## 4 Experimental Results and Discussion
### Feasibility of Normal Vectors and Curvature  
The accuracy of normal vector and curvature estimation depends on the effectiveness of the adaptive neighborhood selection method. Due to the simplicity of the magnetic tile dataset, we used the publicly available Stanford Bunny dataset for validation. As shown in Figure 12, we selected the Bunny and Dragon models from the dataset and determined the optimal radius for each point through adaptive neighborhood selection. Subsequently, a principal component analysis was applied to the neighboring points within the optimal radius to compute the best normal vector for each point. Finally, a consistent orientation was assigned to all normal vectors using an extended Gaussian image. Specifically, we selected eight distinct \(k\) values (50, 45, 40, 35, 30, 25, 20, and 15) and computed the corresponding normal vectors for each point. The average of these vectors was taken as the reference normal vector for each point. Subsequently, the normal vectors obtained for each \(k\) value, as well as the optimal normal vectors, were compared against the reference normals to compute their angular deviations, yielding the overall mean error (ME) and root-mean-square error (RMSE). Furthermore, since the accuracy of normal vector estimation is influenced by point cloud density, we performed random sampling at different levels: 100%, 80%, 60%, and 40% of the original point cloud. The selection of the Bunny and Dragon models was intentional, as the Bunny dataset represents a lower density point cloud with 34,834 points, while the Dragon dataset features a higher density with 435,545 points. For the Bunny dataset, we set parameters \(r_{min}=0.0002\), \(r_{max}=0.0064\), \(\Delta_{r}=0.0002\), while for the Dragon dataset, the parameters were set to \(r_{min}=0.0002\), \(r_{max}=0.0054\), \(\Delta_{r}=0.0002\). As shown in Figure 13, the overall mean and root-mean-square errors increased as the point cloud density decreased. However, the proposed adaptive method consistently outperformed fixed-\(k\)-value approaches in terms of lower error. When using normal vector deviation to detect significant surface defects, a deviation threshold of \(5^{\circ}\) to \(10^{\circ}\) is typically set, with points exceeding this threshold considered defect points. For tiny defects, the angle deviation threshold is generally set between \(3^{\circ}\) to \(5^{\circ}\). A threshold that is too small may lead to the misclassification of non-defect points as defects while detecting tiny ones. However, the deviation of our method remained below \(3^{\circ}\) across varying point cloud densities, confirming its feasibility. We further analyzed the Bunny model, quantifying the distribution percentage of the total number of neighborhood points at the optimal radius for each point, as well as the total number of points contained within each optimal radius, as shown in Figure 14a,b. From Figure 14a, it is evident that different points had distinct optimal neighborhoods. While  
Figure 12: Normal estimation on the Stanford Bunny dataset. they may fall within the same range, the number of points in their optimal neighborhoods can vary. Notably, the largest range was between 50 and 55, with a proportion of zero beyond this range. This suggests that the number of optimal neighborhood points at the optimal radius for any given point was a fixed value, unaffected by further increases in the radius, demonstrating the effectiveness of information entropy. This finding emphasizes the uniqueness of the optimal neighborhood selection for each point, reinforcing the importance of adaptive methods in point cloud analyses. Figure 14b further supports this validity. Previously, we set the maximum radius, \(r_{max}\), to 0.0064. As shown, when the radius reached 0.0060, all points had already found their optimal radius, and any further increase in the radius did not affect the outcome. This highlights the precision and stability of the proposed method, which is crucial for accurate and efficient defect detection.