## 2 Theoretical Foundations  
### SWSDS-Net Network Architecture  
The UNet model effectively preserves multi-level feature information by utilizing skip connections and concatenating feature maps at different levels [20], thereby enhancing its representational capacity. Hence, for imaging logging fracture segmentation tasks with limited datasets and high costs involving single-class target semantic segmentation, employing UNet as a baseline model is a favorable solution. UNet comprises an encoder part and a decoder part. The encoder consists of multiple convolutional layers and pooling layers that progressively reduce the image's spatial resolution while extracting features [21]. Typically, each convolutional layer is followed by a batch normalization layer and an activation function to augment the model's learning capability. The final convolutional layer in the encoder generates a low-resolution feature map, which serves as input for the decoder. The decoder comprises multiple convolutional layers and upsampling layers that gradually restore the image's spatial resolution while reconstructing features. Similar to the encoder, each convolutional layer in the decoder is usually accompanied by a batch normalization layer and an activation function to enhance learning ability. To guide feature reconstruction, each convolutional layer in the decoder is concatenated with its corresponding counterpart in the encoder through skip connections, effectively preserving multi-level feature information and improving segmentation accuracy. Finally, the last convolutional layer of the decoder produces a high-resolution feature map, which serves as the final segmentation result. The network architecture, named SimAM with slicing deformable strip (SWSDS-Net), is constructed based on UNet. It incorporates SWS into both the encoder and the decoder, replacing the original convolution with DSCN. This integration effectively addresses the challenges posed by variations in fracture shapes, enhancing the model's robustness in complex scenarios while reducing parameters and computational cost. Consequently, it accelerates the training process. The overall architecture of SWSDS-Net, as depicted in the figure, adopts a symmetrical U-shaped structure. The left pathway is responsible for feature extraction and encoding, while the right pathway handles feature reconstruction and decoding. The left pathway comprises convolutional layers and pooling layers that progressively increase channel numbers and reduce feature map sizes to extract shallow target features. Conversely, the right pathway consists of convolutional layers and upsampling layers that gradually decrease channel numbers and enlarge feature map sizes to extract deep target features. Between these pathways, skip connections are employed to integrate shallow features from the left pathway with deep features from the right pathway, thereby achieving comprehensive recognition and segmentation of the target [22]. In the feature extraction process of the UNet network, redundant features, such as background noise [23], may be present. These features contribute minimally to the final segmentation task but significantly increase the computational burden of the model. Spatial weighted sum (SWS) effectively mitigates these redundant features by learning weights for each feature map, thereby enhancing feature extraction efficiency. Moreover, when processing objects with complex shapes in UNet, challenges like blurred edges or inaccurate shapes can arise. Dynamic shape convolutional networks (DSCNs), through learning offsets, adaptively adjust the receptive field of convolutional kernels to better suit irregularly shaped objects like fractures and enhance model adaptability to complex shapes. Furthermore, compared to traditional convolution operations, DSCNs have fewer parameters and lower computational costs, which effectively reduces computational burden while optimizing resource utilization.