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A technique to jointly estimate depth and depth uncertainty for unmanned aerial vehicles

Michaël Fonder, Marc Van Droogenbroeck

TL;DR

This paper tackles the problem of obtaining reliable depth estimates with quantified uncertainty for UAVs. It extends M4Depth to jointly estimate depth and depth uncertainty by introducing uncertainty outputs at each pyramid level and by converting parallax uncertainty into depth uncertainty. A baseline probabilistic approach on depth is compared against an elaborate parallax-centered conversion, with the latter (M4Depth+U$_\rho$) showing superior calibration and robustness, especially in zero-shot transfer. Across Mid-Air, KITTI, and TartanAir, the method preserves depth accuracy while delivering more reliable uncertainty estimates, and on the Robust MVD benchmark it remains competitive with state-of-the-art methods while being substantially faster and causal. Overall, M4Depth+U$_\rho$ enables real-time, end-to-end joint depth and uncertainty estimation suitable for UAV planning and obstacle avoidance, with code released for public use.

Abstract

When used by autonomous vehicles for trajectory planning or obstacle avoidance, depth estimation methods need to be reliable. Therefore, estimating the quality of the depth outputs is critical. In this paper, we show how M4Depth, a state-of-the-art depth estimation method designed for unmanned aerial vehicle (UAV) applications, can be enhanced to perform joint depth and uncertainty estimation. For that, we present a solution to convert the uncertainty estimates related to parallax generated by M4Depth into uncertainty estimates related to depth, and show that it outperforms the standard probabilistic approach. Our experiments on various public datasets demonstrate that our method performs consistently, even in zero-shot transfer. Besides, our method offers a compelling value when compared to existing multi-view depth estimation methods as it performs similarly on a multi-view depth estimation benchmark despite being 2.5 times faster and causal, as opposed to other methods. The code of our method is publicly available at https://github.com/michael-fonder/M4DepthU .

A technique to jointly estimate depth and depth uncertainty for unmanned aerial vehicles

TL;DR

This paper tackles the problem of obtaining reliable depth estimates with quantified uncertainty for UAVs. It extends M4Depth to jointly estimate depth and depth uncertainty by introducing uncertainty outputs at each pyramid level and by converting parallax uncertainty into depth uncertainty. A baseline probabilistic approach on depth is compared against an elaborate parallax-centered conversion, with the latter (M4Depth+U) showing superior calibration and robustness, especially in zero-shot transfer. Across Mid-Air, KITTI, and TartanAir, the method preserves depth accuracy while delivering more reliable uncertainty estimates, and on the Robust MVD benchmark it remains competitive with state-of-the-art methods while being substantially faster and causal. Overall, M4Depth+U enables real-time, end-to-end joint depth and uncertainty estimation suitable for UAV planning and obstacle avoidance, with code released for public use.

Abstract

When used by autonomous vehicles for trajectory planning or obstacle avoidance, depth estimation methods need to be reliable. Therefore, estimating the quality of the depth outputs is critical. In this paper, we show how M4Depth, a state-of-the-art depth estimation method designed for unmanned aerial vehicle (UAV) applications, can be enhanced to perform joint depth and uncertainty estimation. For that, we present a solution to convert the uncertainty estimates related to parallax generated by M4Depth into uncertainty estimates related to depth, and show that it outperforms the standard probabilistic approach. Our experiments on various public datasets demonstrate that our method performs consistently, even in zero-shot transfer. Besides, our method offers a compelling value when compared to existing multi-view depth estimation methods as it performs similarly on a multi-view depth estimation benchmark despite being 2.5 times faster and causal, as opposed to other methods. The code of our method is publicly available at https://github.com/michael-fonder/M4DepthU .
Paper Structure (11 sections, 10 equations, 3 figures, 2 tables)

This paper contains 11 sections, 10 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related works
  3. Uncertainty estimation using M4Depth
  4. M4Depth working principles
  5. Correspondence between depth and parallax uncertainties
  6. Baseline: the probabilistic framework
  7. Elaborate conversion of the uncertainty
  8. Experiments
  9. Experimental setup
  10. Results
  11. Conclusion

Figures (3)

  • Figure 1: Illustration of depth and uncertainty estimates produced by the method presented in this work for two setups. Row 1: trained and tested on the Mid-Air Fonder2019MidAir dataset. Row 2: tested in zero-shot transfer on the KITTI Geiger2012AreWe dataset. Lighter colors correspond to higher uncertainty values.
  • Figure 2: Illustration of the correspondence between a Laplace distribution (blue curve) and its inverse (orange curve) when applied to the relation linking parallax to depth for different standard deviations of the Laplace distribution. We propose to use $\Delta_{\rho}$ as an uncertainty measure on the parallax, whose correspondence for depth is $\Delta_{\text{z}}$.
  • Figure 3: Sparsification error (S.E.) curves on the absolute relative error for M4Depth+U$_\text{z}$ and M4Depth+U$_\rho$ on the KITTI dataset, and on the "Old Town" set of TartanAir (TtA-O).