# AuxDepthNet: Real-Time Monocular 3D Object Detection with Depth-Sensitive Features
## 3 Proposed Method
### Depth-Sensitive Feature Enhancement
#### 3.2.1. Backbone Network Architecture and Multi-Scale Feature Extraction  
Figure 4 illustrates the changes in input image size and channel dimensions as the Backbone processes the input. We assume that the input image has a resolution of \(1280\times 288\times 3\) (\(height\times width\times channels\)). In the first layer of the Backbone, the image undergoes an initial convolution operation, resulting in a feature map with a size of \(640\times 144\times 16\). As the network progresses, the spatial dimensions of the feature map gradually decrease, while the number of channels increases. Specifically, at Level 0, the feature map retains the same size of \(640\times 144\times 16\), but at Level 1, after downsampling, the feature map size reduces to  
Figure 3. Architecture of the Auxiliary Depth Feature Module. (**a**) Generate the initial depth-sensitive feature \(F_{init}\) and determine the depth distribution \(P_{depth}\). (**b**) P [d] represents the feature representation of the depth prototype. (**c**) The depth prototype enhanced feature \(F_{enhanced}\) is generated and fused with \(F_{init}\).  
\(320\times 72\times 32\). Further down the network, the feature map dimensions continue to shrink while the channel depth continues to grow. At Level 2, the output is \(160\times 36\times 128\), at Level 3 it is \(80\times 18\times 256\), at Level 4 it is \(40\times 9\times 512\), and finally, at Level 5, the feature map size becomes \(20\times 5\times 1024\). This process demonstrates the gradual extraction of deeper features from the image through successive downsampling and convolution operations.  
Additionally, the DLA-102\(\times\) network includes a feature aggregation module, which fuses feature maps from different layers. Through this aggregation process, the final output feature map has a size of \(320\times 72\times 256\), containing information from multiple scales that enhances the subsequent depth-sensitive feature extraction process.  
Mathematically, let the input image \(I\) have a size of \(H\times W\times 3\); the Backbone network first applies convolution to produce an initial feature map \(F_{0}\):  
\[F_{0}=Backbone(I),\ F_{0}\in R^{\text{C}_{0}\times H_{0}\times W_{0}} \tag{1}\]  
where \(C_{0}\) is the number of channels in the feature map, and \(H_{0},W_{0}\) are the spatial dimensions after convolution and pooling. As the network deepens, each layer generates deeper feature representations through convolution operations and downsampling, gradually reducing the spatial dimensions and increasing the number of channels. After n layers, the feature map's size and channels become the following:  
\[F_{n}=Backbone_{n}(F_{n-1}),\ F_{n}\in R^{\text{C}_{n}\times H_{n}\times W_{n}} \tag{2}\]  
Finally, after the feature aggregation module, the resulting feature map \(F_{aggregated}\) has the following dimensions:  
\[F_{aggregated}\in R^{\text{C}_{aggregated}\times H_{aggregated}\times W_{ aggregated}} \tag{3}\]  
This aggregated feature map serves as the foundation for subsequent depth-sensitive feature extraction, providing rich visual information for depth estimation and object detection tasks. This input-output definition not only provides clear guidance for understanding the feature extraction process in the Backbone but also forms a solid foundation for extracting depth-sensitive features, ensuring the success of the subsequent tasks.