## 5 Conclusions  
Manual inspection of surface defects in magnet tiles is highly subjective, inefficient, and prone to high false detection rates. Traditional defect detection algorithms based on 2D imaging impose stringent requirements on image quality, which are often unmet by standard industrial cameras, making it challenging to capture subtle, concealed microscopic defects. These limitations pose potential safety risks to the stable operation of permanent magnet motors. With the rapid advancement of sensor technology, high-resolution 3D vision sensors offer a more competitive alternative for defect detection. This study developed a surface defect detection and quantitative evaluation framework for magnetic tiles using high-resolution 3D laser scanning technology. To ensure defect detection accuracy, we first applied height-based and statistical filtering to eliminate noise and outliers in the high-resolution point cloud. Next, we introduced a luminance and point cloud mapping scheme, wherein bilinear interpolation effectively reconstructed the surface color of the magnet tile, enhancing visual details crucial for microscopic defect detection. To improve normal vector and curvature estimation, we proposed an adaptive neighborhood selection method based on an improved weighted covariance matrix and information entropy. Unlike the conventional covariance matrix, the proposed weighted version assigned varying weights to neighboring points, with closer points exhibiting stronger correlations with the central point, thereby receiving higher weights. A singular value decomposition was then performed on the weighted covariance matrix to extract eigenvalues, which were used to construct an entropy-based criterion,where a lower entropy value indicated a stronger local point correlation. The proposed entropy measure integrated linearity, planarity, and scattering metrics to characterize the disorder and unstructured nature of the point cloud. The optimal neighborhood selection derived from this entropy criterion significantly enhanced the accuracy of normal vector and curvature estimation, particularly at critical regions such as edges and corner points. This improvement laid the foundation for precise microscopic defect thresholding. An initial screening of microscopic defect candidates was performed using normal vector and curvature deviation thresholds; however, this method was less sensitive to macroscopic defects. To address this limitation, we proposed a single-frame and multi-frame point cloud fitting approach based on the topological structure of the magnet tile surface. This approach enabled the simultaneous extraction of both macroscopic and microscopic defects while ensuring accurate defect depth measurement. During this process, kernel density estimation was employed to transform the fitting residuals into probabilities, which significantly enhanced the robustness of the entire detection algorithm. Finally, we implemented defect completion and segmentation using region-growing and DBSCAN clustering, effectively reducing both false positive and false negative rates. For segmented defects, the maximum defect depth was calculated based on a residual analysis. A Principal Component Analysis (PCA) was then applied for dimensionality reduction, allowing the extraction of the maximum length and width of the defect region using the components along the first and second principal axes. Compared to conventional 2D image-based defect detection algorithms, the proposed method demonstrated a significant advantage in identifying defects that were challenging to detect with the naked eye. It was capable of detecting defects as small as approximately 0.07 mm\({}^{2}\) while simultaneously enabling a precise quantitative evaluation. This provides a valuable reference for subsequent quality control in magnet tile manufacturing.