## 3 Proposed Method
### Distortion Correction Network
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layers (Size, Kernel Size, Stride)** & **Step** & **Type** & **Input** & **Output** \\ \hline ImageInputLayer (\(408\times 568\)) & - & & 1 & 64 \\ Conv\_Relu (\(7\times 7\),\(1\)) & - & Pad (same) & 64 & 64 \\ Max\_Pooling & Block\_1 & Pad (0) & 64 & 64 \\ \({}^{*}\)Conv\_Relu\_Block\_1 (\(5\times 5\),\(1\)) & Block\_((1\)–\(2\)) & Pad (same) & 64–\(128\) & 64–\(128\) \\ Conv\_Relu\_Block\_1 (\(5\times 5\),\(1\)) & Block\_((1\)–\(2\)) & Pad (same) & 64–\(128\) & 64–\(128\) \\ Conv\_Relu\_Block\_1 (\(5\times 5\),\(1\)) & Block\_((1\)–\(2\)) & Pad (same) & 64–\(128\) & 64–\(128\) \\ Drop\_Out (\(204\times 284\)) & Block\_2 & \(50\%\) & 128 & 128 \\ Max\_Pooling (\(102\times 142\)) & Block\_2 & Pad (0) & 256 & 256 \\ Conv\_Relu\_Bridge (\(5\times 5\),\(1\)) & Bridge & Pad (same) & 256 & 256 \\ Conv\_Relu\_Bridge (\(5\times 5\),\(1\)) & Bridge & Pad (same) & 256 & 256 \\ Drop\_Out & Bridge & \(50\%\) & 256 & 256 \\ \({}^{*}\)TransConv\_UpRelu(\(2\times 2\),\(2\)) & Block\_((3\)–\(4\)) & Crop (0,0) & 128–\(64\) & 128–\(64\) \\ Conv\_Relu\_Bridge (\(5\times 5\),\(1\)) & Block\_((3\)–\(4\)) & Pad (same) & 128–\(64\) & 128–\(64\) \\ Conv\_Relu\_Bridge (\(5\times 5\),\(1\)) & Block\_((3\)–\(4\)) & Pad (same) & 128–\(64\) & 128–\(64\) \\ Conv\_Relu\_(3\times 3\),\(1\)) & - & Pad (same) & 64 & 1 \\ Final\_Reg\_Out & - & & 1 & Pixel-Pr \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The detailed structure of the distortion correction network. Tag * means that the convolution information there was extracted, then directly superimposed with the information of the symmetric transposed convolution channel, and finally fused by convolution. Figure 5: Diagram of the distortion correction network. Blue(Conv) represents the convolution layer, yellow(TransConv) represents the transposed convolution layer, and red and orange(Relu) represent the corresponding activation functions. directions. To reduce the influence of outliers, we used the Charbonnier penalty \(\rho(x)=\left(x^{2}+\epsilon^{2}\right)^{\alpha}\). \(h\) and \(\omega\) are the height and width of the images (\(l_{1}\) and \(l_{2}\)), respectively. Because most of the distortion will cause a non-closed interval, we used the smoothness loss to manage the aperture problem that caused ambiguity in estimating details of the distortion in non-textured regions. It was calculated using:  
\[L_{smooth}=\rho(\
abla V_{x}^{x})+\rho\Big{(}\
abla V_{y}^{x}\Big{)}+\rho \Big{(}\
abla V_{x}^{y}\Big{)}+\rho\Big{(}\
abla V_{y}^{y}\Big{)}, \tag{3}\]  
where \(\
abla V_{x}^{x}\) and \(\
abla V_{y}^{x}\) are the gradients of the estimated \(V^{x}\) in each direction, and \(\
abla V_{x}^{y}\) and \(\
abla V_{y}^{y}\) are the same as \(V^{y}\). By comparing the characteristic graphs \(I_{1n}\) and \(I_{1n}\) before and after the partition reconstruction, we can know the degree of correction within the network. Finally, we combined several loss functions to form an objective function, as shown in Equation (4):  
\[L_{S}=L_{pixel}+L_{smooth} \tag{4}\]  
In order to evaluate the distortion performance of the system, we used the image similarity coefficient as the reference index. For this similarity evaluation, we used a comparison parameter to evaluate the reconstruction quality. \(SSIM\) represents the structural similarity between the target and the predicted image [22], as follows:  
\[SSIM\Big{(}I_{p1},I_{p2}\Big{)}=\frac{\Big{(}2\mu_{p1}\mu_{p2}+c_{1}\Big{)} \Big{(}2\sigma_{p1p2}+c_{2}\Big{)}}{\Big{(}\mu_{p1}^{2}+\mu_{p2}^{2}+c_{1} \Big{)}\Big{(}\sigma_{p1}^{2}+\sigma_{p2}^{2}+c_{2}\Big{)}}. \tag{5}\]  
To calculate the efficiency, we split and compared the whole graph, and finally obtained the similarity coefficients, where \(\mu_{p1}\) and \(\mu_{p2}\) are the mean values of the input images. \(\sigma_{p1}\) and \(\sigma_{p2}\) are the variance of the images, and \(\sigma_{p1p2}\) is the covariance of these inputs.