We introduce VA-DepthNet, a simple, effective, and accurate deep neural
network approach for the single-image depth prediction (SIDP) problem. The
proposed approach advocates using classical first-order variational constraints
for this problem. While state-of-the-art deep neural network methods for SIDP
learn the scene depth from images in a supervised setting, they often overlook
the invaluable invariances and priors in the rigid scene space, such as the
regularity of the scene. The paper's main contribution is to reveal the benefit
of classical and well-founded variational constraints in the neural network
design for the SIDP task. It is shown that imposing first-order variational
constraints in the scene space together with popular encoder-decoder-based
network architecture design provides excellent results for the supervised SIDP
task. The imposed first-order variational constraint makes the network aware of
the depth gradient in the scene space, i.e., regularity. The paper demonstrates
the usefulness of the proposed approach via extensive evaluation and ablation
analysis over several benchmark datasets, such as KITTI, NYU Depth V2, and SUN
RGB-D. The VA-DepthNet at test time shows considerable improvements in depth
prediction accuracy compared to the prior art and is accurate also at
high-frequency regions in the scene space. At the time of writing this paper,
our method -- labeled as VA-DepthNet, when tested on the KITTI depth-prediction
evaluation set benchmarks, shows state-of-the-art results, and is the
top-performing published approach.

VA-DepthNet 是一种基于首阶变分约束的神经网络方法，能够在单张图像中预测场景深度，摒弃了简单监督学习方法所忽视的场景空间不变性和先验知识，并在多个基准数据集上得到了较高的预测准确度。

VA-DepthNet: 单张图像深度预测的变分方法

VA-DepthNet: A Variational Approach to Single Image Depth Prediction

There has been tremendous research progress in estimating the depth of a
scene from a monocular camera image. Existing methods for single-image depth
prediction are exclusively based on deep neural networks, and their training
can be unsupervised using stereo image pairs, supervised using LiDAR point
clouds, or semi-supervised using both stereo and LiDAR. In general,
semi-supervised training is preferred as it does not suffer from the weaknesses
of either supervised training, resulting from the difference in the cameras and
the LiDARs field of view, or unsupervised training, resulting from the poor
depth accuracy that can be recovered from a stereo pair. In this paper, we
present our research in single image depth prediction using semi-supervised
training that outperforms the state-of-the-art. We achieve this through a loss
function that explicitly exploits left-right consistency in a stereo
reconstruction, which has not been adopted in previous semi-supervised
training. In addition, we describe the correct use of ground truth depth
derived from LiDAR that can significantly reduce prediction error. The
performance of our depth prediction model is evaluated on popular datasets, and
the importance of each aspect of our semi-supervised training approach is
demonstrated through experimental results. Our deep neural network model has
been made publicly available.

通过语义监督训练单张图像深度预测模型，进一步应用 LiDAR 导出的深度图纠正误差，提出了具有左右一致性损失函数的深度神经网络，着重于强调半监督训练方法的重要性和正确使用 LiDAR 测量数据的技术。