# Design of a Lung Lesion Target Detection Algorithm Based on a Domain-Adaptive Neural Network Model
## 3 Methodology  
### CNN and Resnet for Feature Extraction  
CNNs are deep learning architectures specifically designed to process grid-structured data, such as images. Their core strength lies in the efficient extraction of localized features from input data while significantly reducing the number of parameters, making them highly effective for handling high-dimensional datasets. The extraction of local features is accomplished through the application of convolutional kernels (filters), which scan the input image systematically. This process operates as follows:  
\[y^{k}_{i,j}=\sum_{m}\sum_{n}x_{i+m,j+n}\cdot w^{k}_{m,n}+b^{k} \tag{1}\]where \(x\) is the image, each corner marker represents its corresponding pixel position, while \(y\) represents its associated output. Building on this foundation, further feature extraction is achieved through the application of the ReLU activation function. Typically, a single layer of a CNN is insufficient; instead, multiple layers are interconnected via pooling layers and fully connected layers to enhance the model's overall performance and its capacity to leverage extracted features effectively [29].  
Beyond traditional CNNs, to address the varying applicability of features across volumes and networks, we accelerate feature integration at the multi-feature fusion layer by employing the ResNet architecture. ResNet, an enhanced deep CNN framework, overcomes the challenges of gradient vanishing and network degradation in deeper architectures through the introduction of \"residual connections\". These connections simplify the training of deep networks while delivering superior performance. Unlike traditional deep networks that directly approximate the objective function \(H(x)\), ResNet introduces a residual function, defined as follows:  
\[F(x)=H(x)-x \tag{2}\]  
We make the network learn the residuals \((x)\), and pass the input directly to the output via jump connections, where \(F(x,\{W_{i}\})\) is the residual function, which is fitted by the convolutional layer. This design enables the network layers to concentrate on learning subtle differences between inputs and outputs, thereby enhancing the efficiency and performance of deep networks. The convolutional layers in CNNs extract fundamental features--such as edges and textures--from lung CT images via localized receptive fields, laying the groundwork for detailed lesion area identification. Through successive layers of convolutional stacking, the network progressively captures higher-level features, including the morphology and density characteristics of lesion regions.  
ResNet further refines the deep feature extraction process by leveraging residual connections to mitigate the issue of gradient vanishing, thereby ensuring effective training of deep networks. In domain-adaptive scenarios, ResNet delivers stable and accurate feature representations, facilitating the reduction in distributional discrepancies between source and target domains [30]. Moreover, the multi-scale feature extraction layer integrates convolutional operations at varying scales, enhancing the network's ability to detect diverse lesions and bolstering robustness and detection accuracy in complex environments. To strengthen the model's generalization capabilities and ensure robustness across different domains, we employ domain-adaptive feature transfer through CT images with varying levels and gray scales. This approach preserves model performance by harmonizing feature representations across heterogeneous domains.