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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:

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

BEVerse-Tiny

Corruption NDS mAP mATE mASE mAOE mAVE mAAE
Clean 0.4665 0.3214 0.6807 0.2782 0.4657 0.3281 0.1893
Cam Crash 0.3181 0.1218 0.7447 0.3545 0.5479 0.4974 0.2833
Frame Lost 0.3037 0.1466 0.7892 0.3511 0.6217 0.6491 0.2844
Color Quant 0.2600 0.1497 0.8577 0.4758 0.6711 0.6931 0.4676
Motion Blur 0.2647 0.1456 0.8139 0.4269 0.6275 0.8103 0.4225
Brightness 0.2656 0.1512 0.8120 0.4548 0.6799 0.7029 0.4507
Low Light 0.0593 0.0235 0.9744 0.7926 0.9961 0.9437 0.8304
Fog 0.2781 0.1348 0.8467 0.3967 0.6135 0.6596 0.3764
Snow 0.0644 0.0251 0.9662 0.7966 0.8893 0.9829 0.8464

Experiment Log

Time: Fri Jan 27 17:36:37 2023

Camera Crash

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3886 0.1928 0.7212 0.2857 0.5062 0.3777 0.1876
Moderate 0.2973 0.0890 0.7908 0.3478 0.5551 0.5042 0.2746
Hard 0.2685 0.0834 0.7221 0.4301 0.5823 0.6103 0.3878
Average 0.3181 0.1218 0.7447 0.3545 0.5479 0.4974 0.2833

Frame Lost

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.4131 0.2628 0.7314 0.2878 0.5277 0.4371 0.1990
Moderate 0.3025 0.1287 0.8078 0.3129 0.6440 0.6379 0.2159
Hard 0.1956 0.0482 0.8283 0.4527 0.6934 0.8722 0.4384
Average 0.3037 0.1466 0.7892 0.3511 0.6217 0.6491 0.2844

Color Quant

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.4349 0.2802 0.7130 0.2810 0.4865 0.3622 0.2099
Moderate 0.2760 0.1487 0.8523 0.4235 0.6118 0.6739 0.4225
Hard 0.0692 0.0201 1.0079 0.7228 0.9151 1.0433 0.7703
Average 0.2600 0.1497 0.8577 0.4758 0.6711 0.6931 0.4676

Motion Blur

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.4139 0.2568 0.7438 0.2867 0.4955 0.4274 0.1917
Moderate 0.2281 0.1131 0.8005 0.4239 0.6969 0.9409 0.4229
Hard 0.1523 0.0668 0.8975 0.5702 0.6900 1.0627 0.6530
Average 0.2647 0.1456 0.8139 0.4269 0.6275 0.8103 0.4225

Brightness

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3697 0.2385 0.7157 0.3664 0.5749 0.5122 0.3269
Moderate 0.2623 0.1368 0.8140 0.4242 0.6759 0.7325 0.4148
Hard 0.1648 0.0783 0.9064 0.5737 0.7889 0.8639 0.6103
Average 0.2656 0.1512 0.8120 0.4548 0.6799 0.7029 0.4507

Low Light

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.0719 0.0375 0.9701 0.7919 0.9588 0.9258 0.8223
Moderate 0.0591 0.0242 0.9748 0.7930 0.9916 0.9409 0.8296
Hard 0.0469 0.0087 0.9784 0.7929 1.0379 0.9644 0.8392
Average 0.0674 0.0330 0.9721 0.7923 0.9705 0.9314 0.8249

Fog

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3297 0.1721 0.8259 0.3396 0.5572 0.5544 0.2863
Moderate 0.2655 0.1323 0.8435 0.4215 0.6340 0.6928 0.4147
Hard 0.2392 0.1001 0.8707 0.4289 0.6493 0.7316 0.4281
Average 0.2781 0.1348 0.8467 0.3967 0.6135 0.6596 0.3764

Snow

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.1157 0.0463 0.9584 0.6531 0.7724 0.9625 0.7278
Moderate 0.0381 0.0116 0.9676 0.8715 0.9468 0.9868 0.9046
Hard 0.0394 0.0173 0.9727 0.8653 0.9487 0.9993 0.9067
Average 0.0644 0.0251 0.9662 0.7966 0.8893 0.9829 0.8464

References

@article{zhang2022beverse,
  title={Beverse: Unified perception and prediction in birds-eye-view for vision-centric autonomous driving},
  author={Zhang, Yunpeng and Zhu, Zheng and Zheng, Wenzhao and Huang, Junjie and Huang, Guan and Zhou, Jie and Lu, Jiwen},
  journal={arXiv preprint arXiv:2205.09743},
  year={2022}
}