## 4 Experimental Results and Analyses
### Comparison with Other Methods
#### 4.2.4 Experiments on the PUCPR+ Dataset  
On the PUCPR+ dataset, we compared MS-WFFNet with the mainstream vehicle counting methods proposed in recent years, and the detailed results are shown in Table 6. RAQNet combines quantum calibration technology with innovatively designed quantum attention units to globally calibrate input features. With its innovative network architecture and optimization strategy, it achieves the lowest MAE and RMSE of 1.7 and 2.5, respectively. RPNet follows closely, using plant attention modules and joint loss functions to achieve accurate counting effects, with an MAE and RMSE of 3.1 and 3.8, respectively.  
Our model achieves third place with an MAE of 3.2 and an RMSE of 3.8, performing comparably to RPNet but still showing a noticeable gap compared to RAQNet. This discrepancy may stem from the inherent limitations of density map-based methods when handling specific object morphologies in this dataset. The density map is constructed by diffusing the center point of each object (value of 1) into a square area with a sum of 1 using a Gaussian kernel. However, most vehicles in this dataset exhibit rectangular shapes. When  
Figure 9: Visualization results of the various methods on the URCAL dataset.  
an adaptive Gaussian kernel is applied to define the diffusion range, the resulting Gaussian area may fail to fully encompass the shape of some vehicles, particularly those under severe occlusion. Consequently, the features of these vehicles are not entirely captured, hindering the model's performance in scenarios with complex occlusions. This limitation likely contributes to the observed performance gap between our method and RAQNet.  
As shown in Figure 10, we selected four representative images from the PUCPR+ dataset to compare the prediction effects of MS-WFFNet and other mainstream counting algorithms. The first and second columns in the figure show the original image and the corresponding GT density map, respectively, and the following five columns show the prediction results of MS-WFFNet, RPNet, FIDTM, CSRNet, and MCNN. As can be seen from the first and second rows, the performance of MS-WFFNet, RPNet, and MCNN are all affected to a certain extent under the interference of leaves and grass. This is especially true for MCNN, because it pays the same attention to the pixel values of the object and background and is most significantly affected, resulting in a significant increase in the number of false detections. It is worth mentioning that although the overall performance of FIDTM is slightly inferior to our method, its visual dot plot results perform well, which shows that its dot plot supervision strategy has strong practicability in specific scenarios. We plan to introduce point-map supervision in subsequent work to further improve the model's performance in counting tasks and its ability to adapt to complex backgrounds.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Venue** & **MAE** & **RMSE** \\ \hline MCNN [35] & CVPR 2016 & 21.9 & 29.5 \\ CSRNet [48] & CVPR 2018 & 8.7 & 10.2 \\ BL [59] & ICCV 2019 & 6.5 & 8.1 \\ TASNet [60] & Remote Sensing 2022 & 5.2 & 6.8 \\ FIDTM [44] & TMM 2022 & 4.2 & 5.5 \\ RPNet [47] & Crop J 2023 & 3.1 & 3.8 \\ ASANet [46] & JEI 2024 & 3.3 & 4.2 \\ RAQNet [56] & IEEE T-CE 2024 & **1.7** & **2.5** \\ Ours & This Paper & 3.2 & 3.8 \\ \hline \hline \end{tabular} Note: the best results are highlighted in **bold**, and the second-best results are double-underlined.  
\end{table}
Table 6: Experimental results on the PUCPR+ dataset.  
Figure 10: Visualization results of the various methods on the PUCPR+ dataset.