Abstract In this paper, we propose Geometric Neural Network (GeoNet) to jointly predict depth and surface normal maps from a single image. Building on top of two-stream CNNs, our GeoNet incorporates geometric relation between depth and surface normal via the new depth-to-normal and normalto-depth networks. Depth-to-normal network exploits the least square solution of surface normal from depth and improves its quality with a residual module. Normal-to-depth network, contrarily, refifines the depth map based on the constraints from the surface normal through a kernel regression module, which has no parameter to learn. These two networks enforce the underlying model to effificiently predict depth and surface normal for high consistency and corresponding accuracy. Our experiments on NYU v2 dataset verify that our GeoNet is able to predict geometrically consistent depth and normal maps. It achieves top performance on surface normal estimation and is on par with state-of-theart depth estimation methods