## 3 The Proposed Model
### Training Loss  
**Image-Reconstruction Loss:** Figure 1 shows several loss functions required for training. The network is trained to generate a disparity map used to synthesize an input as closely as possible to the target. The image-reconstruction loss refers to the numerical difference between the reconstructed and target images, which is similar to the role of IQA algorithms. Therefore, if an IQA algorithm as a loss function could accurately quantify the differences between images, the accuracy of the disparity map could be increased by gradually decreasing this value. PieAPP [11], one of the learning-based IQA algorithms,  
Figure 1: Illustration of the detailed framework and loss functions for the proposed unsupervised depth-estimation model. (\(l_{l}\): left image, \(l_{l}\): right image, \(d_{l}\): disparity map to warp left, \(d_{l}\): disparity map to warp right, \(w_{+}\): warping right, \(w_{-}\): warping left, \(l_{l}\): reconstructed left image, \(\hat{l}_{r}\): reconstructed right image, \(L^{L1}\): L1 loss between the reconstructed and target images, \(L^{Diapp}\): PieAPP loss between the reconstructed and target images, \(L^{Con}\): left-right consistency loss, \(L^{Smoothness}\): smoothness loss). shows great performance in the IQA field. As compared to manual methods, the PieAPP model learned to mimic the complexity of human visual systems. While there are other learning-based studies that train on human-labeled datasets, they have difficulties in obtaining large, high-quality datasets. The authors of PieAPP presented a new dataset for a pairwise learning framework that compares two given images and identifies them according to their similarity to a reference, which could be used to achieve better performance. We trained our network under the assumption that using this excellent IQA algorithm as the main loss function \(L^{pienapp}\) would contribute to increasing the whole performance. L1 loss \(L^{L1}\) is added to compensate for the quality of the reconstructed image and is used to minimize the absolute pixel-wise distance between the reconstructed and target images. Altogether, the image-reconstruction loss \(L^{rec}\) is defined as:  
\[L_{r}^{pienapp}=\sum||P(I_{r}^{f,m,c})-P(\hat{I}_{r}^{f,m,c})|| \tag{1}\]  
\[L_{l}^{pienapp}=\sum||P(I_{l}^{f,m,c})-P(\hat{I}_{l}^{f,m,c})|| \tag{2}\]  
\[L^{pienapp}=L_{r}^{pienapp}+L_{l}^{pienapp} \tag{3}\]  
\[L_{r}^{L1}=\sum||I_{r}^{f,m,c}-f_{w_{+}}(d_{l}^{f,m,c},I_{l}^{f,m,c})|| \tag{4}\]  
\[=\sum||I_{r}^{f,m,c}-I_{r}^{f,m,c}|| \tag{5}\]  
\[L_{l}^{L1}=\sum||I_{l}^{f,m,c}-\hat{I}_{l}^{f,m,c}|| \tag{6}\]  
\[L^{rec}=\alpha*L^{pienapp}+(1-\alpha)*L^{L1}, \tag{7}\]  
where \(P()\), \(f_{w_{+}}\), and \(f_{w_{-}}\) represent the pre-trained PieAPP model [33], right-warping function, and left-warping function, respectively. \(\alpha\) in Equation (7) represents the weight ratio of the \(L^{L1}\) loss and \(L^{pienapp}\) loss among the total image-reconstruction loss, and it is optimally pre-determined through experiments. **Left-Right Consistency Loss:** Additionally, we employed the left-right consistency loss from [PERSON] et al. [6] to reinforce the consistency between the left-to-right disparity map \(d_{left2 right}\) and the right-to-left disparity map \(d_{right2 left}\).