## 2 Construction of the Contact Group Contact Model
### Morphological Feature Extraction of Contact Groups
#### 2.2.4 Contact Group Feature Matching and Difference Plane Construction  
For the selected feature area contour, perform iterative error calculations using the central ablation area as the reference, and ultimately take the image corresponding to the minimum error value as the feature-matching image, conducting iterative calculations according to Equation (14). Contact group feature-matching diagrams are shown in Figure 7.  
\[\begin{bmatrix}x^{\prime}\\ y^{\prime}\end{bmatrix}=s\begin{bmatrix}cos\Delta\theta&-sin\Delta\theta\\ sin\Delta\theta&cos\Delta\theta\end{bmatrix}\begin{bmatrix}x-x^{0}+\Delta x \\ y-y^{0}+\Delta y\end{bmatrix}+\begin{bmatrix}x^{0}\\ y^{0}\end{bmatrix} \tag{14}\]  
In which, \(\Delta x\) is the deviation of the image's horizontal axis length, less than 10% of the horizontal axis length, \(\Delta y\) is the deviation of the image's vertical axis length, less than 10% of the vertical axis length, \(x^{0}\) is the horizontal coordinate of the ablation center of the static contact point, \(y^{0}\) is the vertical coordinate of the ablation center of the static contact point.  
Figure 5: The result of AMR: **(a)** AMR segmentation, where \(n=3\); **(b)** AMR segmentation, where \(n=4\).  
Figure 6: ARM feature recognition flowchart based on LOG features.  
The contact feature extraction indicators use the probability rand index (PRI), global consistency error index (GCE), and boundary displacement error (BDE). Use the extracted moving and static contact profiles as the benchmark for evaluating the fused image. \(PRI\in\left[0,\infty\right),\) The higher the PRI value, the greater the consistency between the two clustering results, and the better the segmentation result. \(GCE\in\left[0,\infty\right),\) A smaller GCE value indicates a smaller refinement error and a better segmentation effect. \(BDE\in\left[0,\infty\right),\) The smaller the value, the smaller the boundary difference between the two, indicating a better segmentation effect [21]. The performance evaluation parameters from Table 2 suggest that the feature extraction effect is good.  
Using a non-contact 3D profilometer to scan the moving and static contact points of a relay, extract the point cloud height data from the contact surfaces, perform mirror symmetry on the moving contact point surface height data, and finally achieve in-situ calibration and restoration of the actual contact state of the contact group. The plane formed by the maximum sum of the heights of the moving and static contact points' surfaces is used as the reference plane for establishing the difference plane [15]. The three-dimensional morphology restoration diagram of the contact point group difference plane thus established is shown in Figure 8.  
Due to the presence of numerous micro-structures on the surface of the contact point, which are different from the distinct layers of ordinary macroscopic images, Gauss filtering is used to remove the incoherence of illumination and structure. An entropy segmentation method based on LOG extraction of image contour features and adaptive morphological  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Evaluation Indicators** & **Moving Contact** & **Static Contact** & **Mixed Data** \\ \hline PRI & 0.92 & 0.94 & 0.89 \\ GCE & 0.14 & 0.12 & 0.15 \\ BDE & 6.6 & 6.8 & 7.4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Feature Extraction Evaluation.  
Figure 8: Differential plane diagram (the color range from blue to red in this image indicates a change in surface height from low to high).  
Figure 7: Contact group feature-matching diagrams: (**a**) static contact image; (**b**) moving contact image; (**c**) mixed image.  
rate (AMR) is used to extract the ablation features. Due to the strong correlation between the moving and static contact points, the ablation features extracted are used to calibrate the in-situ contact positions of the moving and static contact points, providing a theoretical basis for the correlation analysis of the moving and static contact points.