# Monocular Depth Estimation Based on Dilated Convolutions and Feature Fusion
## 3 Method Design and Implementation
### Multi-Receptive Field Feature Fusion  
The design of the multi-receptive field feature fusion module draws inspiration from the FPN architecture commonly used in object detection tasks. FPN enhances the detection accuracy of small objects through the integration of feature maps from various scales at the channel level. The multi-receptive field feature fusion module proposed in this study comprises two components: dilated convolution and channel-level feature fusion. By enlarging the effective receptive field of the convolution kernel and creating a multi-scale feature representation pyramid, this module improves the network's capacity to capture contextual semantic information and its sensitivity to detailed features.  
The specific structure is depicted in Figure 6. First, the input feature map \(\chi\) undergoes convolution by applying a \(1\times 1\) convolution kernel, resulting in the feature map \(\chi_{1}\). Next, the input feature map \(\chi\) undergoes convolution by applying a \(3\times 3\) dilated convolution kernel with a dilation rate of 6, resulting in the feature map \(\chi_{2}\). Then, a \(3\times 3\) dilated convolution kernel with a dilation rate of 12 is applied to \(\chi\) to obtain the feature map \(\chi_{3}\). Likewise, a \(3\times 3\) dilated convolution kernel with a dilation rate of 18 is applied to the input feature map \(\chi\) to generate the output feature map \(\chi_{4}\). The feature maps \(\chi_{1}\), \(\chi_{2}\), \(\chi_{3}\), and \(\chi_{4}\) are subsequently concatenated at the channel level to produce the feature map \(\gamma\). Finally, the feature map \(\gamma\) is subjected to \(1\times 1\) convolution and upsampling operations to generate a prediction outcome that aligns with the dimensions of the input image data. In this procedure, the \(1\times 1\) convolutional operation modifies the channel dimensions of the resulting feature map to align with the predetermined number of predicted classes, which is established as 240 in this study. The process of upsampling is implemented to guarantee that the resultant feature map aligns with the dimensions of the input image, which have been specified as \(640\times 480\) in this study. The convolutions utilized in the multi-receptive field feature fusion module are exclusively dilated convolutions. Dilated convolutions enhance the effective receptive field of the convolutional kernel compared to standard convolutions by employing varying dilation rates. This approach reduces the parameter count while preserving resolution.  
During the feature fusion stage, the feature maps with varying receptive fields are combined with the original feature map at the channel level. This process results in a feature map that encompasses both low-level detailed features and high-level contour information. This augmentation enhances the network model's capability to extract features from targets of varying scales and increases its sensitivity to intricate information.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Network Layer** & **Convolutional Architecture** & **Output Channel** & **Output Size** \\ \hline \multirow{2}{*}{CON1} & \(7\times 7\) conv, stride 2 & \multirow{2}{*}{64} & \multirow{2}{*}{\(160\times 120\)} \\  & \(3\times 3\) max pool, stride 1 & & \\ \hline \multirow{2}{*}{DEN1} & \(\begin{pmatrix}1\times 1&\text{conv}\\ 3\times 3&\text{conv}\end{pmatrix}\times 3\) & \multirow{2}{*}{256} & \multirow{2}{*}{\(160\times 120\)} \\  & \(1\times 1\) conv & & \\  & \(2\times 2\) max pool, stride 2 & & \\ \hline \multirow{2}{*}{DEN2} & \(\begin{pmatrix}1\times 1&\text{conv}\\ 3\times 3&\text{conv}\end{pmatrix}\times 6\) & \multirow{2}{*}{512} & \multirow{2}{*}{\(80\times 60\)} \\  & \(1\times 1\) conv & & \\  & \(2\times 2\) max pool, stride 2 & & \\ \hline \multirow{2}{*}{DEN3} & \(\begin{pmatrix}1\times 1&\text{conv}\\ 3\times 3&\text{conv}\end{pmatrix}\times 12\) & \multirow{2}{*}{1024} & \multirow{2}{*}{\(40\times 30\)} \\  & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Configurations of DNET backbone.