CORE: Co-planarity Regularized Monocular Geometry Estimation with Weak Supervision

The ill-posed nature of monocular 3D geometry (depth map and surface normals) estimation makes it rely mostly on data-driven approaches such as Deep Neural Networks (DNN). However, data acquisition of surface normals, especially the reliable normals, is acknowledged difficult. Commonly, reconstruction of surface normals with high quality is heuristic and time-consuming. Such fact urges methodologies to minimize dependency on ground-truth normals when predicting 3D geometry. In this work, we devise CO-planarity REgularized (CORE) loss functions and Structure-Aware Normal Estimator (SANE). Without involving any knowledge of ground-truth normals, these two designs enable pixel-wise 3D geometry estimation weakly supervised by only ground-truth depth map. For CORE loss functions, the key idea is to exploit locally linear depth-normal orthogonality under spherical coordinates as pixel-level constraints, and utilize our designed Adaptive Polar Regularization (APR) to resolve underlying numerical degeneracies. Meanwhile, SANE easily establishes multi-task learning with CORE loss functions on both depth and surface normal estimation, leading to the whole performance leap. Extensive experiments present the effectiveness of our method on various DNN architectures and data benchmarks. The experimental results demonstrate that our depth estimation achieves the state-of-the-art performance across all metrics on indoor scenes and comparable performance on outdoor scenes. In addition, our surface normal estimation is overall superior.