The morphology of natural micro-fractures in shale reservoirs is a key factor controlling their fluid flow capacity and mechanical stability, while the microscopic distribution of minerals significantly influences the development characteristics of local micro-fractures. Accurately extracting the geometry of micro-fractures and establishing its relationship with mineral types and spatial distribution are essential for a deeper understanding of wellbore instability mechanisms in shale formations. However, due to the strong heterogeneity of the shale matrix, conventional threshold-based segmentation methods struggle to precisely distinguish micro-fractures from mineral boundaries, leading to considerable uncertainty in the extraction of fracture morphological parameters. To address this issue, this study proposes a TS-LSTM fracture extraction method based on scanning electron microscopy (SEM) images, which combines threshold segmentation with a long short-term memory neural network to achieve high-precision segmentation and completion of micro-fractures. Using the extracted fracture morphologies, the width and tortuosity of the fractures are quantitatively characterized. To quantify the mineral distribution around the fractures, different distances outward from the fracture boundaries are defined, and the area percentage of a specific mineral within each distance zone is designated as the threshold mineral percentage content. On this basis, correlation analysis is applied to investigate the statistical relationships between the local content of three major minerals-quartz, albite, and illite-and fracture width and tortuosity. The results show that the TS-LSTM fracture extraction method can effectively extract micro-fracture regions from complex shale SEM images, with strong completion capability particularly for discontinuous fractures. Using the threshold mineral percentage content at different distances, the mineral distribution around fractures can be quantitatively described. Illite content exhibits a negative correlation with fracture width and a strong positive correlation with tortuosity, indicating that fractures in illite-rich zones are narrower and more tortuous. Quartz content is positively correlated with fracture width and overall negatively correlated with tortuosity, which favors the formation of wider and straighter fractures. However, in local areas with dense quartz grains, fractures may propagate around the grains, leading to increased local tortuosity near quartz. Although albite content shows a certain positive correlation with fracture width, its relationship with tortuosity is more complex. In summary, the type and spatial distribution of minerals collectively shape the complex propagation paths of fractures. This study establishes, through an intelligent approach, the relationship between minerals and micro-fracture morphology, providing a new pathway for developing micro-scale models of wellbore stability in shale formations.