SlowGuess/NeurIPS_2023_OCR huggingface dataset:
The KRadar Dataset [35] is a recently published 4D radar dataset, which contains 58 sequences, i.e. 35K frames of synchronized multi-modality data. However, we have limited time to obtain the full data via shipping, so we only provide results on the sub-dataset stored on Google Drive, which consists of 20 sequences. This so-called KRadar-20 dataset includes 6493 training samples and 6515 test samples, of which  $50\%$  are nighttime data. The training samples are named trainval split, it is further split into train split of 5190 samples and val split of 1303 samples for ablation. Metrics follow KITTI [6] protocols with 40 recall positions. Different from RADIal, it only contains radar formats of range-azimuth map (RA map) and radar point cloud. But the RA map of KRadar contains an extra height dimension, and it enables us to test 3D prediction ability with 4D radar data.
Radar Formats. As introduced in Section 3, there are multiple formats of radar raw data, such as ADC, RT, RD, READ. These formats can be converted sequentially by FFT, which is a linear operation that can be absorbed into the linear layers. So from the perspective of neural network, these formats are equivalent. However, our proposed Polar-Aligned Attention requires a range dimension for indexing key and value in cross-attention, so we choose RT as a representative in the experiments. We also conduct experiments on RA to investigate the necessity of explicit azimuth.
Implementation Details. All our experiments are carried out on eight 3090 GPUs with the same batch size of 8. For the image backbone, we adopt ResNet-50 with pre-trained weights provided by BEVFormer [17]. For LiDAR and radar point cloud branch, we borrow the voxel encoder from PointPillar [15] and use ResNet-50 with modified strides as the backbone. Other representations of radar data share similar modified ResNet-50 as the backbone, but with an extra  $1 \times 1$  convolution at the beginning for channel number alignment. To prevent overfitting, the image-only variant is trained for only 12 epochs while others are trained for 24 epochs. AdamW [25] is adopted as the optimizer and a learning rate of 5e-5 is shared for all models. Due to the limited size of the dataset, we find that the results are unstable across different runs. To make a fair comparison, each experiment is repeated three times. In modality ablation, we show the mean and variance of each experiment result.
Table 3: BEV detection performances on RADial Dataset test split with refined 3D ground-truth bounding box. C, RD, and RT respectively refer to camera, range-Doppler spectrum, and range-time data. The best result of each metric is in bold. Our method exceeds FFTRadNet by a large margin.
Methods	Modality	BEV AP@0.7(%)↑	LET-BEV-AP@0.7(%)↑
Overall	0 - 50m	50 - 100m	Overall	0 - 50m	50 - 100m
FFTRadNet3D[39]	RD	57.26	68.66	52.28	62.81	75.55	57.98
EchoFusion	RT&C	84.92	87.56	91.06	88.86	92.81	94.81
Table 4: BEV detection performances on KRadar Dataset test split with KITTI protocol. 0.3, 0.5, and 0.7 are IoU thresholds. The inputs of EchoFusion are image and range-azimuth map. The best result of each metric is in **bold**.
Training Set	Method	BEV AP(%)↑	3D AP(%)↑
AP@0.3	AP@0.5	AP@0.7	AP@0.3	AP@0.5	AP@0.7
KRadar	RTNH[35]	58.04	42.60	10.69	49.65	17.87	0.45
KRadar-20-trainval	RTNH[35]	61.38	46.47	10.47	53.05	17.98	3.03
KRadar-20-trainval	EchoFusion	69.95	57.28	33.07	68.35	43.87	14.00
5.2 Comparison to State-of-the-art Methods
5.2.1 Results on RADial Dataset
We first compare our method with state-of-the-art detectors on AP, AR, range error, and azimuth error defined in RADIal [39], with original object-level point annotations<sup>1</sup>. The results are illustrated in Table 2. Our method significantly improves AR and F1 performance and achieves a remarkable improvement over all existing detectors including CMS [10], which also integrates both radar raw data and camera data. Note that RE and AE are not quite informative because these two metrics are calculated on all the recalled objects of a method, which is unfair to high-recall models like ours.
To evaluate in a more rigorous and informative way, we also conduct experiments on the refined annotations and vastly adopted metrics in 3D object detection. FFTRadNet [39] is lifted up with additional branches to predict the scale and orientation of targets. We can only compare with this FFTRadNet variant since codes of other algorithms [7; 10; 52] are not available yet. The results in Table 3 show that the proposed method outperforms FFTRadNet by a large margin. This significant improvement reveals the huge benefit of unleashing the power of radar data in multi-modality fusion.
