# A Progressive Semantic-Aware Fusion Network for Remote Sensing Object Detection
## 3 Proposed Method
### Auxiliary Dynamic Loss Function  
IoU loss [38] accurately quantifies the spatial congruence between detected region proposals and their corresponding ground-truth annotations, enabling the model to capture spatial localization details during training. Serving as a key element in widely used loss functions used for bounding box prediction, IoU is defined as follows:  
\[\text{IoU}=\frac{A\cap B}{A\cup B} \tag{20}\]  
where IoU loss, which quantifies the overlap between the predicted bounding box (A) and the ground truth (B), is defined as follows:  
\[L_{IoU}=1-IoU \tag{21}\]  
To date, loss functions based on IoU have increasingly become the standard approach, with most approaches incorporating additional loss terms on top of IoU. Generalized IoU (GIoU) [39] addresses the issue of zero gradients when two bounding boxes do not overlap. Distance IoU (DIoU) [40] considers not only the overlap between two boxes but also their relative distance and scale. However, the aspect ratio, one of the three key factors in bounding box regression, has not yet been explicitly accounted for in the loss function. This was later introduced by Complete IoU (CIoU) [41], which incorporates both the overlap and shape similarity between two bounding boxes by considering their aspect ratio. In remote sensing images, the wide range of object sizes presents difficulties for conventional IoU-based methods. Inner-IoU [42] alleviates this issue by introducing supplementary bounding boxes of different sizes to calculate the loss, which is adaptively based on different regression samples. This approach inspired us to explore dynamically adjusting specific loss terms to better accommodate objects of different scales. Scale-awareDistance IoU (SDIoU) [43] achieves this by dynamically adjusting the influence of object size on scale and localization losses, thereby improving the model's capability in detecting objects across multiple scales. Inspired by these advancements, we propose an auxiliary dynamic IoU Loss (ADIoU Loss), which integrates scale-adaptive IoU computation with auxiliary bounding boxes to optimize the bounding box alignment mechanism while improving target localization precision. The ADIoU loss function is formulated as follows:  
\[\mathcal{L}_{1} =1-IoU^{linear}+\alpha v,\quad\mathcal{L}_{2}=\frac{\rho^{2}(b_{p},b_{gt})}{c^{2}} \tag{22}\] \[R_{\text{OC}} =\frac{w_{o}\times h_{o}}{w_{c}\times h_{c}}\] (23) \[\beta_{B} =\min\biggl{(}\frac{B_{gt}}{B_{gt\max}}\times R_{\text{OC}}\times \delta,\delta\biggr{)}\] (24) \[\beta_{M} =\min\biggl{(}\frac{M_{gt}}{M_{gt\max}}\times R_{\text{OC}}\times \delta,\delta\biggr{)}\] (25) \[\beta_{\mathcal{L}_{1}} =1-\delta+\beta_{B},\quad\beta_{\mathcal{L}_{2}}=1+\delta-\beta_ {B}\] (26) \[\mathcal{L}_{AD} =\beta_{\mathcal{L}_{1}}\times\mathcal{L}_{1}+\beta_{\mathcal{L} _{2}}\times\mathcal{L}_{2} \tag{27}\]  
where the \(IoU^{linear}\) metric quantifies spatial alignment precision, while parameter \(v\) regulates aspect ratio consistency between predicted and annotated targets. Spatial displacement metric \(\rho(.)\) calculates the Euclidean distance separating the geometric centers of detected bounding boxes and their annotated references. The \(R_{\text{OC}}\) encodes scale correspondence between input imagery and feature representations, computed as the ratio of original image dimensions to current feature map resolutions. \(B_{b}\) and \(B_{m}\) are the influence coefficients for the bounding box and the mask mentioned in SDIoU. According to SDIoU, \(B_{gt\max}=M_{gt\max}=81\) is the maximum size defined by the Optical Instrument Engineers Association ([PERSON], [PERSON], and [PERSON], 2003) [44]. Loss modulation parameters dynamically adjust based on target bounding area, with variation bounds controlled by hyperparameter \(\delta\), \(\beta_{\mathcal{L}_{1}}\) and \(\beta_{\mathcal{L}_{2}}\) are the influence factors for \(\mathcal{L}_{1}\) and \(\mathcal{L}_{2}\), respectively.