## 3 The Proposed Method
### Multi-Attribute NMS  
Based on the analysis above, we propose a Multi-Attribute NMS (MA-NMS) algorithm that adaptively adjusts suppression based on density and count attributes. MA-NMS takes into account that the proposals whose bounding boxes have moderate overlap with their neighboring bounding boxes may still represent potentially occluded pedestrians. Therefore, instead of using absolute operations like discarding or retaining, MA-NMS applies suppression with weak intensity to provide protection. Specifically, for each pedestrian, MA-NMS refines the traditional single suppression interval into strong and weak suppression intervals to adaptively handle duplicate proposals and proposals belonging to occluded pedestrians. The division between the strong suppression interval (SSI) and weak suppression interval (WSI) is determined as follows:  
\[d_{i}:=\underset{b_{j}\in G,j\
eq j}{max}IoU\left(b_{i},b_{j}\right), \tag{2}\]  
\[N_{m}=max(d_{i},N_{t}), \tag{3}\]  
\[SSI=[N_{m},1], \tag{4}\]  
\[WSI=[N_{t},N_{m}), \tag{5}\]  
where \(N_{t}\) represents the rigid threshold used in Greedy NMS. The dynamic threshold \(N_{m}\) is consistent with Adaptive NMS, and is calculated using Equation (3). Within the SSI, numerous duplicate proposals that closely overlap with \(M\) are present, while only a few pedestrians occluded by \(M\) may be included. Therefore, strong suppression is applied within the interval to effectively remove duplicate proposals. In order to ensure the fair treatment of occluded pedestrians with different densities, the strong suppression weight function \(f_{s}\) incorporates the parameter \(N_{m}\), as shown in Equation (6). Within the WSI, there are a number of occluded pedestrians, along with a few duplicate proposals that are distant from the annotations. Hence, weak suppression is applied to preserve the potentially occluded pedestrians, while mildly penalizing duplicate ones as a complement to the strong suppression. The weak suppression weight function \(f_{w}\) is expressed in Equation (7). By utilizing both the strong and weak suppression, the re-scoring strategy of MA-NMS is described in Equation (8). \[f_{s}(M,b_{i},d_{M})=\left(\frac{iou(M,b_{i})}{N_{m}}\right)^{C_{1}}, \tag{6}\]  
\[f_{w}(M,b_{i},d_{M})=1-(IoU(M,b_{i})-N_{t}), \tag{7}\]  
\[s_{i}=\left\{ \begin{array}{l}s_{i},IoU(M,b_{i})<N_{t},\\ s_{i}f_{w}(M,b_{i},d_{M}),N_{t}\leq IoU(M,b_{i})<N_{m},\\ s_{i}f_{s}(M,b_{i},d_{M}),IoU(M,b_{i})\geq N_{m},\end{array} \right. \tag{8}\]  
where \(C_{1}\) is a constant, and the experiments show that the detector achieves optimal performance when a value of 4 is used. Additionally, we note that the count of surrounding occluded pedestrians varies greatly between pedestrians, particularly for pedestrians located at the edge of the crowd and those in the center. For a given pedestrian, if all the occluded pedestrians surrounding them have been retained, the remaining proposals within the occluded pedestrian's strong and weak suppression intervals would only be duplicates. In order to further remove duplicate proposals, MA-NMS takes into account the count attribute. Based on the count attribute, the suppression intensity within each interval is adjusted using the suppression factors. By considering both density and count attributes, MA-NMS can be described using Algorithm 1. The re-scoring function of MA-NMS is expressed in Equation (9). \[s_{i}=\left\{ \begin{array}{l}s_{i},IoI(M,b_{i})<\text{N}_{t},\\ s_{i}f_{w}(M,b_{i},d_{M},c_{i}),N_{t}\leq IoI(M,b_{i})<N_{m},\\ s_{i}f_{s}(M,b_{i},d_{M},c_{i}),IoI(M,b_{i})\geq N_{m},\end{array} \right. \tag{9}\]  
\[f_{w}(M,b_{i},d_{M},c_{i})=\left(f_{w}(M,b_{i},d_{M})\right)^{x}, \tag{10}\]  
\[f_{s}(M,b_{i},d_{M},c_{i})=\left(f_{s}(M,b_{i},d_{M})\right)^{y}, \tag{11}\]  
where \(c_{i}\) is the count attribute of the \(i\)th pedestrian and represents the count of surrounding pedestrians occluded by them. Specifically, \(x\) and \(y\) are suppression factors, which are initially set to 1.