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RoboBEV Benchmark

The official nuScenes metrics are considered in our benchmark:

Average Precision (AP)

The average precision (AP) defines a match by thresholding the 2D center distance d on the ground plane instead of the intersection over union (IoU). This is done in order to decouple detection from object size and orientation but also because objects with small footprints, like pedestrians and bikes, if detected with a small translation error, give $0$ IoU. We then calculate AP as the normalized area under the precision-recall curve for recall and precision over 10%. Operating points where recall or precision is less than $10$% are removed in order to minimize the impact of noise commonly seen in low precision and recall regions. If no operating point in this region is achieved, the AP for that class is set to zero. We then average over-matching thresholds of $\mathbb{D}={0.5, 1, 2, 4}$ meters and the set of classes $\mathbb{C}$ :

$$ \text{mAP}= \frac{1}{|\mathbb{C}||\mathbb{D}|}\sum_{c\in\mathbb{C}}\sum_{d\in\mathbb{D}}\text{AP}_{c,d} . $$

True Positive (TP)

All TP metrics are calculated using $d=2$ m center distance during matching, and they are all designed to be positive scalars. Matching and scoring happen independently per class and each metric is the average of the cumulative mean at each achieved recall level above $10$%. If a $10$% recall is not achieved for a particular class, all TP errors for that class are set to $1$.

  • Average Translation Error (ATE) is the Euclidean center distance in 2D (units in meters).
  • Average Scale Error (ASE) is the 3D intersection-over-union (IoU) after aligning orientation and translation ($1$ − IoU).
  • Average Orientation Error (AOE) is the smallest yaw angle difference between prediction and ground truth (radians). All angles are measured on a full $360$-degree period except for barriers where they are measured on a $180$-degree period.
  • Average Velocity Error (AVE) is the absolute velocity error as the L2 norm of the velocity differences in 2D (m/s).
  • Average Attribute Error (AAE) is defined as $1$ minus attribute classification accuracy ($1$ − acc).

nuScenes Detection Score (NDS)

mAP with a threshold on IoU is perhaps the most popular metric for object detection. However, this metric can not capture all aspects of the nuScenes detection tasks, like velocity and attribute estimation. Further, it couples location, size, and orientation estimates. nuScenes proposed instead consolidating the different error types into a scalar score:

$$ \text{NDS} = \frac{1}{10} [5\text{mAP}+\sum_{\text{mTP}\in\mathbb{TP}} (1-\min(1, \text{mTP}))] . $$

BEVDet-r50

Corruption NDS mAP mATE mASE mAOE mAVE mAAE
Clean 0.3770 0.2987 0.7336 0.2744 0.5713 0.9051 0.2394
Cam Crash 0.2486 0.0990 0.8147 0.2975 0.6402 0.9990 0.2842
Frame Lost 0.1924 0.0781 0.8545 0.4413 0.7179 1.0247 0.4780
Color Quant 0.2408 0.1542 0.8718 0.3579 0.7376 1.2194 0.3958
Motion Blur 0.2061 0.1156 0.8891 0.4020 0.7693 1.1521 0.4645
Brightness 0.2565 0.1787 0.8380 0.3736 0.7216 1.2912 0.3955
Low Light 0.1102 0.0470 0.9867 0.5308 0.9443 1.2841 0.6708
Fog 0.2461 0.1404 0.8801 0.3018 0.7483 1.1610 0.3112
Snow 0.0625 0.0254 0.9853 0.7204 1.0029 1.1642 0.8160

Experiment Log

Time: Mon Feb 13 15:52:59 2023

Camera Crash

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.2905 0.1581 0.7915 0.2749 0.6302 0.9313 0.2574
Moderate 0.2223 0.0679 0.8403 0.3309 0.6208 1.0798 0.3247
Hard 0.2329 0.0709 0.8124 0.2868 0.6697 0.9858 0.2706
Average 0.2486 0.0990 0.8147 0.2975 0.6402 0.9990 0.2842

Frame Lost

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3027 0.1752 0.7857 0.2774 0.6143 0.9262 0.2451
Moderate 0.2076 0.0508 0.8516 0.3338 0.6586 1.1364 0.3342
Hard 0.0667 0.0083 0.9261 0.7126 0.8808 1.0116 0.8546
Average 0.1924 0.0781 0.8545 0.4413 0.7179 1.0247 0.4780

Color Quant

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3373 0.2608 0.7665 0.2770 0.6201 1.0288 0.2678
Moderate 0.2450 0.1599 0.8534 0.3639 0.7289 1.2417 0.4031
Hard 0.1400 0.0419 0.9956 0.4329 0.8639 1.3876 0.5166
Average 0.2408 0.1542 0.8718 0.3579 0.7376 1.2194 0.3958

Motion Blur

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3172 0.2214 0.7986 0.2796 0.6347 0.9760 0.2457
Moderate 0.1816 0.0786 0.9320 0.3637 0.8502 1.1827 0.4312
Hard 0.1194 0.0467 0.9366 0.5627 0.8231 1.2976 0.7166
Average 0.2061 0.1156 0.8891 0.4020 0.7693 1.1521 0.4645

Brightness

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3226 0.2420 0.7818 0.2834 0.6731 1.0987 0.2456
Moderate 0.2415 0.1713 0.8363 0.4140 0.7245 1.3378 0.4670
Hard 0.2053 0.1228 0.8959 0.4233 0.7673 1.4370 0.4739
Average 0.2565 0.1787 0.8380 0.3736 0.7216 1.2912 0.3955

Low Light

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.1503 0.0742 0.9799 0.4318 0.9123 1.3062 0.5445
Moderate 0.1297 0.0487 0.9837 0.4343 0.9618 1.4317 0.5661
Hard 0.0507 0.0181 0.9966 0.7264 0.9587 1.1143 0.9018
Average 0.1102 0.0470 0.9867 0.5308 0.9443 1.2841 0.6708

Fog

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.2780 0.1790 0.8460 0.2798 0.7233 1.0716 0.2658
Moderate 0.2477 0.1364 0.8822 0.2888 0.7533 1.1280 0.2809
Hard 0.2125 0.1059 0.9122 0.3368 0.7684 1.2835 0.3868
Average 0.2461 0.1404 0.8801 0.3018 0.7483 1.1610 0.3112

Snow

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.1206 0.0466 0.9653 0.5091 0.9417 1.2147 0.6114
Moderate 0.0420 0.0200 0.9896 0.7920 1.0515 1.1336 0.8985
Hard 0.0249 0.0095 1.0010 0.8601 1.0156 1.1442 0.9381
Average 0.0625 0.0254 0.9853 0.7204 1.0029 1.1642 0.8160

References

@article{huang2021bevdet,
  title={Bevdet: High-performance multi-camera 3d object detection in bird-eye-view},
  author={Huang, Junjie and Huang, Guan and Zhu, Zheng and Du, Dalong},
  journal={arXiv preprint arXiv:2112.11790},
  year={2021}
}
}