Despite significant progress in monocular depth estimation in the wild, recent state-of-the-art methods cannot be used to recover accurate 3D scene shape due to an unknown depth shift induced by shift-invariant reconstruction losses used in mixed-data depth prediction training, and possible unknown camera focal length. We investigate this problem in detail, and propose a two-stage framework that first predicts depth up to an unknown scale and shift from a single monocular image, and then use 3D point cloud encoders to predict the missing depth shift and focal length that allow us to recover a realistic 3D scene shape. In addition, we propose an image-level normalized regression loss and a normal-based geometry loss to enhance depth prediction models trained on mixed datasets. We test our depth model on nine unseen datasets and achieve state-of-the-art performance on zero-shot dataset generalization. Code is available at: https://git.io/Depth
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