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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:

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

PolarFormer-R101

Corruption NDS mAP mATE mASE mAOE mAVE mAAE
Clean 0.4602 0.3916 0.7060 0.2718 0.3610 0.8079 0.2093
Cam Crash 0.3133 0.1425 0.7746 0.2840 0.4440 0.8524 0.2250
Frame Lost 0.2808 0.1134 0.8034 0.3093 0.4981 0.8988 0.2498
Color Quant 0.3509 0.2538 0.8059 0.2999 0.4812 0.9724 0.2592
Motion Blur 0.3221 0.2117 0.8196 0.2946 0.5727 0.9379 0.2258
Brightness 0.4304 0.3574 0.7390 0.2738 0.4149 0.8522 0.2032
Low Light 0.2554 0.1393 0.8418 0.3557 0.6087 1.2004 0.3364
Fog 0.4262 0.3518 0.7338 0.2735 0.4143 0.8672 0.2082
Snow 0.2304 0.1058 0.9125 0.3363 0.6592 1.2284 0.3174

Experiment Log

Time: Fri Feb 17 18:56:16 2023

Camera Crash

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3619 0.2181 0.7442 0.2770 0.3972 0.8414 0.2112
Moderate 0.2849 0.1004 0.8018 0.2877 0.4279 0.9142 0.2217
Hard 0.2930 0.1092 0.7777 0.2874 0.5069 0.8017 0.2420
Average 0.3133 0.1425 0.7746 0.2840 0.4440 0.8524 0.2250

Frame Lost

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3761 0.2419 0.7369 0.2759 0.3936 0.8353 0.2071
Moderate 0.2734 0.0817 0.7985 0.2900 0.4869 0.8785 0.2212
Hard 0.1929 0.0166 0.8747 0.3619 0.6138 0.9827 0.3210
Average 0.2808 0.1134 0.8034 0.3093 0.4981 0.8988 0.2498

Color Quant

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.4364 0.3618 0.7339 0.2726 0.3862 0.8410 0.2111
Moderate 0.3681 0.2703 0.7991 0.2785 0.4676 0.8986 0.2265
Hard 0.2483 0.1293 0.8848 0.3487 0.5898 1.1776 0.3401
Average 0.3509 0.2538 0.8059 0.2999 0.4812 0.9724 0.2592

Motion Blur

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.4197 0.3333 0.7282 0.2766 0.4191 0.8390 0.2064
Moderate 0.3006 0.1807 0.8348 0.2957 0.6035 0.9351 0.2281
Hard 0.2459 0.1210 0.8957 0.3116 0.6955 1.0397 0.2430
Average 0.3221 0.2117 0.8196 0.2946 0.5727 0.9379 0.2258

Brightness

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.4534 0.3840 0.7119 0.2717 0.3816 0.8180 0.2023
Moderate 0.4313 0.3587 0.7418 0.2736 0.4046 0.8606 0.1998
Hard 0.4065 0.3296 0.7632 0.2762 0.4584 0.8780 0.2074
Average 0.4304 0.3574 0.7390 0.2738 0.4149 0.8522 0.2032

Low Light

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3239 0.2155 0.7927 0.2947 0.5082 1.0073 0.2432
Moderate 0.2641 0.1389 0.8525 0.3165 0.6156 1.1961 0.2689
Hard 0.1782 0.0636 0.8802 0.4560 0.7024 1.3978 0.4972
Average 0.2554 0.1393 0.8418 0.3557 0.6087 1.2004 0.3364

Fog

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.4414 0.3684 0.7242 0.2719 0.3911 0.8395 0.2016
Moderate 0.4291 0.3552 0.7261 0.2730 0.4094 0.8677 0.2091
Hard 0.4082 0.3319 0.7512 0.2755 0.4424 0.8943 0.2140
Average 0.4262 0.3518 0.7338 0.2735 0.4143 0.8672 0.2082

Snow

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.2828 0.1619 0.8581 0.3101 0.5360 1.1919 0.2776
Moderate 0.2014 0.0729 0.9367 0.3594 0.7171 1.2392 0.3374
Hard 0.2069 0.0827 0.9426 0.3394 0.7246 1.2540 0.3373
Average 0.2304 0.1058 0.9125 0.3363 0.6592 1.2284 0.3174

References

@article{jiang2022polarformer,
  title={Polarformer: Multi-camera 3d object detection with polar transformers},
  author={Jiang, Yanqin and Zhang, Li and Miao, Zhenwei and Zhu, Xiatian and Gao, Jin and Hu, Weiming and Jiang, Yu-Gang},
  journal={arXiv preprint arXiv:2206.15398},
  year={2022}
}