Abstract Learning to estimate 3D geometry in a single image by watching unlabeled videos via deep convolutional network is attracting signifificant attention. In this paper, we introduce a “3D as-smooth-as-possible (3D-ASAP)” prior inside the pipeline, which enables joint estimation of edges and 3D scene, yielding results with signifificant improvement in accuracy for fifine detailed structures. Specififically, we defifine the 3D-ASAP prior by requiring that any two points recovered in 3D from an image should lie on an existing planar surface if no other cues provided. We design an unsupervised framework that Learns Edges and Geometry (depth, normal) all at Once (LEGO). The predicted edges are embedded into depth and surface normal smoothness terms, where pixels without edges in-between are constrained to satisfy the prior. In our framework, the predicted depths, normals and edges are forced to be consistent all the time. We conduct experiments on KITTI to evaluate our estimated geometry and CityScapes to perform edge evaluation. We show that in all of the tasks, i.e.depth, normal and edge, our algorithm vastly outperforms other state-of-theart (SOTA) algorithms, demonstrating the benefifits of our approach