# Dual-Kernel-Based Aggregated Residual Network for Surface Defect Inspection in Injection
## 4 Case Study
The experiment was performed 10 times, and the average TPR, TNR, and accuracy are presented in Table 7. We compared the proposed models (PE-ResNeXt-\(101(32\times 8\mathrm{d})\) and DF-ResNeXt-\(101\ (32\times 8\mathrm{d})\)) with ResNeXt-\(101\ (32\times 8\mathrm{d})\) and Deformable ConvNet V2. DF-ResNeXt-\(101\ (32\times 8\mathrm{d})\) exhibited the highest classification accuracy of 98.5%, while PE-ResNeXt-\(101\ (32\times 8\mathrm{d})\) had an accuracy of 97.8%. All four models tend to have a slightly higher TNR than TPR, which means that the sensitivity of the model is slightly lower than the specificity. Figure 10 shows the average accuracy and standard deviation of each model. The model with the highest variability was PE-ResNeXt-\(101\ (32\times 8\mathrm{d})\). The standard deviation was 0.7898, which was significantly higher than other models. The model with the smallest variability was DF-ResNet-\(101\ (32\times 8\mathrm{d})\). The standard deviation was the lowest at 0.3444, but there was no significant difference with ResNeXt-\(101\ (32\times 8\mathrm{d})\) and Deformable ConvNet V2. The standard deviations of ResNeXt-\(101\ (32\times 8\mathrm{d})\) and Deformable ConvNet V2 are 0.4115 and 0.5332, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Criteria** & **Front** & **Back** & **Side** & **Head** & **Tail** \\ \hline Black spot & FB & BB & SB & HB & TB \\ \hline Short shot & FS & BS & SS & HS & TS \\ \hline Cutting & FC & BC & SC & HC & TC \\ \hline Nondefect & FN & BN & SN & HN & TN \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Output classes of PE-ResNeXt. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Criteria (\%)** & \begin{tabular}{c} **DF-ResNeXt-** \\ **101**\((32\times 8\mathrm{d})\) \\ \end{tabular} & \begin{tabular}{c} **PE-ResNeXt-101** \\ \((32\times 8\mathrm{d})\) \\ \end{tabular} & \
\begin{tabular}{c} **ResNeXt-101** \\ \((32\times 8\mathrm{d})\) \\ \end{tabular} &
\begin{tabular}{c} **Deformable** \\ **ConvNet V2** \\ \end{tabular} \\ \hline TPR & 97.4 & 96.6 & 92.3 & 85.3 \\ \hline TNR & 100 & 99.0 & 95.0 & 93.6 \\ \hline Accuracy & 98.5 & 97.8 & 94.6 & 91.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experimental results for the case study. Figure 9: DK-ResNeXt used for the case study. The most frequent error in this case study was to classify black spots as short shots. The black spots used in the experiment can be defined as a normal spot, smeared spots, and crack spot, as shown in Figure 11. Normal spots were classified with excellent accuracy in most experiment cases, but smeared spots and crack spots were occasionally classified as short shots. In particular, a case in which crack spots were classified as short shots occurred in the DK-ResNeXt-101 (\(32\times 8\)d) experiment. We assumed that cropping and feeding of the DK-ResNeXt-101 (\(32\times 8\)d) could be a drawback that causes misclassification of the black spot and short shot (see Figure 12). Further research should identify and analyze this drawback that may arise from the interactions of the multimodal. Even though one of our models proposed in this study (i.e., DF-ResNeXt-101 (\(32\times 8\)d)) gave the highest classification accuracy compared to other models, it is not enough to apply the model to the real production process immediately. The DAGM dataset has clearly independent background textures and types of defects for each class. Defects in real injection-molded products, however, may occur on all sides of the product. PE-ResNeXt occasionally does not classify accurate locations (front, back, side, head, or tail) of defects and only identifies the type of defects. Therefore, the classification performance of the model using real product data is slightly lower than that using DAGM data. The methodology proposed in this study, however, has the potential to be improved via a detailed analysis of defect types and locations or strategies of data acquisition.