# DBCAN: DFormer-Based Cross-Attention Network for RGB Depth Semantic Segmentation
## 3 Methodology
### Feature-Region Relation Module  
The Feature-Region Relation Module (FRRM) is designed to enhance the representation of RGB and depth features in the target classification regions by integrating features and incorporating attention mechanisms. Initially, the module projects multi-stage features into a unified feature space to ensure effective fusion. Attention mechanisms are then applied to model the relationship between features and target regions, dynamically adjusting feature weights to improve classification accuracy. Finally, through further fusion, the FRRM strengthens the connection between semantic features and classification regions, resulting in more precise feature representation. FRRM consists of three components: the Feature Projector, Feature-Region Attention, and Feature-Region Fusion. In this model, the FRRM independently processes RGB and spatial features in parallel. The Feature Projector is responsible for projecting the concatenated features from multiple stages into a new feature space. The Feature-Region Attention and Feature-Region Fusion components work together to enhance the attention of RGB (or spatial) features towards the classification region, thereby improving the predictive capability of the features. When specifically referring to this module for RGB or spatial features, we use the terms RFRRM (RGB Feature-Region Relation Module) or SFRRM (Spatial Feature-Region Relation Module), respectively. The specific details of this module are illustrated in Figure 2. Initially, we input \(f_{r1}\) and \(f_{s1}\) into two parallel Feature Projectors to obtain new feature maps. Subsequently, multiple attention operations are performed on these new feature maps and \(f_{org}\) to strengthen the relationship between semantic (or spatial) features and the object region. Since RGB and depth features are processed separately in these two modules, for convenience, we will focus on explaining them using RGB features only. The feature \(f_{r1}\) is generated through concatenation, resulting in its information being distributed across three different feature spaces. To integrate this information into a unified feature space, we propose the Feature Projector Module. This operation can be expressed as follows:  
\[f_{r2}=\phi(f_{r1}) \tag{2}\]  
where \(\phi()\) represents a transformation function and \(f_{r2}\in R^{512\times h\times\upsilon}\). This step aims to extract the output \(f_{s1}\) and project features from different spaces into a unified space, facilitating their integration. Following this, \(f_{r2}\) contains rich fused semantic information. However, we further consider enhancing the connection between features and object classification regions. To ad  
Figure 2: Feature-Region Relation Module. dress this, the Feature-Region Attention Module has been designed. The operation can be expressed as:  
\[f_{r2^{\prime}}=View(f_{r2}),f_{r2^{\prime}}\in R^{512\times hw} \tag{3}\]  
\[f_{org^{\prime}}=Softmax(Permute(View((f_{org}))), \tag{4}\]  
\[f_{org^{\prime}}\in R^{hw\times k}\]  
\[F_{attn}=Permute(f_{org^{\prime}}f_{s2^{\prime}}),F_{attn}\in R^{512\times k} \tag{5}\]  
The \(View()\) operation is used to reshape the feature sizes of \(f_{r2}\) and \(f_{org}\) from \(R^{512\times h\times w}\) and \(R^{k\times h\times w}\) to \(R^{512\times hw}\) and \(R^{k\times hw}\), respectively. In the subsequent steps, \(f_{org}\) is permuted to change the feature dimension to \(R^{hw\times k}\), followed by applying the \(Softmax\) operation on \(f_{org}\) to obtain the attention scores for each feature point corresponding to the object regions. The attention scores are then used in a matrix multiplication operation with \(f_{r2}\) to obtain the attention given by the RGB features to each object region. Finally, the resulting feature is permuted to obtain \(F_{attn}\) with dimensions \(R^{512\times k}\). The Feature-Region Attention Module enhances the connection between RGB features and the object regions, resulting in the classification region feature \(F_{attn}\).