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EC-IoU: Orienting Safety for Object Detectors via Ego-Centric Intersection-over-Union

Brian Hsuan-Cheng Liao, Chih-Hong Cheng, Hasan Esen, Alois Knoll

TL;DR

EC-IoU introduces an ego-centric weighting scheme for evaluating object detectors, redefining IoU to emphasize ground-truth regions nearer to the ego vehicle. By weighting ground-truth points with ω_G(x,y) = [ρ(x_G,y_G)/ρ(x,y)]^α and approximating the weighted area via a mean-weight implementation, EC-IoU provides a safety-sensitive metric and learning signal. Empirical results on nuScenes and KITTI show EC-IoU can reveal safety gaps not captured by standard IoU and, when used as a loss, can improve downstream mAP and EC-AP in several scenarios. The work demonstrates how safety principles can be concretely integrated into evaluation and training for BEV/3D object detection, with avenues for adaptive weighting and online monitoring.

Abstract

This paper presents Ego-Centric Intersection-over-Union (EC-IoU), addressing the limitation of the standard IoU measure in characterizing safety-related performance for object detectors in navigating contexts. Concretely, we propose a weighting mechanism to refine IoU, allowing it to assign a higher score to a prediction that covers closer points of a ground-truth object from the ego agent's perspective. The proposed EC-IoU measure can be used in typical evaluation processes to select object detectors with better safety-related performance for downstream tasks. It can also be integrated into common loss functions for model fine-tuning. While geared towards safety, our experiment with the KITTI dataset demonstrates the performance of a model trained on EC-IoU can be better than that of a variant trained on IoU in terms of mean Average Precision as well.

EC-IoU: Orienting Safety for Object Detectors via Ego-Centric Intersection-over-Union

TL;DR

EC-IoU introduces an ego-centric weighting scheme for evaluating object detectors, redefining IoU to emphasize ground-truth regions nearer to the ego vehicle. By weighting ground-truth points with ω_G(x,y) = [ρ(x_G,y_G)/ρ(x,y)]^α and approximating the weighted area via a mean-weight implementation, EC-IoU provides a safety-sensitive metric and learning signal. Empirical results on nuScenes and KITTI show EC-IoU can reveal safety gaps not captured by standard IoU and, when used as a loss, can improve downstream mAP and EC-AP in several scenarios. The work demonstrates how safety principles can be concretely integrated into evaluation and training for BEV/3D object detection, with avenues for adaptive weighting and online monitoring.

Abstract

This paper presents Ego-Centric Intersection-over-Union (EC-IoU), addressing the limitation of the standard IoU measure in characterizing safety-related performance for object detectors in navigating contexts. Concretely, we propose a weighting mechanism to refine IoU, allowing it to assign a higher score to a prediction that covers closer points of a ground-truth object from the ego agent's perspective. The proposed EC-IoU measure can be used in typical evaluation processes to select object detectors with better safety-related performance for downstream tasks. It can also be integrated into common loss functions for model fine-tuning. While geared towards safety, our experiment with the KITTI dataset demonstrates the performance of a model trained on EC-IoU can be better than that of a variant trained on IoU in terms of mean Average Precision as well.
Paper Structure (15 sections, 4 theorems, 20 equations, 7 figures, 2 tables)

This paper contains 15 sections, 4 theorems, 20 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. The EC-IoU Measure
  5. Safety-critical weighting for a ground truth
  6. Formulation of the EC-IoU Measure
  7. Computing Weighted Areas and EC-IoU
  8. Complexity and Usage
  9. Experimental Results and Discussions
  10. Benchmarking EC-IoU-Based Loss Functions
  11. Real-World Object Detector Evaluation
  12. nuScenes
  13. KITTI
  14. Real-World Object Detector Fine-Tuning
  15. Conclusion

Key Result

Lemma 1

Given a ground truth $\mathbf{G}$ represented by $(x_\mathbf{G}, y_\mathbf{G}, l_\mathbf{G}, w_\mathbf{G}, \theta_\mathbf{G})$ with $\overline{\omega_\mathbf{G}}$ and $\underline{\omega_\mathbf{G}}$ being its maximum and minimum weights, if $\rho(x_\mathbf{G}, y_\mathbf{G}) \rightarrow \infty$, then

Figures (7)

  • Figure 1: A diagram showing our motivation. All blue and red predictions have an IoU of roughly $0.7$. However, the blue ones should be prioritized to avoid potential collisions at the front of the objects from the angle of the (red) ego car.
  • Figure 2: An example showing a prediction $\mathbf{P}_1$ will be favored by EC-IoU over another prediction $\mathbf{P}_2$ thanks to its better coverage on the safety-critical portion of the ground truth $\mathbf{G}$. As depicted by the gradient effect in $\mathbf{G}$, safety criticality is defined based on point distances to the origin; the darker, the more critical.
  • Figure 3: IoU and EC-IoU with various $\alpha$, computed using the geometric mean, for predictions centered along the x-axis. We assume the ego vehicle is located at $x=0$ and the ground truth $\mathbf{G}$ at $x=10$. The blue box depicts a prediction $\mathbf{P}$ centered at $x=7$.
  • Figure 4: For EC-IoU with $\alpha=8$, under the same configuration as Fig. \ref{['fig:ec_iou_valuation']}, we compare the curves produced by (1) geometric mean approximation ($\mathsf{Geom}$), (2) arithmetic mean approximation ($\mathsf{Arim}$), and (3) solving the original function via Monte Carlo numerical integration ($\mathsf{Num}$) with $6000$ random samples for every prediction centered at $x$.
  • Figure 5: Simulation setup.
  • ...and 2 more figures

Theorems & Definitions (8)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof