## 3 Multi-Scale Feature Fusion Siamese Network Guided by Edge Contour Model Design
### Edge Contour-Guided Feature Fusion Residual Network  
The MFS-GC model designed in this paper introduces the SPADE module into the backbone feature extraction network at the feature extraction stage, and then the output feature maps of the four stages are used as inputs to the SPADE model, which uses the edge contour binary image information of the bone stick image to guide the feature maps of the Resnet50 neural network to be normalized, and it intervenes by continually adding edge contour binary images so that each stage of the Resnet50 network is able to learn the edge contour features. Finally, the fused features Ri output from the four stages are obtained. The MFS-GC model proposed in this study includes the SPADE module in the core feature extraction network during the feature extraction phase. The output feature maps generated from the four stages are then used as inputs to the SPADE module. This module uses information from the edge contour of the bone stick image to guide the normalization of the feature maps within the Resnet50 neural network. Each stage of the Resnet50 network is able to learn the edge contour features This results in the fused features, denoted as Ri, being outputted from the four stages. Inspired by the Feature Pyramid Networks (FPNs) [22; 23; 24], this study introduces a multi-scale approach by reusing feature maps during the feature extraction phase. This method effectively integrates deep-level features with shallow-level features. The channel concatenation method, as illustrated in Figure 5, involves adding two feature vectors along the channel dimension. Deep neural networks often neglect low-level information while extracting high-level semantic features. However, in the domain of bone stick rejoining, both the low-level and high-level information of two-dimensional damaged bone stick images are equally significant. Hence, outputs from four convolutional layers of different scales collectively contribute to the representation of the feature vectors. This approach overcomes the limitations of conventional convolutional neural networks in extracting texture and contour feature information, thereby enhancing the model's capability to extract detailed features. This paper proposes the construction of two contour-guided feature fusion residual networks with shared weights. The feature extraction network of a single branch is illustrated in Figure 6 with Resnet50 serving as the backbone of the network. The network consists of 49 convolutional layers and 1 fully connected layer. The overall structure of Resnet50 is divided into five stages: Stage 0, Stage 1, Stage 2, Stage 3, and Stage 4. Among them, the Stage 0 structure is simple and is considered as the preprocessing stage for input images. The subsequent four stages all include residual network units, where each residual unit is composed of three convolutional layers. The unit first employs a \(1\times 1\) convolution to achieve dimension reduction; then, it utilizes a \(3\times 3\) convolution to extract features channel-wise and finally employs a \(1\times 1\) convolution to achieve dimension expansion. Figure 5: Multi-scale feature channel stitching. The entire network begins with Stage 0, where the input image has a shape of (224, 224, 3). It undergoes convolutional layers, Batch Normalization (BN) layers, Rectified Linear Unit (RELU) activation functions, and a max-pooling layer, resulting in an output shape of (56, 56, 64). In Stage 1, the output from the previous stage, (56, 56, 64), serves as input to obtain the output scale 1 with dimensions (56, 56, 256). Subsequently, the SPADE model takes scale 1 as input 1 and the contour map of the bone marker as input 2. It learns detailed contour features of the bone marker. The contour map is first resized and passed through a convolutional layer, which is followed by two 3 \(\times\) 3 convolutions.