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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:

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

BEVFormer-Small

Corruption NDS mAP mATE mASE mAOE mAVE mAAE
Clean 0.4787 0.3700 0.7212 0.2792 0.4065 0.4364 0.2201
Cam Crash 0.2771 0.1130 0.8627 0.3099 0.5398 0.8376 0.2446
Frame Lost 0.2459 0.0933 0.8959 0.3411 0.5742 0.9154 0.2804
Color Quant 0.3275 0.2109 0.8476 0.2943 0.5234 0.8539 0.2601
Motion Blur 0.2570 0.1344 0.8995 0.3264 0.6774 0.9625 0.2605
Brightness 0.3741 0.2697 0.8064 0.2830 0.4796 0.8162 0.2226
Low Light 0.2413 0.1191 0.8838 0.3598 0.6470 1.0391 0.3323
Fog 0.3583 0.2486 0.8131 0.2862 0.5056 0.8301 0.2251
Snow 0.1809 0.0635 0.9630 0.3855 0.7741 1.1002 0.3863

Experiment Log

Time: Mon Feb 13 13:47:14 2023

Camera Crash

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3295 0.1801 0.8284 0.2943 0.4946 0.7597 0.2285
Moderate 0.2664 0.0965 0.8986 0.3087 0.5365 0.8226 0.2524
Hard 0.2353 0.0625 0.8611 0.3266 0.5884 0.9304 0.2530
Average 0.2771 0.1130 0.8627 0.3099 0.5398 0.8376 0.2446

Frame Lost

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3283 0.1947 0.8296 0.2923 0.4934 0.8405 0.2350
Moderate 0.2378 0.0684 0.9013 0.3229 0.5732 0.9090 0.2576
Hard 0.1717 0.0167 0.9569 0.4081 0.6559 0.9968 0.3486
Average 0.2459 0.0933 0.8959 0.3411 0.5742 0.9154 0.2804

Color Quant

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3896 0.2884 0.7960 0.2806 0.4468 0.7878 0.2345
Moderate 0.3415 0.2247 0.8281 0.2868 0.5023 0.8339 0.2578
Hard 0.2515 0.1197 0.9186 0.3156 0.6211 0.9401 0.2881
Average 0.3275 0.2109 0.8476 0.2943 0.5234 0.8539 0.2601

Motion Blur

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3582 0.2465 0.8195 0.2883 0.4981 0.8146 0.2304
Moderate 0.2246 0.0970 0.9206 0.3333 0.7192 1.0316 0.2657
Hard 0.1883 0.0597 0.9583 0.3575 0.8148 1.0413 0.2853
Average 0.2570 0.1344 0.8995 0.3264 0.6774 0.9625 0.2605

Brightness

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3936 0.2956 0.7911 0.2807 0.4517 0.7910 0.2273
Moderate 0.3735 0.2690 0.8093 0.2844 0.4798 0.8132 0.2237
Hard 0.3551 0.2446 0.8188 0.2840 0.5073 0.8445 0.2168
Average 0.3741 0.2697 0.8064 0.2830 0.4796 0.8162 0.2226

Low Light

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3043 0.1808 0.8480 0.2998 0.5862 0.8789 0.2488
Moderate 0.2449 0.1198 0.9006 0.3235 0.6576 1.0033 0.2687
Hard 0.1748 0.0567 0.9028 0.4560 0.6972 1.2352 0.4795
Average 0.2413 0.1191 0.8838 0.3598 0.6470 1.0391 0.3323

Fog

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3711 0.2650 0.8033 0.2837 0.4920 0.8171 0.2176
Moderate 0.3604 0.2511 0.8082 0.2857 0.5050 0.8275 0.2246
Hard 0.3433 0.2298 0.8279 0.2893 0.5197 0.8458 0.2332
Average 0.3583 0.2486 0.8131 0.2862 0.5056 0.8301 0.2251

Snow

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.2212 0.0951 0.9511 0.3311 0.6783 1.0630 0.3032
Moderate 0.1648 0.0509 0.9654 0.4098 0.8067 1.0791 0.4246
Hard 0.1567 0.0446 0.9724 0.4155 0.8374 1.1585 0.4310
Average 0.1809 0.0635 0.9630 0.3855 0.7741 1.1002 0.3863

References

@article{li2022bevformer,
  title = {BEVFormer: Learning Bird’s-Eye-View Representation from Multi-Camera Images via Spatiotemporal Transformers},
  author = {Li, Zhiqi and Wang, Wenhai and Li, Hongyang and Xie, Enze and Sima, Chonghao and Lu, Tong and Qiao, Yu and Dai, Jifeng},
  journal = {arXiv preprint arXiv:2203.17270},
  year = {2022},
}