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Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in the evaluation metrics such as the pixel-wise relative error, most methods neglect the geometric constraints in the 3D space. In this work, we show the importance of the high-order 3D geometric constraints for depth prediction. By designing a loss term that enforces a simple geometric constraint, namely, virtual normal directions determined by randomly sampled three points in the reconstructed 3D space, we significantly improve the accuracy and robustness of monocular depth estimation. Importantly, the virtual normal loss can not only improve the performance of learning metric depth, but also disentangle the scale information and enrich the model with better shape information. Therefore, when not having access to absolute metric depth training data, we can use virtual normal to learn a robust affine-invariant depth generated on diverse scenes. Our experiments demonstrate state-of-the-art results of learning metric depth on NYU Depth-V2 and KITTI. From the high-quality predicted depth, we are now able to recover good 3D structures of the scene such as the point cloud and surface normal directly, eliminating the necessity of relying on additional models as was previously done. To demonstrate the excellent generalization capability of learning affine-invariant depth on diverse data with the virtual normal loss, we construct a large-scale and diverse dataset for training affine-invariant depth, termed Diverse Scene Depth dataset (DiverseDepth), and test on five datasets with the zero-shot test setting. Code is available at: https://git.io/Depth.

Virtual Normal: Enforcing Geometric Constraints for Accurate and Robust Depth Prediction