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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:

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

BEVFusion Camera

Corruption NDS mAP mATE mASE mAOE mAVE mAAE
Clean 0.4122 0.3556 0.6677 0.2727 0.5612 0.8954 0.2593
Cam Crash 0.2777 0.1232 0.7343 0.2745 0.6202 0.9324 0.2846
Frame Lost 0.2255 0.0968 0.7888 0.3835 0.6476 1.0360 0.4393
Color Quant 0.2763 0.1896 0.8245 0.3308 0.6832 1.1253 0.3633
Motion Blur 0.2788 0.1895 0.7902 0.3204 0.7041 1.0588 0.3635
Brightness 0.2902 0.2158 0.7857 0.3390 0.7030 1.2076 0.3497
Low Light 0.1076 0.0422 0.9707 0.5462 0.9279 1.2293 0.6904
Fog 0.3041 0.2084 0.8228 0.2829 0.6373 1.0004 0.2774
Snow 0.1461 0.0787 0.9101 0.5238 0.8463 1.2869 0.6526

Experiment Log

Time: Thu Apr 6 10:06:26 2023

Camera Crash

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3137 0.1908 0.7159 0.2716 0.6189 0.9407 0.2697
Moderate 0.2509 0.0859 0.7500 0.2747 0.6010 1.0205 0.2944
Hard 0.2684 0.0930 0.7370 0.2772 0.6407 0.8359 0.2897
Average 0.2777 0.1232 0.7343 0.2745 0.6202 0.9324 0.2846

Frame Lost

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3308 0.2128 0.7183 0.2716 0.5973 0.9089 0.2598
Moderate 0.2238 0.0662 0.7833 0.3263 0.6317 1.0767 0.3520
Hard 0.1220 0.0115 0.8649 0.5526 0.7137 1.1223 0.7061
Average 0.2255 0.0968 0.7888 0.3835 0.6476 1.0360 0.4393

Color Quant

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3821 0.3165 0.6928 0.2748 0.5747 0.9495 0.2702
Moderate 0.2990 0.1993 0.7945 0.2857 0.6366 1.0470 0.2890
Hard 0.1478 0.0531 0.9861 0.4318 0.8384 1.3793 0.5306
Average 0.2763 0.1896 0.8245 0.3308 0.6832 1.1253 0.3633

Motion Blur

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3707 0.3018 0.7237 0.2748 0.5953 0.9422 0.2657
Moderate 0.2695 0.1631 0.8029 0.2810 0.7244 1.0163 0.3125
Hard 0.1963 0.1035 0.8441 0.4055 0.7927 1.2178 0.5122
Average 0.2788 0.1895 0.7902 0.3204 0.7041 1.0588 0.3635

Brightness

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3579 0.2925 0.7268 0.2816 0.5994 1.0685 0.2754
Moderate 0.2733 0.2011 0.7903 0.3640 0.7303 1.2392 0.3881
Hard 0.2392 0.1537 0.8400 0.3715 0.7793 1.3150 0.3855
Average 0.2902 0.2158 0.7857 0.3390 0.7030 1.2076 0.3497

Low Light

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.1552 0.0645 0.9514 0.4168 0.8588 1.4046 0.5438
Moderate 0.1178 0.0433 0.9656 0.5019 0.9491 1.1622 0.6220
Hard 0.0497 0.0186 0.9951 0.7199 0.9757 1.1210 0.9055
Average 0.1076 0.0422 0.9707 0.5462 0.9279 1.2293 0.6904

Fog

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3347 0.2489 0.7846 0.2797 0.6110 0.9490 0.2729
Moderate 0.3036 0.2077 0.8254 0.2828 0.6288 0.9917 0.2737
Hard 0.2741 0.1685 0.8583 0.2861 0.6722 1.0604 0.2855
Average 0.3041 0.2084 0.8228 0.2829 0.6373 1.0004 0.2774

Snow

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.2176 0.1355 0.8505 0.4126 0.7409 1.2643 0.4978
Moderate 0.1096 0.0484 0.9359 0.5794 0.9024 1.3256 0.7289
Hard 0.1111 0.0521 0.9440 0.5793 0.8955 1.2709 0.7311
Average 0.1461 0.0787 0.9101 0.5238 0.8463 1.2869 0.6526

References

@inproceedings{liu2022bevfusion,
  title={BEVFusion: Multi-Task Multi-Sensor Fusion with Unified Bird's-Eye View Representation},
  author={Liu, Zhijian and Tang, Haotian and Amini, Alexander and Yang, Xingyu and Mao, Huizi and Rus, Daniela and Han, Song},
  booktitle={IEEE International Conference on Robotics and Automation (ICRA)},
  year={2023}
}