## 4 Experimental Results and Discussion
### Case Study of Defect Detection  
In this section, we present the results of surface defect detection on magnetic tiles to highlight the practical effectiveness of the proposed method. Figure 17 compares our approach with alternative methods based solely on normal vector deviation (Nd), curvature deviation (Cd), or multi-frame fitting (Mf). The figure displays detection results for various types of defects, including severe defects (such as dents and cracks, characterized by a large size and significant depth), tiny defects (small in size but relatively deep), severe scratches (shallow in depth with a very dark color), and light scratches (shallow with negligible depth but high brightness). For peeling and bulging defects, these were classified as severe defects due to their impact and characteristics. It is important to note that our primary goal was defect detection and quantification, rather than defect classification. Before analyzing the results, we first provide a summary of some manually set parameters used during the experiment, as detailed in Table 2. All other parameters were automatically computed during the algorithm's execution. For further details on the equations, refer to Appendix A. A key consideration was the Otsu threshold, which occasionally required fine-tuning. As shown in Figure 18, we initially calculated the Otsu threshold for both dark and bright regions using histogram analysis. However, this method alone did not fully separate dark scratches and bright scratches from the background, especially in cases where the defects exhibited subtle differences in color or brightness. Consequently, minor adjustments were necessary to fine-tune the threshold, and the required adjustment values  
Figure 17: Detection results for certain types of defects. varied depending on the specific characteristics of the point cloud. These adjustments were crucial in improving the accuracy of defect detection, ensuring that both dark and light scratches were properly distinguished from the background, and thus enhancing the overall detection performance. Overall, the experimental results demonstrate that our proposed method outperformed traditional techniques by providing a more robust and accurate detection framework, capable of handling a variety of defect types and surface conditions. First, let us examine the defect detection results based on the Nd. It is evident that this method was sensitive to edges and corners, which was due to the fact that during the neighbor search, the region within a boundary sphere of a fixed radius was examined. Edges and corners were prone to sudden changes, which could cause deviations to exceed the set threshold. Furthermore, for non-defective areas where data were missing, the surrounding points were spaced farther apart, creating larger differences, which made them more likely to be incorrectly identified as defects. This issue was largely attributable to the quality of the collected data. Importantly, for larger defects, this method only detected the approximate boundary of the defect. This was because the differences between neighboring points within the defect region were relatively small. In other words, this method could only serve as a rough localization of the defect but could not fully detect it and was prone to false positives. The defect detection results based on Cd were similar to those based on Nd. It also lacked robustness when detecting larger defects. However, it could detect more boundary points of the defect, as it was more sensitive to curvature. Additionally, its sensitivity to edges and corners was lower than that of Nd. Now, consider the method based on Mf. Its primary advantage was that it could detect both large and small defects, depending on the threshold set. However, it was not sensitive to cracks, as some cracks may simply be interrupted at certain points without involving significant changes in depth. Consequently, the residuals were minimal, and no matter how the threshold was set, such cracks could not be detected.