## 3 The Proposed Method
### Explicit Visual Center  
The explicit visual center is composed of the multilayer perceptron (MLP) and the learnable visual center (LVC), whose architecture is shown in Figure 6. While the lightweight MLP architecture is for capturing long-range dependencies, the LVC is for aggregating local corner regions of the input image [29]. In addition, for smoothing the feature, a Stem block, contributed by a \(7\times 7\) convolution, a batch normalization (BN) layer, and an activation function layer, is added between these two parallel blocks.  
Figure 5: Structure diagram of C2f_DCN.  
Figure 6: Structure of explicit visual center.  
The MLP is composed of two residual modules: a depth-separable convolution-based module and a channel MLP-based module. In this case, the input of the MLP module is the output of the depth-separable convolution module. Both modules undergo channel scaling and tuning operations to improve feature generalization and robustness. The input for the depth-separable convolution module is the group-normalized feature map \(\widetilde{\mathrm{X}}_{\text{in}}\), and the output result \(\widetilde{\mathrm{X}}_{\text{in}}\) can be expressed as  
\[\widetilde{\mathrm{X}}_{in}=DConv(GN(X_{in}))+X_{in} \tag{2}\]  
The input for the channel MLP module is the output of the depth-separable convolution module, which is group-normalized before the channel MLP operation. The process can be expressed as  
\[MLP(X_{in})=CMLP\bigg{(}GN\bigg{(}\widetilde{\mathrm{X}}_{in}\bigg{)}\bigg{)} +\widetilde{\mathrm{X}}_{in} \tag{3}\]  
The LVC is an encoder with an intrinsic dictionary, consisting of an intrinsic codebook and a set of learnable vision-centered scale factors. The processing of LVC consists of two steps. The input features are convolved using a convolutional layer with CBR processing firstly, and then the features processed in the first step are combined with the codebook by means of a learnable scale factor, which maps the position information to \(\widetilde{\mathrm{X}}_{\text{i}}\) and \(b_{k}\). The formula is as follows:  
\[e_{k}=\sum_{i=1}^{N}\frac{e^{-S_{k}\big{|}\widetilde{\mathrm{X}}_{i}-b_{k} \big{|}^{2}}}{\sum_{j=1}^{K}e^{-S_{k}\big{|}\widetilde{\mathrm{X}}_{i}-b_{k} \big{|}^{2}}}\bigg{(}\widetilde{\mathrm{X}}_{i}-b_{k}\bigg{)}, \tag{4}\]  
where S is the scale factor, \(\widetilde{\mathrm{X}}_{\text{i}}\) is the ith pixel, and \(b_{k}\) is the kth visual code. The ReLU and BN computations are implemented using \(\phi\) with all \(e_{k}\) combined, followed by channel multiplication and channel addition of the input \(X_{in}\) and the local features Z. The computational formulas are given below:  
\[e=\sum_{k=1}^{K}\phi(e_{k}), \tag{5}\]  
\[Z=X_{in}\otimes(\delta(Conv_{1\times 1}(e))), \tag{6}\]  
\[LVC(X_{in})=X_{in}\oplus Z \tag{7}\]  
Using the channel dimension, the feature maps of the two modules are stitched together as the output of the EVC. The output expression is as follows:  
\[X=cat(MLP(X_{in});LVC(X_{in})), \tag{8}\]  
where \(MLP(X_{in})\) represents the long-range dependencies and \(LVC(X_{in})\) represents the local corner regions. The integrated signature encompasses the strengths of both modules, allowing the detection model to learn a full range of discriminative feature representations. ECV assigns the features in the feature pyramid to different targets, and it achieves this by computing information such as the size, shape, and position of each target, assigning a region of interest (ROI) to each target, and then weighting the fusion of these ROIs with features from the feature pyramid. This enables better detection of targets of different sizes.