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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:

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

BEVDet-swin-tiny

Corruption NDS mAP mATE mASE mAOE mAVE mAAE
Clean 0.4037 0.3080 0.6648 0.2729 0.5323 0.8278 0.2050
Cam Crash 0.2609 0.1053 0.7786 0.3246 0.5761 0.9821 0.2822
Frame Lost 0.2115 0.0826 0.8174 0.4207 0.6710 1.0138 0.4294
Color Quant 0.2278 0.1487 0.8236 0.4518 0.7461 1.1668 0.4742
Motion Blur 0.2128 0.1235 0.8455 0.4457 0.7074 1.1857 0.5080
Brightness 0.2191 0.1370 0.8300 0.4523 0.7277 1.2995 0.4833
Low Light 0.0490 0.0180 0.9883 0.7696 1.0083 1.1225 0.8607
Fog 0.2450 0.1396 0.8459 0.3656 0.6839 1.2694 0.3520
Snow 0.0680 0.0312 0.9730 0.7665 0.8973 1.2609 0.8393

Experiment Log

Time: Fri Feb 24 19:37:37 2023

Camera Crash

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3125 0.1667 0.7428 0.2849 0.5806 0.8800 0.2201
Moderate 0.2328 0.0731 0.8256 0.3425 0.5669 1.0773 0.3019
Hard 0.2373 0.0762 0.7675 0.3463 0.5809 0.9891 0.3246
Average 0.2609 0.1053 0.7786 0.3246 0.5761 0.9821 0.2822

Frame Lost

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3245 0.1821 0.7239 0.2775 0.5814 0.8791 0.2037
Moderate 0.2180 0.0556 0.8139 0.3420 0.6295 1.0409 0.3125
Hard 0.0920 0.0102 0.9145 0.6425 0.8021 1.1214 0.7719
Average 0.2115 0.0826 0.8174 0.4207 0.6710 1.0138 0.4294

Color Quant

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3663 0.2685 0.6904 0.2770 0.5618 0.9104 0.2393
Moderate 0.2520 0.1513 0.7961 0.3625 0.6922 1.1799 0.3854
Hard 0.0649 0.0263 0.9843 0.7159 0.9842 1.4101 0.7979
Average 0.2278 0.1487 0.8236 0.4518 0.7461 1.1668 0.4742

Motion Blur

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3418 0.2385 0.7391 0.2849 0.5824 0.9489 0.2189
Moderate 0.1722 0.0846 0.8716 0.4882 0.7527 1.3531 0.5882
Hard 0.1244 0.0475 0.9257 0.5641 0.7872 1.2551 0.7168
Average 0.2128 0.1235 0.8455 0.4457 0.7074 1.1857 0.5080

Brightness

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3292 0.2258 0.7301 0.2936 0.5961 1.0621 0.2176
Moderate 0.2127 0.1183 0.8289 0.4238 0.7548 1.5022 0.4571
Hard 0.1156 0.0668 0.9310 0.6396 0.8323 1.3342 0.7753
Average 0.2191 0.1370 0.8300 0.4523 0.7277 1.2995 0.4833

Low Light

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.0649 0.0303 0.9777 0.7249 0.9451 1.1186 0.8546
Moderate 0.0447 0.0182 0.9918 0.7915 1.0292 1.1262 0.8607
Hard 0.0373 0.0056 0.9955 0.7925 1.0506 1.1226 0.8669
Average 0.0490 0.0180 0.9883 0.7696 1.0083 1.1225 0.8607

Fog

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.2769 0.1742 0.8119 0.3349 0.6491 1.1858 0.3061
Moderate 0.2504 0.1370 0.8493 0.3425 0.6720 1.2905 0.3168
Hard 0.2078 0.1075 0.8765 0.4194 0.7307 1.3318 0.4331
Average 0.2450 0.1396 0.8459 0.3656 0.6839 1.2694 0.3520

Snow

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.1342 0.0578 0.9422 0.5731 0.7594 1.4467 0.6721
Moderate 0.0337 0.0162 0.9872 0.8634 0.9679 1.1824 0.9249
Hard 0.0360 0.0197 0.9897 0.8630 0.9645 1.1535 0.9209
Average 0.0680 0.0312 0.9730 0.7665 0.8973 1.2609 0.8393

References

@article{huang2021bevdet,
  title={Bevdet: High-performance multi-camera 3d object detection in bird-eye-view},
  author={Huang, Junjie and Huang, Guan and Zhu, Zheng and Du, Dalong},
  journal={arXiv preprint arXiv:2112.11790},
  year={2021}
}
}