Revisiting Gradient-based Uncertainty for Monocular Depth Estimation

Abstract: Monocular depth estimation, similar to other image-based tasks, is prone to erroneous predictions due to ambiguities in the image, for example, caused by dynamic objects or shadows. For this reason, pixel-wise uncertainty assessment is required for safety-critical applications to highlight the areas where the prediction is unreliable. We address this in a post hoc manner and introduce gradient-based uncertainty estimation for already trained depth estimation models. To extract gradients without depending on the ground truth depth, we introduce an auxiliary loss function based on the consistency of the predicted depth and a reference depth. The reference depth, which acts as pseudo ground truth, is in fact generated using a simple image or feature augmentation, making our approach simple and effective. To obtain the final uncertainty score, the derivatives w.r.t. the feature maps from single or multiple layers are calculated using back-propagation. We demonstrate that our gradient-based approach is effective in determining the uncertainty without re-training using the two standard depth estimation benchmarks KITTI and NYU. In particular, for models trained with monocular sequences and therefore most prone to uncertainty, our method outperforms related approaches. In addition, we publicly provide our code and models: https://github.com/jhornauer/GrUMoDepth

• The paper introduces a post hoc gradient-based uncertainty estimation method that bypasses retraining while enhancing reliability in monocular depth predictions.
• The technique leverages backpropagated gradients and an auxiliary loss based on transformed reference depths to accurately identify uncertain regions.
• Evaluation on KITTI and NYU Depth V2 datasets demonstrates improved uncertainty metrics and reduced computational overhead compared to ensemble methods.

Revisiting Gradient-based Uncertainty for Monocular Depth Estimation

The paper "Revisiting Gradient-based Uncertainty for Monocular Depth Estimation" presents a novel framework for estimating uncertainty in monocular depth predictions using gradient-based methods. This research addresses the critical issue of uncertainty quantification in depth estimation models—to enhance reliability in safety-critical applications like autonomous driving and robotics—without necessitating model retraining. The authors, Hornauer, El-Ghoussani, and Belagiannis, propose a post hoc approach that leverages gradients derived from trained models, providing an efficient alternative to traditional uncertainty estimation methods that often require retraining or additional model complexity.

Methodology Overview

The core technique introduced is the use of gradient-based uncertainty estimation which derives uncertainty scores using back-propagated gradients within an existing model. The authors propose a novel auxiliary loss function dependent on a reference depth generated through simple image or feature augmentations. This auxiliary loss, unlike typical training objectives, is used solely for the backpropagation of gradients to identify regions of high uncertainty in the predicted depth map. The reference depth acts as surrogate ground truth and is calculated by applying geometric or feature space transformations, such as horizontal flips, to the input image or encoded features.

Numerical Results and Analysis

The evaluation of the proposed gradient-based uncertainty estimation is conducted using two benchmark datasets: KITTI and NYU Depth V2. The research demonstrates that for models trained with monocular sequences—which are particularly vulnerable to uncertainty—the proposed method not only surpasses existing approaches but also provides stable, state-of-the-art uncertainty estimates across different depth estimation scenarios. Notable metrics include the normalised Uncertainty Calibration Error (nUCE) and standard sparsification plots, which conclusively show the effectiveness of the proposed method in various test setups. Specifically, the authors highlight that their approach greatly reduces computational overhead compared to ensemble or dropout approaches and does not necessitate retraining the model, offering a clear advantage in scenarios where computational resources or data access for retraining are limited.

Implications and Future Directions

From a theoretical perspective, this paper refines the understanding of how gradient-based methods can be used to assess and quantify uncertainty in dense prediction tasks like depth estimation. Practically, the flexibility and minimal computational cost of this post hoc method are significant, providing immediate applicability in industries prioritizing both performance and computational efficiency, such as autonomous vehicle systems.

The proposed methodology opens multiple avenues for future exploration. Further investigation could explore the adaptability of this approach to other dense prediction tasks, such as semantic segmentation or optical flow, potentially offering a unified framework for uncertainty estimation across various vision applications. Additionally, exploring different types of transformations, beyond those evaluated, could optimize the generation of the reference depth, enhancing the accuracy and robustness of the uncertainty estimation.

Conclusion

The paper provides a comprehensive evaluation of gradient-based uncertainty estimation, offering a significant contribution to the field of monocular depth estimation. By presenting a method that effectively balances computational efficiency with high-quality uncertainty estimates, this research demonstrates substantial potential for deployment in real-world applications where understanding prediction confidence is as crucial as the prediction accuracy itself. The authors' provision of code and models further emphasizes transparency and encourages the application and validation of their methods within the broader research community.