# Weak-Edge Extraction of Nuclear Plate Fuel Neutron Images at Low Lining Degree
## 4 Results and Discussion
\[FOM=\frac{1}{max(N_{e},N_{d})}\sum_{k=1}^{Nd}\frac{1}{\left(1+\beta d(k)^{2} \right)}, \tag{14}\]  
where \(N_{e}\) and \(N_{d}\) denote the number of edge pixels in the reference edge image and the actual extracted edge image, respectively; \(\beta\) is the scale constant, usually taken as \(1/9\); \(d(k)\) is the Euclidean distance between the \(k\)th actual edge pixel and the detected edge pixel. The FOM ranges between 0 and 1, and the closer the value is to 1, the higher the localization accuracy of edge pixels. Since there is currently neither an existing dataset of fuel plate neutron images nor a corresponding standard reference image of edges (i.e., ground truth image), we used the strong edge results extracted by Canny as the ground truth images. Specifically, the optimal Canny threshold is selected through multiple experiments to extract complete and continuous fuel element pellet edges, followed by morphological operations to remove the non-edge image information. The ground truth images of plate nuclear fuel elements obtained by Canny for FOM evaluation are shown in Figure 6. The calculated results are shown in Table 3. According to Table 3, we can see that the FOM of this method is a high 0.9443, which further proves that the edge extraction accuracy of our method is comparable to the Canny detection and performs well in detecting accurate edge pixels. To verify the effectiveness and generality of this algorithm for neutron images in weak edge detection. We add experimental tests on neutron images of zirconium alloy, rod fuel \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Image and Method**} & **A** & **B** & **C** & **C/A** & **C/B** \\ \hline fuel plate neutron & Canny & 48,539 & 5971 & 318 & 0.0066 & 0.0533 \\ image (left) & Sobel & 20,336 & 7786 & 2822 & 0.1388 & 0.3624 \\  & Ours & 6323 & 449 & 8 & 0.0013 & 0.0178 \\ \hline fuel plate neutron & Canny & 62,406 & 7508 & 407 & 0.0065 & 0.0542 \\ image (middle) & Sobel & 22,893 & 8316 & 3015 & 0.1317 & 0.3626 \\  & Ours & 5990 & 395 & 3 & \(5.0083\times 10^{-4}\) & 0.0076 \\ \hline fuel plate neutron & Canny & 39,835 & 4777 & 255 & 0.0064 & 0.0534 \\ image (right) & Sobel & 27,072 & 10,285 & 3713 & 0.1372 & 0.3610 \\  & Ours & 7490 & 724 & 12 & 0.0026 & 0.0166 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Result of edge evaluation method based on connection component for plate fuel neutron images. Figure 6: The ground truth images of plate nuclear fuel elements obtained by Canny for FOM evaluation: (**a**) left; (**b**) middle; (**c**) right. Figure 7 and Table 4 provide evidence that the edges detected by our algorithm are continuous and precise, with minimal noise or artifacts. In particular, it can extract the location and shape of weak boundaries more accurately, such as the zirconium alloy edges, fuel rod cladding, and internal details in the mechanical structural component, which are less broken or over-extended. Based on subjective and objective analysis, the proposed method achieves the best validated visual and statistical results against conventional edge detection approaches. It maintains the advantages of traditional algorithms and detects more low-intensity weak edges, which they cannot detect. Overall, the fact that the algorithm can perform well on different types of neutron images indicates that it has a certain level of robustness and flexibility.