## 3 Proposed Method
### Multi-Receptive Field Fusion-Based Network (MRFFN)
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Layers** & **Filter Size/Stride** & **Output Size** & **Depth** & **1 \(\times\) 1** & **3 \(\times\) 3 Reduce** & **3 \(\times\) 3** & **5 \(\times\) 5 Reduce** & **5 \(\times\) 5** \\ \hline Input & - & 224 \(\times\) 224 \(\times\) 3 & - & - & - & - & - & - \\ Conv 1 & 7 \(\times\) 7/2 & 112 \(\times\) 112 \(\times\) 64 & 1 & - & - & - & - & - \\ M. Pool 1 & 3 \(\times\) 3/2 & 56 \(\times\) 56 \(\times\) 64 & 0 & - & - & - & - & - \\ Conv 2-reduce & 3 \(\times\) 3/1 & 56 \(\times\) 56 \(\times\) 64 & 1 & - & - & - & - & - \\ Conv 2 & 3 \(\times\) 3/1 & 56 \(\times\) 56 \(\times\) 192 & 1 & - & - & - & - & - \\ M. Pool 2 & 3 \(\times\) 3/2 & 28 \(\times\) 28 \(\times\) 192 & 0 & - & - & - & - & - \\ Inception 3a & - & 28 \(\times\) 28 \(\times\) 256 & 2 & 64 & 96 & 128 & 16 & 32 \\ Inception 3b & - & 28 \(\times\) 28 \(\times\) 480 & 2 & 128 & 128 & 192 & 32 & 96 \\ M. Pool 3 & 3 \(\times\) 3/2 & 14 \(\times\) 14 \(\times\) 480 & 0 & - & - & - & - & - \\ Inception 4a & - & 14 \(\times\) 14 \(\times\) 512 & 2 & 192 & 96 & 208 & 16 & 48 \\ Inception 4b & - & 14 \(\times\) 14 \(\times\) 512 & 2 & 160 & 112 & 224 & 24 & 64 \\ Inception 4c & - & 14 \(\times\) 14 \(\times\) 512 & 2 & 128 & 128 & 256 & 24 & 64 \\ Inception 4d & - & 14 \(\times\) 14 \(\times\) 528 & 2 & 112 & 144 & 288 & 32 & 64 \\ Inception 4e & - & 14 \(\times\) 14 \(\times\) 832 & 2 & 256 & 160 & 320 & 32 & 128 \\ M. Pool 4 & 3 \(\times\) 3/2 & 7 \(\times\) 7 \(\times\) 832 & 0 & - & - & - & - & - \\ Inception 5a & - & 7 \(\times\) 7 \(\times\) 832 & 2 & 256 & 160 & 320 & 32 & 128 \\ Inception 5b & - & 7 \(\times\) 7 \(\times\) 1024 & 2 & 384 & 192 & 384 & 48 & 128 \\ Average Pool & 7 \(\times\) 7/1 & 1 \(\times\) 1\(\times\) 1024 & 0 & - & - & - & - & - \\ Dropout & - & 1 \(\times\) 1\(\times\) 1024 & 0 & - & - & - & - & - \\ FC & - & 1 \(\times\) 1 \(\times\) 1000 & 1 & - & - & - & - & - \\ Softmax & - & 1 \(\times\) 1 \(\times\) 1000 & 0 & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The details of the pre-trained GoogLeNet structure. Figure 3: The overall framework of the proposed method. First, the original images are decomposed by the Gaussian pyramid. Then, level 0 and level 1 are trained individually by the low-level and high-level images. Lastly, the confidence scores of both networks are fused to obtain the final result. original network is replaced with a new fully connected layer that has the same output as the NEU dataset classes. Lastly, the final prediction scores can be derived by fusing both the level 0 and level 1 network prediction results using the equation below:  
\[s_{i}= \begin{cases}0.6\psi_{i}^{0}+0.4y_{i}^{1}&s_{top1}=s_{top2}\\ 0.5y_{i}^{0}+0.5y_{i}^{1}&\textit{otherwise}\end{cases}  \tag{3}\]  
where \(s_{top1}\) and \(s_{top2}\) indicate the highest and the second-highest predictions scores on the arbitrary testing image, and \(y_{i}^{0}\) and \(y_{i}^{1}\) indicate the probabilities of the class \(i\) defect according to level 0 and level 1 models, respectively. In order to avoid \(s_{i}\) contains two highest prediction scores, the weights of level 0 and level 1 models are set as 0.6 and 0.4, while \(s_{top1}\) and \(s_{top2}\) are the same, and the explanation will be shown in Section 5.2.