# Three-Dimensional Convolutional Vehicle Black Smoke Detection Model with Fused Temporal Features
## 5 Experiments
### Comparative Analysis  
The model proposed in this paper is evaluated against several prominent vehicle black smoke detection and identification models, including MobileNet v3 [30], YOLOv7 [31], YOLOv8 [32], as well as methods presented in the literature [1; 4; 5], and the C3D [33] model. We also implemented [8] as our baseline. In these baselines, MobileNet, YOLOv7, and YOLOv8 are all classical model architectures in the detection, and here we use their pre-trained models on the COCO dataset \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Name** & **Value** \\ \hline Batch Size & 8 \\ Frame Size & 6 \\ Epoch & 200 \\ \hline Initial learning rate & 0.01 \\ Recurring learning rate & 0.01 \\ Weight Decay & 0.9 \\ Loss factor for IoU & 0.2 \\ Loss factor for Cross-entropy & 1 \\ Thresholds for IoU training & 0.5 \\ \hline Hue (fraction) & 0.015 \\ Saturation (fraction) & 0.7 \\ Luminance (fraction) & 0.4 \\ Rotation angle (\(+/-\) deg) & 10.0 \\ Translation (\(+/-\) fractions) & 0.1 \\ Image scaling (\(+/-\) gain) & 0.5 \\ Probability of performing a up-down flip & 0 \\ Probability of performing a left-right flip & 0.5 \\ Probability of performing Mosaic & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The hyper-parameters we used consist of three parts: training parameters, gradient descent parameters and data enhancement parameters. because we find that the COCO dataset contains a large number of road scenes [14], which are similar to what is filmed in the roadway CCTV. Note that MobileNet, YOLOv7, and YOLOv8 are fine-tuned on our proposed dataset, since the original COCO dataset does not have a class named \"black smoke\". This pre-training and fine-tuning paradigm has a wide range of applications in many tasks [34; 35]. For the rest of the baselines, since no pre-trained versions are provided, we train them directly from scratch. The results are presented in Table 2. We can obtain the following observation:  
* MobileNetv3, YOLOv7, and YOLOv8 are all two-dimensional convolutional network detection models that do not account for the dynamic characteristics of black smoke influenced by noise, leading to lower accuracy. * Refs. [1; 4] enhance the network's feature extraction capability by incorporating an attention mechanism, which can mitigate background noise to some extent. * Ref. [5] employs the YOLOv5 network to extract black smoke features but only captures the static features, failing to distinguish clearly between black smoke and other disturbances such as vehicle shadows, road stains, and tree shades. * The C3D model uses fully connected 3D convolution for vehicle black smoke detection, improving accuracy but suffering from a large number of parameters and low inference efficiency, making it unsuitable for real-time detection scenarios. * Ref. [8] is an integrated solution that contains a semantic segmentation model (i.e., YOLOv5-s) and a detection model (i.e., MobileNetv3). Although this approach uses a semantic segmentation mechanism, the features that provide guidance for semantic segmentation are still obtained from a YOLOv5 model. Thus, from a feature extraction perspective, this is effectively equivalent to the integration of YOLOv5 and MobileNetv3, still limited by the usage to the temporal features. Different to these baselines, our model integrates 3D convolution to fully capture the temporal features between adjacent frames of continuous black smoke images at different resolutions. This model enhances the extraction ability of black smoke features by fusing temporal and semantic dimensions, effectively reducing the impact of occlusion and noise in video sequences, thereby improving the accuracy of vehicle black smoke detection. To get a staged view, we plotted our model's loss and accuracy over time during training, and the results are displayed in Figure 7.