Enforcing geometric constraints of virtual normal for depth prediction (1907.12209v2)

Abstract: 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.

• The paper introduces the virtual normal (VN) as a robust high-order geometric constraint for more stable depth prediction from single RGB images.
• It combines pixel-wise depth loss with VN constraints to boost accuracy, achieving state-of-the-art improvements on NYU Depth-V2 and KITTI benchmarks.
• The method enables high-quality 3D reconstructions, benefiting applications such as robotic perception, autonomous driving, and augmented reality.

Overview of "Enforcing Geometric Constraints of Virtual Normal for Depth Prediction"

The paper "Enforcing Geometric Constraints of Virtual Normal for Depth Prediction" presents a novel approach to monocular depth prediction, a key challenge in understanding 3D scene geometry from a single RGB image. Monocular depth estimation is often plagued by its ill-posed nature, since multiple 3D configurations can result in the same 2D projection. Recent advancements in deep convolutional neural networks (DCNNs) have significantly advanced this field, yet many existing methods fail to incorporate geometric constraints, which are crucial for accurate 3D scene reconstruction.

Key Contributions

1. Virtual Normal for Geometric Constraints: The authors introduce a high-order geometric constraint called the "Virtual Normal" (VN). The VN is computed by forming a plane from three non-collinear, randomly selected points in the predicted 3D point cloud, and calculating the normal vector of this plane. This VN serves as a robust constraint in the 3D space. Compared to traditional surface normals, VNs are shown to be more stable and less sensitive to noise due to their reliance on long-range dependencies.
2. Improved Depth Prediction: By integrating virtual normal constraints with pixel-wise depth supervision, the approach educates the network not just with 2D information but also with important high-order 3D cues, significantly improving depth estimation accuracy. The combination of high-order geometric loss with pixel-wise depth loss achieves superior results on standard benchmarks like NYU Depth-V2 and KITTI.
3. Reconstruction of 3D Features: A noteworthy byproduct of the predicted depth being sufficiently accurate is the ability to reconstruct high-quality 3D scenes, including point clouds and surface normals, without the need for additional sub-models dedicated to each task.

Results and Implications

The paper reports superior results in depth prediction benchmarks, with state-of-the-art performance on the NYU Depth-V2 and KITTI datasets. The method provides a significant accuracy improvement of up to 29% over previous real-time systems when employing a lightweight backbone architecture like MobileNetV2, highlighting its efficiency and applicability in resource-constrained environments.

A particularly impressive aspect of this work is its simultaneous contribution to both task-specific and general depth prediction. It paves the way for further integrating depth prediction with other 3D scene understanding tasks, potentially benefiting the fields of robotic perception, autonomous driving, and augmented reality, where monocular depth estimation is increasingly critical.

Speculations and Future Directions

The paper's introduction of virtual normals to enforce geometric constraints creates novel pathways for depth prediction research. Future exploration might involve leveraging this method in multi-task learning scenarios where 3D reconstruction accuracy is paramount. Furthermore, integrating this approach with transformer-based architectures could potentially yield even more refined depth predictions, given transformers' capability to model long-range dependencies. There is also the opportunity to examine this method's applicability in more diverse and complex scenes, possibly involving dynamic or less-structured environments.

In conclusion, the work significantly advances the precision of monocular depth prediction by bridging the gap between 2D and 3D representations through a practical and novel geometric loss function. It encourages the broader employment of deep learning methods that judiciously incorporate geometrical insights into scene understanding tasks.