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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:

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

BEVDepth-r50

Corruption NDS mAP mATE mASE mAOE mAVE mAAE
Clean 0.4058 0.3328 0.6633 0.2714 0.5581 0.8763 0.2369
Cam Crash 0.2638 0.1111 0.7407 0.2959 0.6373 1.0079 0.2749
Frame Lost 0.2141 0.0876 0.7890 0.4134 0.6728 1.0536 0.4498
Color Quant 0.2751 0.1865 0.8190 0.3292 0.6946 1.2008 0.3552
Motion Blur 0.2513 0.1508 0.8320 0.3516 0.7135 1.1084 0.3765
Brightness 0.2879 0.2090 0.7520 0.3646 0.6724 1.2089 0.3766
Low Light 0.1757 0.0820 0.8540 0.4509 0.8073 1.3149 0.5410
Fog 0.2903 0.1973 0.7900 0.3021 0.6973 1.0640 0.2940
Snow 0.0863 0.0350 0.9529 0.6682 0.9107 1.2750 0.7802

Experiment Log

Time: Mon Feb 13 17:09:27 2023

Camera Crash

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3132 0.1771 0.7131 0.2750 0.6217 0.9053 0.2379
Moderate 0.2282 0.0759 0.7800 0.3319 0.6699 1.0951 0.3160
Hard 0.2500 0.0802 0.7289 0.2807 0.6204 1.0232 0.2709
Average 0.2638 0.1111 0.7407 0.2959 0.6373 1.0079 0.2749

Frame Lost

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3251 0.1962 0.7049 0.2735 0.5954 0.9158 0.2398
Moderate 0.2209 0.0576 0.7749 0.3321 0.6382 1.1222 0.3333
Hard 0.0962 0.0090 0.8872 0.6345 0.7849 1.1228 0.7764
Average 0.2141 0.0876 0.7890 0.4134 0.6728 1.0536 0.4498

Color Quant

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3748 0.2986 0.6970 0.2704 0.5783 0.9511 0.2475
Moderate 0.2981 0.1960 0.8174 0.2824 0.6306 1.1438 0.2688
Hard 0.1523 0.0650 0.9426 0.4348 0.8748 1.5074 0.5494
Average 0.2751 0.1865 0.8190 0.3292 0.6946 1.2008 0.3552

Motion Blur

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3639 0.2705 0.7008 0.2739 0.6008 0.9018 0.2361
Moderate 0.2387 0.1139 0.8566 0.2890 0.7532 1.0651 0.2836
Hard 0.1513 0.0680 0.9385 0.4918 0.7865 1.3584 0.6099
Average 0.2513 0.1508 0.8320 0.3516 0.7135 1.1084 0.3765

Brightness

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3568 0.2755 0.7028 0.2741 0.5896 1.0115 0.2428
Moderate 0.2706 0.1986 0.7529 0.4059 0.6913 1.2522 0.4370
Hard 0.2364 0.1529 0.8004 0.4137 0.7364 1.3629 0.4501
Average 0.2879 0.2090 0.7520 0.3646 0.6724 1.2089 0.3766

Low Light

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.2284 0.1263 0.8128 0.3639 0.7764 1.1842 0.3948
Moderate 0.1869 0.0848 0.8311 0.4170 0.8184 1.3781 0.4882
Hard 0.1118 0.0350 0.9182 0.5719 0.8270 1.3823 0.7400
Average 0.1757 0.0820 0.8540 0.4509 0.8073 1.3149 0.5410

Fog

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3205 0.2267 0.7648 0.2719 0.6404 1.0073 0.2507
Moderate 0.2980 0.1968 0.7906 0.2757 0.6809 1.0621 0.2563
Hard 0.2524 0.1685 0.8146 0.3586 0.7705 1.1227 0.3751
Average 0.2903 0.1973 0.7900 0.3021 0.6973 1.0640 0.2940

Snow

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.1716 0.0709 0.8735 0.4202 0.8563 1.5095 0.4884
Moderate 0.0513 0.0238 0.9843 0.7900 0.9088 1.1445 0.9236
Hard 0.0362 0.0103 1.0010 0.7943 0.9669 1.1709 0.9287
Average 0.0863 0.0350 0.9529 0.6682 0.9107 1.2750 0.7802

References

@article{li2022bevdepth,
  title={Bevdepth: Acquisition of reliable depth for multi-view 3d object detection},
  author={Li, Yinhao and Ge, Zheng and Yu, Guanyi and Yang, Jinrong and Wang, Zengran and Shi, Yukang and Sun, Jianjian and Li, Zeming},
  journal={arXiv preprint arXiv:2206.10092},
  year={2022}
}