The study of monocular depth estimation is the basis of many vision tasks. Obtaining a depth map with clear edges and rich details from an image is important for subsequent tasks. Aiming at the problem that the current monocular depth estimation model cannot deeply integrate image semantic information and can not make good use of the edge information of image objects, the superpixel topology relationship map is first constructed, and the graph neural network is used to extract the relationship between local edge information. The topological relationship graph with superpixels as nodes is obtained. Secondly, a joint model of depth estimation and semantic segmentation based on the encoder-decoder structure is constructed. By optimizing the joint objective function, the model can fuse edge semantic information, thereby improving the model"s ability to extract local structural information. Through experimental verification in the NYU-Depth V2 dataset, the results show that the model can construct a depth map with rich details and clear edges, which improves the quality of monocular depth visual estimation. Compared with other models, this model has certain advantages.