## 4 Experimental Results and Analysis
### Location Experiments of Occluded Parts  
The type information of the part is obtained by the identification algorithm. Then, the same type of template can be used to effectively estimate the pose matrix and complete the localization. To verify the efficacy and accuracy of the positioning method, the occluded parts are rotated at various angles and then placed randomly to record their respective position information. The pose transition matrix of the occluded parts in 200 images is calculated to obtain the localization accuracy of the algorithm.  
In the experiments, the localization algorithm obtains the geometric feature points for template matching based on the adjacency factor and contour curvature features of the Freeman chain code. To verify the accuracy of the feature extraction algorithm, it is compared with the Harris, Shi-Tomasi, and CSS (curvature scale space) operators. The various algorithms are analyzed by detecting the contour corner points of the part template, and the detection results of several algorithms are displayed in Figure 19.  
According to Figure 19, the number of missing corner points in the detection results of the Harris operator and Shi-Tomasi operator is small, and there are some pseudo-corner points. More corner points are missed in the detection results of the CSS operator. In contrast, the improved algorithm in this paper can obtain the corner points of irregular parts and effectively capture the feature points of some parts with weak contour changes, and there are no pseudo-corner points with high accuracy.  
Figure 17: Segmentation and identification of the part contours: (**a**) segmentation of template part’s contour, (**b**) segmentation of stacked parts’ contours, and (**c**) separately identified two parts of the contour segments.  
Figure 18: Accuracy of the identification algorithm at different occlusion rates.  
The geometric features of the inspected part are obtained by the algorithm. Figure 20 shows the feature point coordinates, curvature circle, and curvature radius of the part. The contour matched point pairs of the template and the inspected part are extracted to obtain the part's positional transformation matrix, as in the following equations:  
\[M_{1}=\begin{bmatrix}0.9106&0.4031&-226.5685\\ -0.4031&0.9106&187.6361\end{bmatrix} \tag{18}\]  
\[M_{2}=\begin{bmatrix}0.9960&-0.0047&5.8746\\ 0.0047&0.9960&-3.2181\end{bmatrix} \tag{19}\]  
Due to the part's irregular shape, its center of gravity is chosen as the grasping point. The part's center of gravity is calculated to obtain the position error. The pose angle error is obtained by comparing the workpiece's pose angle with the actual rotation angle. Error analysis is conducted on 200 test data results, and the results are displayed in Table 1.  
Figure 19: Comparison of the results of multiple corner point detection algorithms: **(a)** Harris corner detection, **(b)** Shi-Tomasi corner detection, **(c)** CSS corner extraction operator, and **(d)** the corner point detection algorithm proposed in this paper.  
Figure 20: Corner points of sheet metal part contours.  
Table 1 shows the mean error and root mean square error of the localization algorithm. According to the root mean square error, the positioning error of the stacked parts is less than 0.8 mm, and the pose angle error is less than 0.6\({}^{\circ}\). The localization algorithm can precisely determine the pose transformation matrix of occluded parts to localize occluded targets.  
To further demonstrate the efficacy of the method, the localization results for irregular parts at various angles or occlusion rates are provided. Figure 21a,b display the results of the algorithm for estimating the parts' position at 20% and 40% occlusion rates. The algorithm can find the same parts as the template, even when they are occluded by non-identical shaped parts, as in Figure 21c. The algorithm is also applicable when multiple parts are stacked, as in Figure 21d, and can be used to locate parts that are occluded in multiple parts.