## 3 Methods
### C3k2_SC-Conv
#### 3.2.1 Self-Calibrated Convolutions  
The self-calibration mechanism within SC-Conv allows the model to dynamically adjust feature representations based on spatial and channel-specific information. This adaptability improves the robustness of object detection. Moreover, SC-Conv enhances the performance of conventional convolutional layers without adding extra parameters or increasing computational complexity. Its straightforward, plug-and-play design makes it easy to integrate into existing neural network frameworks. To efficiently and effectively gather valuable contextual information for each spatial location, self-calibrated convolution uses convolutional feature transformations in two different spatial scales: one is the original scale space where the feature map retains the same resolution as the input, and the other is a downsampled latent space. As illustrated in Figure 4, SC-Conv begins by partitioning the input \(X\) into two parts, denoted as \(X_{1}\) and \(X_{2}\). These two parts are then fed into specialized paths to extract different types of contextual information. Among them, \(X_{1}\) undergoes a self-calibration operation to obtain \(Y_{1}\). In this process, the parameter \(r\) dynamically adjusts the receptive field for each spatial position, enabling the model to capture deep semantic knowledge from distant spatial locations and channels, thus enhancing the diversity of the output features. Meanwhile, \(X_{2}\) undergoes a simple convolution operation to obtain \(Y_{2}\), preserving the original spatial contextual relationships. Finally, the intermediate outputs \(Y_{1}\) and \(Y_{2}\) are concatenated to produce the final output \(Y\). Specifically, self-calibration, as described in the upper part of the figure, begins with the output \(X_{1}\). We perform average pooling with a filter size of \(s\times s\) and a stride of \(s\), as follows:  
\[M_{1}=\text{AvgPool}_{r}(X_{1}). \tag{4}\]  
Figure 4: Structure of SC-Conv. The feature transformation in \(M_{1}\) is based on \(K_{2}\):  
\[X_{1}^{\prime}=\text{Upsample}(T_{1}*K_{2}), \tag{5}\]  
where \(\text{Upsample}(\cdot)\) is an operator that uses bilinear interpolation to map the intermediate reference from the reduced-scale space back to the original feature space. This operation can then be written as:  
\[Y_{1}^{\prime}=X_{1}*K_{3}\cdot\sigma(X_{1}+X_{1}^{\prime}), \tag{6}\]  
where \(\sigma\) represents the sigmoid function, and the \"-\" denotes element-wise multiplication. As shown in Equation (6), \(X_{1}^{\prime}\) is used as a residual to form the calibration weight. The final calibrated output can be written as:  
\[Y_{1}=Y_{1}^{\prime}*K_{4}. \tag{7}\]  
The self-calibration mechanism within SC-Conv is pivotal, allowing the model to dynamically adjust feature representations based on both spatial positions and channel-specific information. This adaptability significantly improves the robustness of object detection tasks. Specifically for dangerous driving behavior detection, the self-calibration operation effectively expands the receptive field by considering local context and modeling channel dependencies. This enhanced contextual awareness is crucial, enabling the model to capture a broader scene that includes driver actions, facial expressions, and changes in the vehicle's environment, thereby overcoming the limited receptive field of conventional convolution and leading to more effective identification of diverse dangerous driving cues, from subtle micro-expressions to larger actions. Crucially, SC-Conv achieves these enhancements in feature representation and receptive field without introducing additional parameters or increasing computational complexity when compared to standard convolutions.