# Intelligent Space Object Detection Driven by Data from Space Objects
## 3 Space Object Detection Algorithm Model
### RepPoints and ELAN-R  
As shown in Figure 9, RepPoint is a set of points that learns to position itself above the object flexibly, which restricts the spatial range of the object, representing the locally significant regions with important semantic information [37; 38; 39]. The training of RepPoint is jointly driven by object localization and detection, making it closely related to the ground-truth bounding boxes. Also, the detector is guided to correctly classify the objects. The bounding box is a four-dimensional representation purposed to encode the spatial position of the object, i.e., \(B=(x,\ y,\ w,\ h)\), where \(x\) and \(y\) represent the center point, while \(w\) and \(h\) represent the width and height, respectively. Modern object detectors rely on bounding boxes to represent the objects at various stages of the detection process. However, the four-dimensional bounding box allows the position of an object to be roughly represented, considering only the rectangular spatial extent of the object. However, this overlooks the information about the shape of the object, its pose, and the position of semantically important local areas, which enhances the accuracy of localization and improves the outcome of object feature extraction [40]. To overcome these limitations, RepPoints introduces a set of adaptive sample points for modeling [41], which is expressed as follows:  
\[\mathcal{R}=\{(x_{k},y_{k})\}_{k=1}^{n} \tag{1}\]  
where \(n\) represents the total number of sample points used for representation. The default value of \(n\) is set to 9. The learning of RepPoint is driven by both object localization loss and object detection loss. To calculate object localization loss, a transformation function \(\tau\) is first applied to convert RepPoints into pseudo-boxes. Then, the difference between the transformed pseudo-boxes and the ground-truth bounding boxes is computed as follows.  
\[R_{r}=\{(x_{k}+\Delta x_{k},y_{k}+\Delta y_{k})\}_{k=1}^{n} \tag{2}\]  
where \(\{\Delta x_{k},\Delta y_{k}\}_{k=1}^{n}\) represents the offsets. Unlike the inconsistency of scale in traditional bounding box regression parameters, all the offsets in the process of refining RepPoint are dealt with on the same scale. Thus, scale discrepancy is prevented. During training, annotation is required in the form of bounding boxes, and prediction is converted into the bounding box during evaluation. This requires the transformation of RepPoint into a bounding box. A predefined transformation function \(\tau\) is used to achieve this purpose: Rep-Bp, where Rp represents the RepPoint of an object P, and \(\tau\)(Rp) represents the pseudo-box. The transformation function \(T\) is used to perform a minimum-maximum operation along the two axes to determine Bp as follows.  
\[T=\left\{(max_{x}^{i}(R_{r}),min_{x}^{j}(R_{r})),(max_{y}^{k}(R_{r}),min_{y}^{ l}(R_{r}))\right\} \tag{3}\]  
where \(i,j,k\), and \(l\) represent the maximum and minimum points along the x-axis and the maximum and minimum points along the y-axis on \(R_{r}\), respectively, which is the bounding box over the sample points. By replacing the 3 \(\times\) 3 convolution kernel in the backbone with RepPoint, ELAN-R is obtained. In the core part, the original ELAN modules are still used. With these modifications, YOLOv7-R is created to enhance the capability of the model in terms of geometric deformation modeling [42], as shown in Figure 8a.