Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in 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 one simple type of geometric constraints, namely, virtual normal directions determined by randomly sampled three points in the reconstructed 3D space, we can considerably improve the depth prediction accuracy. Significantly, the byproduct of this predicted depth being sufficiently accurate is that we are now able to recover good 3D structures of the scene such as the point cloud and surface normal directly from the depth, eliminating the necessity of training new sub-models as was previously done. Experiments on two benchmarks: NYU Depth-V2 and KITTI demonstrate the effectiveness of our method and state-of-the-art performance.
In this article, we tackle the problem of depth estimation from single monocular images. Compared with depth estimation using multiple images such as stereo depth perception, depth from monocular images is much more challenging. Prior work typically focuses on exploiting geometric priors or additional sources of information, most using hand-crafted features. Recently, there is mounting evidence that features from deep convolutional neural networks (CNN) set new records for various vision applications. On the other hand, considering the continuous characteristic of the depth values, depth estimation can be naturally formulated as a continuous conditional random field (CRF) learning problem. Therefore, here we present a deep convolutional neural field model for estimating depths from single monocular images, aiming to jointly explore the capacity of deep CNN and continuous CRF. In particular, we propose a deep structured learning scheme which learns the unary and pairwise potentials of continuous CRF in a unified deep CNN framework. We then further propose an equally effective model based on fully convolutional networks and a novel superpixel pooling method, which is about 10 times faster, to speedup the patch-wise convolutions in the deep model. With this more efficient model, we are able to design deeper networks to pursue better performance. Our proposed method can be used for depth estimation of general scenes with no geometric priors nor any extra information injected. In our case, the integral of the partition function can be calculated in a closed form such that we can exactly solve the log-likelihood maximization. Moreover, solving the inference problem for predicting depths of a test image is highly efficient as closed-form solutions exist. Experiments on both indoor and outdoor scene datasets demonstrate that the proposed method outperforms state-of-the-art depth estimation approaches. Monocular depth estimation is an extensively studied computer vision problem with a vast variety of applications. Deep learning-based methods have demonstrated promise for both supervised and unsupervised depth estimation from monocular images. Most existing approaches treat depth estimation as a regression problem with a local pixel-wise loss function. In this work, we innovate beyond existing approaches by using adversarial training to learn a context-aware, non-local loss function. Such an approach penalizes the joint configuration of predicted depth values at the patch-level instead of the pixel-level, which allows networks to incorporate more global information. In this framework, the generator learns a mapping between RGB images and its corresponding depth map, while the discriminator learns to distinguish depth map and RGB pairs from ground truth. This conditional GAN depth estimation framework is stabilized using spectral normalization to prevent mode collapse when learning from diverse datasets. We test this approach using a diverse set of generators that include U-Net and joint CNN-CRF. We benchmark this approach on the NYUv2, Make3D and KITTI datasets, and observe that adversarial training reduces relative error by several fold, achieving state-of-the-art performance.