# Feature Point Identification in Filtel Weld Joints Using an Improved CPDA Method
## 3 Feature Points Extraction Method in Fillet Welding
### Improved CPDA Corner Detection Method
To filter out these incorrect feature points, it is essential to perform a linear normalization process to detect and eliminate false corners:  
\[N_{L}(i)=\frac{h_{L}(i)-\min(h_{L})}{\max(h_{L})-\min(h_{L})} \tag{13}\]  
where \(N_{L}\) is a normalized vector representing the corresponding value of each point on the curve \(P\). \(\max()\) and \(\min()\) represent the maximum and minimum cumulative values of the chord-to-point distance on the curve, respectively. The normalization process prevents a situation where points in some flat planes exhibit large chord-to-point accumulation values. However, it was found in the experiments with noisy arc light interference that there are pseudo-corners and/or missing corners after the linear normalization filtering. To improve computational efficiency while achieving robust feature corners detection in noisy environments, an improved CPDA method with linear polygon approximation and feature point angle monitoring strategy is proposed. The original CPDA detector remains computationally expensive as it calculates the discrete \(h_{L}\) value in Equation (10) for every point on the curve. In the improved CPDA method, we select a set of potential candidate points during the center line extraction through PCA in Equation (8). The eigenvectors \((\textbf{v}_{1},\textbf{v}_{2})\) representing the laser stripe direction at each point on the curve are stored. By monitoring the angle direction between each feature point, the points with large direction variance are chosen as the candidate points. Moreover, the proposed improved CPDA method calculates the angle between each line vector instead of computing the distance, resulting in further computational reduction. The diagram (Figure 4a,b) and steps of the improved CPDA are summarized as follows. With the input images of fillet welding, the feature corner points representing the 3D location of the weld seam on the laser line can be detected as outlined in the flow-chart presented in Figure 5.  
* Establish a straight line connecting the starting point \(A\) and the ending point \(B\);
* Find a point (e.g., denoted as \(C\) in Figure 4) on the original contour curve that is farthest from this line. If the calculated distance exceeds a predetermined threshold, this point is considered a feature corner point;
* Iterate through the above two steps for the segmented contour of the curve until the shortest distance between all points and the polygon falls below the threshold;
* Apart from the calculation of distance, determine the angle between two polygon lines. Select points \(D_{k-1}\) and \(D_{k+1}\) as the points preceding and succeeding and compute the angle between line vectors \(D_{k-1}D_{k}\) and \(D_{k}D_{k+1}\). Figure 4: Schematic of (**a**) linear polygon approximation and (**b**) angle calculation between feature corner points. Compare the obtained angle with the angle represented by the eigenvectors \(\mathbf{(v_{1},v_{2})}\) calculated in the PCA process. Retain the angle if it surpasses a predefined threshold; otherwise, remove it.