P3Depth: Monocular Depth Estimation with a Piecewise Planarity Prior (2204.02091v1)

Abstract: Monocular depth estimation is vital for scene understanding and downstream tasks. We focus on the supervised setup, in which ground-truth depth is available only at training time. Based on knowledge about the high regularity of real 3D scenes, we propose a method that learns to selectively leverage information from coplanar pixels to improve the predicted depth. In particular, we introduce a piecewise planarity prior which states that for each pixel, there is a seed pixel which shares the same planar 3D surface with the former. Motivated by this prior, we design a network with two heads. The first head outputs pixel-level plane coefficients, while the second one outputs a dense offset vector field that identifies the positions of seed pixels. The plane coefficients of seed pixels are then used to predict depth at each position. The resulting prediction is adaptively fused with the initial prediction from the first head via a learned confidence to account for potential deviations from precise local planarity. The entire architecture is trained end-to-end thanks to the differentiability of the proposed modules and it learns to predict regular depth maps, with sharp edges at occlusion boundaries. An extensive evaluation of our method shows that we set the new state of the art in supervised monocular depth estimation, surpassing prior methods on NYU Depth-v2 and on the Garg split of KITTI. Our method delivers depth maps that yield plausible 3D reconstructions of the input scenes. Code is available at: https://github.com/SysCV/P3Depth

• The paper introduces a novel plane coefficient model that enhances monocular depth estimation by leveraging local planar structures.
• It employs dual network heads: one predicts pixel-level plane coefficients, while the other estimates offset vectors to seed pixels.
• Empirical results demonstrate state-of-the-art performance on datasets like NYU Depth-v2 and KITTI with notable RMSE and accuracy gains.

An Evaluation of "P3Depth: Monocular Depth Estimation with a Piecewise Planarity Prior"

Overview

The paper "P3Depth: Monocular Depth Estimation with a Piecewise Planarity Prior" presents a novel approach for supervised monocular depth estimation by introducing a method to selectively leverage coplanar pixel information in a 3D scene. The authors propose the integration of a piecewise planarity prior into a neural network architecture, which employs two separate heads to learn and predict depth. The first head predicts pixel-level plane coefficients, while the second identifies seed pixels via a dense offset vector field, exploiting local planarity to refine depth predictions. This architecture is ultimately trained end-to-end, yielding state-of-the-art results across notable datasets such as NYU Depth-v2 and KITTI.

Methodology

The core methodology involves representing depth by a plane coefficient model. Each pixel is expressed in terms of these coefficients, enabling depth estimation to benefit from planarity. The notion of "seed pixels," which are deemed representative for planar surfaces, facilitates leveraging the plane coefficient representation to yield depth predictions. This seed pixel approach is supported by two network heads: one predicts the plane coefficients while the other estimates offset vectors pointing to the seed pixels and computes a confidence metric for planarity localization. The inclusion of cascaded refinement of offsets and the use of a mean plane loss reinforces the training, enhancing the accuracy of predicted surfaces.

Results and Contributions

The authors assert significant improvements over previous work, particularly in the NYU Depth-v2 dataset by reducing the RMSE to 0.356 and achieving a high threshold accuracy ($\delta_1$) of 0.898. On KITTI, the method also performs strongly, particularly on the Garg split, demonstrating substantial accuracy gains at lower depth ranges, which speaks to the method's robustness in more controlled depth evaluations.

Implications for Practice and Theory

Practically, the results indicate that the proposed method can enhance 3D reconstruction and depth-sensing applications, particularly in environments characterized by predominantly planar surfaces. Theoretically, the reliance on implicit planar assumptions but without stringent dependencies on labeled plane data can inspire further examination of implicit prior usage in deep learning architectures. It offers an avenue for balancing the simplicity of local planarity with the complexity of general scene understanding.

Future Directions

Potential extensions of this work could involve exploring scenarios with dynamic occlusions and developing methods to handle higher-order surface approximations. Furthermore, considering the drop in performance at greater depth ranges, future work might incorporate mechanisms to dynamically adjust planarity assumptions or integrate multi-scale context. Exploring the interaction between learned representations and varied sensor data (e.g., stereo or LIDAR) could also be valuable in broadening the applicability of the piecewise planarity model.

This paper contributes meaningfully to the supervised depth estimation field, particularly in promoting the integration of geometric priors with machine learning methodologies to improve depth estimation.