5.2.2 Results on KRadar Dataset
The baseline on KRadar dataset is the official RTNH [35], which requires radar point cloud. Here, the proposed EchoFusion is input with image and RA map. To align with the baseline, we take the radius and azimuth range respectively as  $[0, 72]$  m and  $[-20, 20]$  degrees by the limit of camera field of view. The results are shown in Table 4. With RA map and image fusion, our EchoFusion improves over 10 points at each metric, except for BEV AP of IoU threshold 0.3. And since KRadar has higher vertical resolution and more accurate 3D groundtruth than RADIal, our method achieves more considerable improvements in 3D metrics.
We ablate the input format to the radar feature extraction network in Table 5. It shows that the decomposition of complex input can improve overall detection performance, especially for long-range perception. The magnitude and phase representation encodes a non-linear transformation of the complex representation, which may relate to the final prediction target better. We also tried to remove the pre-training of the image branch. The result drops significantly, which confirms that in this relatively small dataset, a good pre-training is crucial for good performance.
<sup>1</sup>The official implementation of these metrics are different from common implementations. Specifically, AP and AR are averaged on score thresholds from 0.1 to 0.9 with step of 0.1 and IoU threshold of 0.5. And F1 score is directly calculated from AP and AR defined above.
Table 5: Ablation studies on our EchoFusion. Complex means interpreting input features as real and imaginary (IQ) or magnitude and phase (MP). Pretrain means whether to use the pre-trained image backbone. The best result of each metric is in **bold**.
Conditions	BEV AP@0.7(%)↑	LET-BEV-AP@0.7(%)↑
Complex	Pretrain	Overall	0 - 50m	50 - 100m	Overall	0 - 50m	50 - 100m
MP	w	84.92	87.56	91.06	88.86	92.81	94.81
IQ	w	82.64	87.09	87.81	88.06	92.25	93.24
MP	w/o	74.34	81.26	78.71	78.90	85.44	84.28
Table 6: BEV detection performances of different modality combinations of our algorithm on RADIal Dataset test split. Refined 3D bounding box annotations are applied. C, L, RD, RT, RA, RP respectively refer to the camera, LiDAR, range-Doppler spectrum, range-time data, range-azimuth map, and radar point cloud. The best result without LiDAR of each metric are in bold, and the results with LiDAR are on gray background.
Modality	BEV AP@0.7(%)↑	LET-BEV-AP@0.7(%)↑
C	RT	RA	RP	L	Overall	0 - 50m	50 - 100m	Overall	0 - 50m	50 - 100m
✓	10.07±1.10	21.68±3.11	2.21±0.59	56.92±3.91	78.98±1.41	36.20±5.81
✓	48.26±0.92	62.33±4.00	45.05±0.98	55.04±1.25	68.56±4.11	52.30±1.82
✓	50.67±1.03	65.05±1.59	42.98±0.51	58.53±0.13	72.95±0.78	51.41±0.54
✓	53.55±0.70	66.19±1.72	47.41±1.06	62.59±1.14	76.45±2.06	56.73±1.33
✓	84.47±0.15	86.92±0.61	91.91±0.13	86.07±0.44	88.55±0.79	93.17±0.10
✓	✓	84.92±0.98	87.56±1.58	91.06±1.18	88.86±0.62	92.81±1.37	94.81±0.52
✓	✓	84.77±0.65	87.93±0.60	91.48±0.28	89.54±0.54	93.83±0.56	94.87±0.58
✓	✓	82.35±0.93	86.97±1.01	86.39±0.74	88.35±0.78	93.07±0.80	92.77±0.69
✓	✓	86.35±1.15	88.81±1.40	94.25±1.68	88.44±0.79	91.63±1.34	95.31±1.28
5.4 Comparison of Different Modalities
To further study the effects of different modalities, we change the input format indicated in Figure 2 and corresponding backbones, and test with and without image modality. Table 6 presents the results, more results on KRadar can be found in our appendix, and our findings are listed as follows.
Comparing single-modality results It is not surprising that LiDAR ranks first while the camera is the worst in terms of AP. Though poor in depth estimation, the camera has excellent angular resolution, which is beneficial for LET-BEV-AP. It achieves comparable results with radar in LET-BEV-AP. Besides, without the guidance of image, the radar-only network gets better performance as more hand-crafted post-processing are involved. However, their metrics still lag far from those of LiDAR.
Comparing multi-modality with single modality The power of radar data is released by fusing with image. No matter in what data format, all the radar raw representations gain around 30 points improvement by fusing with images. By combining image and range-time data, we obtain BEV AP that is only 0.03 less than that of LiDAR only method. And the LET-BEV-AP and long-range detection ability are even better. We argue that it is mainly because images provide enough clues to decode the essential information from raw radar representation.
