# Feature Point Identification in Filtel Weld Joints Using an Improved CPDA Method
## 4 Numerical Verification and Experimental Validation Results  
To assess and validate the effectiveness of the proposed method incorporating PCA and the improved CPDA algorithm for identifying the feature corner points in laser stripe during fillet welding, numerical simulated and experimental captured images are used for comparing the performance between several state-of-the-art methods. To provide a \"ground truth\" for subsequent comparisons, a piece-wise linear line is defined with the following analytical equation:  
\[x=\left\{ \begin{aligned} &(y-150)\cot\left(\frac{2\pi}{5}\right)+100, \text{ for }y\in(150,350]\\ &(150-y)\cot\left(\frac{\pi}{3}\right)+100,\text{ for }y\in[0,150)\end{aligned} \right. \tag{14}\]  
The formulated piece-wise linear line as described by Equation (14) is visually represented in Figure 6a. A dilation morphological operation is implemented to the linear line to simulate the width of the laser stripe in the captured image with a 9 \(\times\) 9 square kernel. The dilated laser stripe is shown in Figure 6b. In an effort to make the simulated laser stripe more closely resemble practical situations where a normal distribution is typically observed along the laser line, A Gaussian kernel with a sigma value of 3 is implemented through convolution and illustrated in Figure 6c. When extracting the grayscale distribution along the \(x\) direction with a row index of 100, as demonstrated with a yellow line arrow in Figure 6a,b,c, the simulated laser stripe exhibits a distribution similar to that of the experimental captured laser line in Figure 2b. The center point (denoted as a red dot in Figure 6d), which is the highest point on the piece-wise line, can serve as ground truth for comparisons among different methods. Consequently, the simulated laser stripe images depicted in Figure 6c are used as input for extracting the laser center line via different methods: grayscale gravity method [33], Hessian-matrix-based Steger method [26], and our proposed Gaussian-weighted PCA-based method. The analytical expression of the piece-wise line in Figure 6a serves as the ground truth for the center line. Additionally, zero-mean random noise with different standard deviation is implemented to evaluate the performance of each method in a noisy environment. Figure 5: Flowchart of feature corner points detection with laser center extraction. Several conclusions can be drawn from the results presented in Figure 7 and Table 1:  
* When extracting the grayscale value along the \(x\) direction using the simulated laser stripe images in Figure 7a, it becomes evident that the present of zero-mean Gaussian noise with different sigma values exerts a noticeable impact, as illustrated in Figure 7b. The location of the piece-wise line in this row (marked by the red dot) serves as the ground truth for comparison;
* Figure 7c are the results of center line extraction achieved with different methods using simulated images without noise. The center line obtained through the gravity-based method [33] exhibits obvious discontinuities due to its sensitivity to rotation. Conversely, the Steger method [26] and our developed PCA-based method provide smoother extraction results by accounting for the rotation angle through Hessian matrix and PCA;
* Figure 7d is the error comparison among different methods using image with noise (\(\sigma=1\)). The error is defined as the distance between the extracted center line coordinates and Equation (14): error = \(\sqrt{\Delta x^{2}+\Delta y^{2}}\). It is worth noting that the gravity-based method has higher errors as the inclined angle increases, particularly in the lower part of the simulated laser stripe. In contrast, both the Steger method and our proposed method effectively reduce the effect of an inclined laser stripe in a fillet weld, resulting in lower errors;
* Figure 7e and Table 2 show insights into the sensitivity of different methods to noise.