# Feature Point Identification in Filtel Weld Joints Using an Improved CPDA Method
## 4 Numerical Verification and Experimental Validation Results
The gravity-based method proves to be highly sensitive to noise, while both the Steger and our method demonstrate relatively high robustness. With respect to the extraction time, the Hessian-matrix-based method is computationally expensive, whereas the proposed PCA-based method achieves similar accuracy at a speed that is 10 times faster. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & & & **Computation** \\ \cline{2-5}
**Method** & & & & & **Time** \\ \cline{2-5}  & \(\sigma\) = 0 & \(\sigma\) = 1 & \(\sigma\) = 3 & \(\sigma\) = 5 & \\ \hline Gravity method [33] & (0.83, 1.22) & (4.31, 4.55) & (8.43, 8.25) & (12.0, 13.2) & 0.08 \\ \hline Steger method [26] & (0.45, 0.41) & (0.85, 0.7) & (3.24, 3.51) & (5.23, 4.23) & 1.2 \\ \hline PCA-based method & (0.41, 0.32) & (0.52, 0.92) & (3.62, 3.42) & (6.17, 4.12) & 0.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between different methods. Figure 6: Simulated images. (**a**) Piece-wise linear line in Equation (14); (**b**) after dilation operation; (**c**) after Gaussian convolution; (**d**) grayscale distribution along \(x\) direction. Figure 7: Numerical verification. (**a**) Simulated images with and without noise; (**b**) grayscale value distribution along \(x\) direction; (**c**) center line extraction results using different methods using image without noise; (**d**) error comparison using different methods (gravity method [33] and Steger method [26]) using image with noise of \(\sigma\) = 1; (**e**) average, standard deviation of error and computation time comparison. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Workpiece material & Q235 steel \\ Workpiece thickness & 5 mm \\ Welding current & 70 A \\ Welding voltage & 5 V \\ Welding speed & 6 mm/s \\ Diameter of welding wire & 1 mm \\ Shielding gas & Ar + CO\({}_{2}\) \\ Gas flowrate & 5 L/min \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Welding parameters. The experimental setup with the main components of the welding robot and sensing unit are shown in Figure 8. The captured images, utilized for feature points extraction, are processed on a Windows X64 system computer with an Intel (R) Core (TM) i5-10400F CPU processor. The hardware setup includes a CCD camera MV-EM500M and a linear laser projector with 650 nm wavelength. The programming for image processing is performed using Visual Studio 2015 (version 14.0.27544.0) software and the OpenCV image processing tool. In accordance with the calculations outlined in Section 3 regarding the CPDA algorithm, the value of \(L\) is set as 6 in the experiments. The details of the welding conditions employed in the experiments are summarized in Table 2.  
In the context of automated welding for the automatic creation of a 90\({}^{\circ}\) filled weld structure, as shown in Figure 8b using an industrial robot, the primary challenge lies in the precise identification of feature corner points along the projected laser line. With the feature corner points in each image frame extracted with the proposed method, the 3D coordinates of the fillet weld seam can be reconstructed with Equation (1). To validate the effectiveness of the proposed method for extracting the feature corners in automated fillet robot welding, the robot arm was configured to perform a scanning motion from right to left in Figure 8b. During this single pass of scanning, the CCD camera in the sensing unit was set to capture images at a framerate of 12 FPS (frame per second). A total of 120 frame images were experimentally captured for the subsequent validation. An example of one such captured frame image is shown in Figure 9a. As can be found in Figure 9a,b, the discontinuities due to the laser stripe inclination in center line extraction in fillet welding result in many pseudo-feature-corners () being identified using the original CPDA. With the further normalization in Equation (13), some pseudo-corners are removed.