## 3 Proposed Method  
### Corner Enhancement Module  
To improve the accuracy of corner detection in license plates, this study proposes a CEM based on DCNs. Unlike standard convolution, DCNs perform deformable convolution operations that can adaptively adjust sampling positions based on input features. This is particularly useful for effectively capturing the features of objects that undergo various geometric transformations, such as license plates. In this study, we integrated a DCN module based on DCNv2 into the CEM. DCNv2 is a model that adds a modulation mechanism to DCNv1, allowing for the adaptive adjustment of not only sampling positions but also weights at each position. As illustrated in Figure 1, the operating principle of the DCN module is as follows: offsets and modulation masks are simultaneously generated from the input feature map through offset mask convolution. For the input feature map \(\mathcal{F}\in R^{H\times W\times C}\), the offset and mask calculations are performed as follows. First, offset and mask information are simultaneously generated through a single convolution layer, as calculated in Equation (1). \[O=\text{Conv}_{\text{offset\_mask}}(F)\in R^{H\times W\times(3\times G\times K ^{2})} \tag{1}\]  
where \(G\) is the number of deform groups and \(K\) is the kernel size. The output channels are set to \(3\times G\times K^{2}\), consisting of \(x\)-direction offset, \(y\)-direction offset, and modulation mask. The generated output is split into three equal parts, as performed in Equation (2). \[o_{1},o_{2},\text{mask}_{\text{raw}}=\text{chunk}(O,3,\text{dim}=1) \tag{2}\]  
where each has a size of \(R^{H\times W\times(G\times K^{2})}\). The x-direction and y-direction offsets are concatenated to generate the final offset, as calculated in Equation (3). \[\text{offset}=\text{concat}(o_{1},o_{2})\in R^{H\times W\times(2\times G\times K ^{2})} \tag{3}\]  
The modulation mask is normalized to the [0, 1] range through the sigmoid function, as calculated in Equation (4). \[\text{mask}=\sigma(\text{mask}_{\text{raw}})\in R^{H\times W\times(G\times K ^{2})} \tag{4}\]  
The final sampling position for the \(k\)-th point of deform group \(g\) at each sampling location \((i,j)\) is calculated as shown in Equation (5). \[p_{g,k}^{(i,j)}=p_{0}^{(i,j)}+p_{k}+\Delta p_{g,k}^{(i,j)} \tag{5}\]  
where \(p_{0}^{(i,j)}=(i,j)\) is the center position, \(p_{k}\) is the relative position of the \(k\)-th point within the kernel and \(\Delta p_{g,k}^{(i,j)}\) is the learned offset. Finally, deformable convolution operations are performed as shown in Equation (6). \[y^{(i,j)}=\sum_{g=1}^{G}\sum_{k=1}^{K^{2}}w_{g,k}\cdot\mathcal{F}\Big{(}p_{g,k }^{(i,j)}\Big{)}\cdot\text{mask}_{g,k}^{(i,j)} \tag{6}\]  
where \(w_{g,k}\) is the \(k\)-th kernel weight of deform group \(g\), and \(\mathcal{F}\Big{(}p_{g,k}^{(i,j)}\Big{)}\) is the bilinearly interpolated feature value at \(p_{g,k}^{(i,j)}\). The final output goes through batch normalization and ReLU activation. The DCN module is positioned between channel attention and spatial attention within the CEM, adaptively responding to geometric transformations for features emphasized through channel attention. This is particularly effective in accurately detecting corners of license plates with large angular distortions. In the CEM, channel attention and spatial attention mechanisms are combined to effectively emphasize the corner features of license plates. These two attention mechanisms serve to emphasize features in different dimensions. The channel attention module uses both average pooling and max pooling to learn channel-wise importance from the input feature map. These two pooling results pass through a shared Multi-layer Perceptron (MLP) and are combined to be converted into channel weights between 0 and 1 using a sigmoid function. These weights are multiplied channel-wise with the original input feature map to emphasize important channels. Unlike regular convolution, DCN learns offsets that can adjust sampling positions according to input features.