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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:

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

DETR3D

Corruption NDS mAP mATE mASE mAOE mAVE mAAE
Clean 0.4224 0.3468 0.7647 0.2678 0.3917 0.8754 0.2108
Cam Crash 0.2859 0.1144 0.8400 0.2821 0.4707 0.8992 0.2202
Frame Lost 0.2604 0.0898 0.8647 0.3030 0.5041 0.9297 0.2439
Color Quant 0.3177 0.2165 0.8953 0.2816 0.5266 0.9813 0.2483
Motion Blur 0.2661 0.1479 0.9146 0.3085 0.6351 1.0385 0.2526
Brightness 0.4002 0.3149 0.7915 0.2703 0.4348 0.8733 0.2028
Low Light 0.2786 0.1559 0.8768 0.2947 0.5802 1.0290 0.2654
Fog 0.3912 0.3007 0.7961 0.2711 0.4326 0.8807 0.2110
Snow 0.1913 0.0776 0.9714 0.3752 0.7486 1.2478 0.3797

Experiment Log

Time: Sun Feb 12 14:09:13 2023

Camera Crash

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3284 0.1760 0.8120 0.2769 0.4190 0.8741 0.2138
Moderate 0.2594 0.0776 0.8709 0.2821 0.4674 0.9513 0.2225
Hard 0.2700 0.0895 0.8371 0.2874 0.5258 0.8723 0.2244
Average 0.2859 0.1144 0.8400 0.2821 0.4707 0.8992 0.2202

Frame Lost

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3437 0.2004 0.7959 0.2734 0.4139 0.8753 0.2063
Moderate 0.2514 0.0600 0.8680 0.2880 0.4980 0.9172 0.2145
Hard 0.1860 0.0092 0.9302 0.3476 0.6005 0.9965 0.3110
Average 0.2604 0.0898 0.8647 0.3030 0.5041 0.9297 0.2439

Color Quant

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3990 0.3169 0.8051 0.2678 0.4159 0.8900 0.2163
Moderate 0.3255 0.2277 0.8831 0.2764 0.4983 0.9717 0.2544
Hard 0.2287 0.1049 0.9978 0.3005 0.6657 1.0823 0.2741
Average 0.3177 0.2165 0.8953 0.2816 0.5266 0.9813 0.2483

Motion Blur

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3721 0.2813 0.8103 0.2756 0.4653 0.9047 0.2295
Moderate 0.2343 0.1023 0.9436 0.3137 0.6570 1.0311 0.2545
Hard 0.1918 0.0601 0.9900 0.3363 0.7829 1.1796 0.2738
Average 0.2661 0.1479 0.9146 0.3085 0.6351 1.0385 0.2526

Brightness

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.4225 0.3411 0.7668 0.2680 0.3981 0.8427 0.2052
Moderate 0.4012 0.3161 0.7893 0.2702 0.4301 0.8764 0.2025
Hard 0.3769 0.2876 0.8183 0.2728 0.4763 0.9008 0.2006
Average 0.4002 0.3149 0.7915 0.2703 0.4348 0.8733 0.2028

Low Light

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.3334 0.2231 0.8313 0.2778 0.4988 0.9291 0.2441
Moderate 0.2832 0.1607 0.8551 0.2891 0.5665 1.0100 0.2613
Hard 0.2192 0.0839 0.9439 0.3172 0.6753 1.1478 0.2909
Average 0.2786 0.1559 0.8768 0.2947 0.5802 1.0290 0.2654

Fog

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.4047 0.3161 0.7841 0.2700 0.4216 0.8545 0.2037
Moderate 0.3922 0.3026 0.7923 0.2701 0.4334 0.8813 0.2139
Hard 0.3767 0.2833 0.8118 0.2731 0.4428 0.9064 0.2153
Average 0.3912 0.3007 0.7961 0.2711 0.4326 0.8807 0.2110

Snow

Severity NDS mAP mATE mASE mAOE mAVE mAAE
Easy 0.2432 0.1212 0.9459 0.3114 0.6199 1.1665 0.2973
Moderate 0.1692 0.0602 0.9792 0.4073 0.8043 1.2775 0.4185
Hard 0.1616 0.0514 0.9890 0.4068 0.8215 1.2994 0.4233
Average 0.1913 0.0776 0.9714 0.3752 0.7486 1.2478 0.3797

References

@inproceedings{wang2021detr3d,
   title = {DETR3D: 3D Object Detection from Multi-View Images via 3D-to-2D Queries},
   author = {Wang, Yue and Guizilini, Vitor and Zhang, Tianyuan and Wang, Yilun and Zhao, Hang and and Solomon, Justin M.},
   booktitle = {The Conference on Robot Learning},
   year = {2021},
}