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$10$$\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$$10$$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:

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

PETR-R50

Corruption	NDS	mAP	mATE	mASE	mAOE	mAVE	mAAE
Clean	0.3665	0.3174	0.8397	0.2796	0.6158	0.9543	0.2326
Cam Crash	0.2320	0.1065	0.9383	0.2975	0.7220	1.0169	0.2585
Frame Lost	0.2166	0.0868	0.9513	0.3041	0.7597	1.0081	0.2629
Color Quant	0.2472	0.1734	0.9121	0.3616	0.7807	1.1634	0.3473
Motion Blur	0.2299	0.1378	0.9587	0.3164	0.8461	1.1190	0.2847
Brightness	0.2841	0.2101	0.9049	0.3080	0.7429	1.0838	0.2552
Low Light	0.1571	0.0685	0.9465	0.4222	0.9201	1.4371	0.4971
Fog	0.2876	0.2161	0.9078	0.2928	0.7492	1.1781	0.2549
Snow	0.1417	0.0582	1.0437	0.4411	1.0177	1.3481	0.4713

Experiment Log

Time: Fri Jan 20 23:29:31 2023

Camera Crash

Severity	NDS	mAP	mATE	mASE	mAOE	mAVE	mAAE
Easy	0.2798	0.1766	0.8893	0.2864	0.6690	1.0017	0.2403
Moderate	0.2100	0.0719	0.9598	0.2959	0.7433	1.0592	0.2600
Hard	0.2061	0.0712	0.9658	0.3101	0.7538	0.9898	0.2752
Average	0.2320	0.1065	0.9383	0.2975	0.7220	1.0169	0.2585

Frame Lost

Severity	NDS	mAP	mATE	mASE	mAOE	mAVE	mAAE
Easy	0.2886	0.1896	0.8823	0.2858	0.6668	0.9886	0.2386
Moderate	0.2020	0.0594	0.9510	0.3031	0.7563	1.0284	0.2666
Hard	0.1594	0.0113	1.0206	0.3233	0.8559	1.0074	0.2836
Average	0.2166	0.0868	0.9513	0.3041	0.7597	1.0081	0.2629

Color Quant

Severity	NDS	mAP	mATE	mASE	mAOE	mAVE	mAAE
Easy	0.3411	0.2848	0.8517	0.2827	0.6436	0.9800	0.2553
Moderate	0.2664	0.1814	0.9047	0.2981	0.7528	1.0971	0.2874
Hard	0.1341	0.0541	0.9799	0.5040	0.9458	1.4131	0.4993
Average	0.2472	0.1734	0.9121	0.3616	0.7807	1.1634	0.3473

Motion Blur

Severity	NDS	mAP	mATE	mASE	mAOE	mAVE	mAAE
Easy	0.3239	0.2570	0.8781	0.2858	0.6727	0.9739	0.2356
Moderate	0.2018	0.0986	0.9766	0.3214	0.8868	1.1408	0.2901
Hard	0.1641	0.0579	1.0215	0.3420	0.9787	1.2423	0.3283
Average	0.2299	0.1378	0.9587	0.3164	0.8461	1.1190	0.2847

Brightness

Severity	NDS	mAP	mATE	mASE	mAOE	mAVE	mAAE
Easy	0.3241	0.2669	0.8743	0.2872	0.7033	0.9941	0.2351
Moderate	0.2765	0.1997	0.9052	0.3117	0.7513	1.1250	0.2647
Hard	0.2518	0.1637	0.9352	0.3251	0.7742	1.1324	0.2657
Average	0.2841	0.2101	0.9049	0.3080	0.7429	1.0838	0.2552

Low Light

Severity	NDS	mAP	mATE	mASE	mAOE	mAVE	mAAE
Easy	0.2021	0.1047	0.9132	0.3682	0.8226	1.4326	0.3983
Moderate	0.1570	0.0704	0.9299	0.4364	0.8963	1.4452	0.5194
Hard	0.1120	0.0304	0.9964	0.4619	1.0413	1.4334	0.5737
Average	0.1571	0.0685	0.9465	0.4222	0.9201	1.4371	0.4971

Fog

Severity	NDS	mAP	mATE	mASE	mAOE	mAVE	mAAE
Easy	0.3029	0.2375	0.8984	0.2875	0.7251	1.1419	0.2470
Moderate	0.2860	0.2147	0.9097	0.2918	0.7539	1.1806	0.2582
Hard	0.2739	0.1962	0.9153	0.2991	0.7687	1.2118	0.2595
Average	0.2876	0.2161	0.9078	0.2928	0.7492	1.1781	0.2549

Snow

Severity	NDS	mAP	mATE	mASE	mAOE	mAVE	mAAE
Easy	0.2000	0.1137	0.9863	0.3239	0.8998	1.2796	0.3582
Moderate	0.1190	0.0317	1.0832	0.4815	1.1323	1.3518	0.4872
Hard	0.1060	0.0292	1.0616	0.5178	1.0211	1.4129	0.5685
Average	0.1417	0.0582	1.0437	0.4411	1.0177	1.3481	0.4713

References

@article{liu2022petr,
  title = {PETR: Position Embedding Transformation for Multi-View 3D Object Detection},
  author = {Liu, Yingfei and Wang, Tiancai and Zhang, Xiangyu and Sun, Jian},
  journal = {arXiv preprint arXiv:2203.05625},
  year = {2022},
}