# Study on Image Classification Algorithm Based on Multi-Scale Feature Fusion and Domain Adaptation
## 3 Method  
### Feature Fusion Network  
In computer vision tasks such as object detection, image classification, and semantic segmentation, fusing multi-scale features significantly improves the performance of CNNs. Shallow feature maps, obtained with fewer convolutional operations, capture texture and geometric features of the input image but contain more redundant and low-level semantic information. In contrast, deeper feature maps, produced with more convolutions, offer better semantic representations but can lose critical details. When the performance of a network reaches a certain bottleneck, integrating multi-scale features can provide richer information, enhancing the model's robustness. [PERSON] et al. [34] proposed the Inception network, which combines multi-scale convolution and feature concatenation. The key idea is to use convolutional kernels of different sizes within the same layer to capture multi-scale features, followed by concatenating these features to achieve more comprehensive feature representations. [PERSON] et al. [35] introduced the Res2 Net architecture, a variant of ResNet, which splits the input features into smaller sub-feature maps processed through separate paths and then combines the outputs. This approach enables the extraction of more diverse and detailed features. Image detail enhancement algorithms can be applied to a wide range of electronic products. In this subsection, we derive and analyze the initial model formulation for detail enhancement, proposing a rapid detail enhancement algorithm based on Taylor series analysis. This subsection introduces the Residual Extraction Network based on Taylor series analysis, referred to as the T-NET. Additionally, the T-NET employs an information entropy-based algorithm to integrate ten layers of residual features. Furthermore, we integrate the T-NET with the super-resolution algorithm CARN-M [36] to achieve both the super-resolution and detail enhancement of images. While implementing the engineering aspects, this subsection also theoretically analyzes the algorithm's rationale, error bounds,time complexity, convergence, and information redundancy, contributing certain theoretical innovations to the field. Given a signal (\(f(x)\)), according to detail enhancement theory, the signal can be decomposed into a base layer (\(b(x)\)) and a detail layer (\(d(x)\)), where \(f(x)=b(x)+d(x)\). The existing algorithms aim to optimize the approximation of the \(b(x)\) based on various priors and models. However, due to the complexity of image textures, obtaining a precise \(b(x)\) is challenging, and what is usually obtained is an estimation, denoted as \(b^{\prime}(x)\). Therefore, the enhanced signal can be modeled as follows:  
\[e(x)=b^{\prime}(x)+\alpha\times\big{(}f(x)-b^{\prime}(x)\big{)} \tag{4}\]  
However, Equation (4) can be rewritten as shown in Equation (4) as \(t=\alpha-1\). For a given input image (\(f(x)\)), a network can be used to generate the detail layer signal (\(f(x)\)), where \(d^{\prime}(x)=\text{Net}(f(x))\) is an estimation of the true image detail layer. Additionally, the signal \(f(x)\) is a weighted sum of the signals from multiple layers, represented as follows:  
\[f(x)=\sum_{k=1}^{n}(w_{k}\times f_{k}(x)),\]  
where \(w_{k}\) and \(f_{k}(x)\) are the weights of each layer, and k is the output of the k-th layer of the network. Thus, the task of detail enhancement is reduced to designing the \(w_{k}\) and \(f_{k}(x)\). Equation (5) further clarifies this problem, and Figure 2 illustrates the architecture of the image detail enhancement system based on Taylor series analysis (T-NET):  
\[ \begin{array}{l}e(x)=f(x)+(\alpha-1)\times(f(x)-b^{\prime}(x))\\ =f(x)+t\times d^{\prime}(x)=f(x)+t\times\text{Net}(f(x))\\ =f(x)+t\times\sum_{k=1}^{n}w_{k}\times f_{k}(x)\end{array}  \tag{5}\]  
The feature extractor consists of multi-scale and multi-head attention modules, as depicted in Figure 3.  
Figure 2: Image detail enhancement system based on Taylor series analysis (T-NET).