## 4 Experimental Results and Discussion
### Case Study of Defect Detection
Regarding the effectiveness of texture mapping, or more specifically, the efficacy of the proposed LPM algorithm, its best demonstration was the restoration of the original color of the magnetic tile, given that the point cloud itself lacked color information. As shown in the last column of Figure 17, we added the LPM algorithm on top of each method to detect light and dark scratches. These tiny scratches, which had almost no depth, exhibited a \begin{table}
\begin{tabular}{l l} \hline
**Method Name** & **Parameter Details** \\ \hline Statistical filtering & \(k=50,a=2.2\) \\ Adaptive neighborhood selection & \(r_{min}=0.1,r_{max}=0.2,\Delta_{r}=0.01,k\) adaptive \\ Normal vector deviation & \(a=3:r\): adaptive \\ Curvature deviation & \(\beta=15,k\) adaptive \\ Coarse detection and fine extraction & Corresponding to the top 5 th percentile and top 2 nd percentile, respectively. \\ DBSCAN clustering & \(minP_{ls}=40,e=0.16\) \\ \hline \end{tabular}
\end{table} 
Table 2: Details of the manually specified parameters required for the experiment. Figure 18: Threshold selection for light and dark scratches. significant color difference compared to the surrounding normal points. They were difficult to detect using Nd, Cd, or Mf, but we successfully extracted these defects based on color differences. However, it is worth noting that this method could only detect light and dark scratches with a very obvious change in brightness. Its robustness was relatively poor for more subtle scratches, as relying solely on luminance to color the point cloud was too simplistic. However, following the concept of this method, other color spaces such as hue, chroma, or saturation could be applied to the point cloud to provide more detailed color features. Since our equipment could only capture luminance-related information, we only used luminance to color the point cloud. Finally, we turn to the proposed hybrid approach, which effectively leveraged the strengths of individual methods while compensating for their respective shortcomings through their complementary nature. As seen in the Figure 17, the proposed method not only retained small defects but also significantly reduced the false positive rate. Additionally, the internal regions of larger defects were also fully extracted, demonstrating the feasibility of the method. To further evaluate its performance, we employed three evaluation metrics: _Precision_, _Recall_, and \(F1\)[88], which can be computed using the following formulas:  
\[Precision=\frac{TP}{TP+FP} \tag{24}\]  
\[Recall=\frac{TP}{TP+FN} \tag{25}\]  
\[F1=2\times\frac{Precision\times Recall}{Precision+Recall} \tag{26}\]  
where \(TP\) represents the number of correctly detected defects, \(FP\) denotes the number of false positives, and \(FN\) indicates the number of missed defects. We further validated the performance of the proposed method using the evaluation metrics from Equations (24)-(26), in conjunction with a custom magnetic-tile surface-defect point cloud dataset. This dataset contained 500 point cloud files, with 100 files each for minor defects, severe scratches, and light scratches, and 200 files for severe defects. Table 3 provides the detailed results of the proposed method and the individual methods across the three evaluation metrics. As seen in the table, the proposed method was effective in detecting severe defects, minor defects, and severe scratches, which was attributed to the two-step approach of coarse detection and fine extraction. The former provided candidate defect points, capturing potential defects, while the latter refined these points to filter out false positives, enabling the method to extract both large and small defects without the need for separate processes, thereby effectively capturing the entire defect region. In detecting shallow scratches, the method showed lower robustness, as the single luminance channel provided limited color information, leading to higher false positives and false negatives despite threshold adjustments.