) & \(+40\%\) \\ segmented & \(7\) & \(0\) & \(-100\%\) & \(0\) & \(-100\%\) \\ segmented total points & \(394,437\) & \(394,437\) & \(0\%\) & \(394,437\) & \(0\%\) \\ (downsampled) & \(384,093\) & \(345,932\) & \(-9.94\%\) & \(354,087\) & \(-7.81\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Segmentation result comparison with a spatial planar weldment. Figure 19: Segmentation comparison over a spatial planar weldment. (**a**) Vanilla RANSAC; (**b**) non-clustering RANSAC; (**c**) improved RANSAC. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & **Vanilla RANSAC** & \multicolumn{2}{c}{**Non-Clustering RANSAC**} & \multicolumn{2}{c}{**Improved RANSAC (Proposed)**} \\ \cline{2-5}  & **Value** & **Value** & **Comparison** & **Value** & **Comparison** \\ \hline average error (mm) & \(1.02\) & \(1.26\) & \(+23.5\%\) & \(0.0030\) & \(-99.7\%\) \\ standard deviation & \(0.022\) & \(0.026\) & \(+18.2\%\) & \(0.00065\) & \(-97.0\%\) \\ execution time (s) & \(13.42\) & \(104.93\) & \(+682\%\) & \(20.80\) & \(+55.0\%\) \\ correct planes & \(15/21\) & \(13/21\) & \(-13.3\%\) & \(21/21\) & \(+40\%\) \\ segmented total points (downsampled) & \(10\) & \(9\) & \(-10\%\) & \(0\) & \(-100\%\) \\ inliers & \(85,501\) & \(85,501\) & \(0\%\) & \(85,501\) & \(0\%\) \\ inliers & \(84,677\) & \(84,395\) & \(-0.33\%\) & \(81,002\) & \(-4.3\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Segmentation result comparison with an icosahedral column. By applying the improved RANSAC algorithm, consecutive plane segmentation is performed on the weldments, Figure 20 illustrates the process. The segmentation results of the weldments are displayed in Figure 21, where photographs of the weldments, segmentation results, and the corresponding normal vector clustering results are arranged for comparison. Figure 21: Plane segmentation for several weldments. (**Row one**): photos of the physical weldments. (**Row two**): segmentation results rendering each plane with a different color. (**Row three**): normal vector clustering results of the corresponding segmentations. Figure 20: Part of the process of consecutive plane segmentation. One plane is segmented in each stage of (**a**–**i**).