Comparing multi-modality results When integrating with images, the LiDAR-fused method still outperforms other radar-fused methods. In terms of different representations of radar data, both RT and RA outperform traditional cloud points, especially in the 50-100m range, in which the difference is as large as 4 points in AP. We owe this finding to the information loss and false alarm of radar point cloud as shown in Figure 1. The performance gap between RT and RA with camera modality is within the error bar, indicating that it is not necessary to explicitly solve the azimuth, nor necessary to permute the Doppler-angle dimensions as FFTRadNet [39] does.
5.5 Discussion and Limitation
Firstly, it is worth noticing that although the overall performance of radar is improved by fusing with the camera, the performance in the short-range is lower than that in the long-range. We speculate the main reason is inaccurate annotation. The 16-beam LiDAR provided in RADial is too sparse at
Table 7: 3D detection performances on RADial Dataset test split with refined 3D ground-truth bounding box. C, L, and RT respectively refer to camera, LiDAR, and radar-time data. The best result of each metric is in bold.
Modality	3D AP@0.5(%)↑	Average Error@0.5↓
Overall	0 - 50m	50 - 100m	ATE	ASE	AOE
L	62.69	80.04	54.26	0.243	0.171	0.027
L&C	68.36	84.74	61.54	0.239	0.180	0.020
RT&C	39.81	56.05	31.24	0.301	0.173	0.020
a farther distance for annotators to give an accurate size for the long-range objects. In such cases, they are required to assign a template with a fixed size to these objects. These annotations make the problem much easier for farther distances, which leads to higher performance than near distances.
Secondly, though the radial speed label is included in the original annotations of RADial, radial speed is not quite useful for downstream modules like planning since they need accurate longitudinal and lateral velocity to predict whether the vehicles will interfere with the ego vehicle. However, the synchronized frames are not consecutive in this dataset, it is hard to label velocities for the objects. Considering these factors, velocity prediction is not included in our task.
Finally, as shown in Table 7, our method still lags far from LiDAR-based methods. The primary limitation can be attributed to imperfect z localization, resulting in relatively high Average Localization Error (ATE). The inferior performance is mainly due to coarse LiDAR annotation and inferior radar elevation resolution. The low elevation distinguishing power of LiDAR makes annotation error much worse at long range. As a result, both LiDAR-based and radar-based methods experience a significant drop in 3D AP within the  $50 - 100\mathrm{m}$  interval. But when equipped with high elevation resolution and accurate 3D groundtruth provided by KRadar, our method shows excellent performance in 3D metrics, as shown in Table 4. This emphasizes the pressing need for a raw radar dataset of higher quality that enables better exploration of radar data usage.
In this work, we have proposed a novel method for radar raw data fusion with other sensors in a BEV space. Our proposed EchoFusion is concise and effective, which outperforms previous work by a significant margin. We are the first to demonstrate the potential of radar as a low-cost alternative for LiDAR in autonomous driving systems through thorough analyses and experiments.
This work is only a starting point to study how raw radar data can be exploited. However, many attempts are limited by the available datasets. We urge a large-scale and high-quality dataset. However, the acquisition of high-quality multi-modality data with accurate annotation needs great effort and deliberate design for clock synchronization and high storage demand. We will try to build the dataset to facilitate further research.
Societal Impacts Our method can be deployed in the autonomous driving system. Performance loss caused by improper usage may increase security risks.
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A Proof for column and pillar correspondence
In this section, we will provide a detailed proof for the correspondence between pillar in radar coordinate and column in camera coordinate as described in Section 4.2 of our main paper.
Suppose that the rotation matrix and translation vector between radar and camera are:
$$
R = \left( \begin{array}{l l l} a _ {1} & b _ {1} & c _ {1} \\ a _ {2} & b _ {2} & c _ {2} \\ a _ {3} & b _ {3} & c _ {3} \end{array} \right), T = \left( \begin{array}{l} d _ {1} \\ d _ {2} \\ d _ {3} \end{array} \right). \tag {S1}
$$
Then for a point located at  $(r_{bev}, \phi_{bev}, z)$  under radar's polar coordinate, it has cartesian coordinate  $(x_R, y_R, z_R)$ :
$$
x _ {R} = r _ {b e v} \cos (\phi_ {b e v}), y _ {R} = r _ {b e v} \sin (\phi_ {b e v}), z _ {R} = z, \tag {S2}
$$
and it can be projected to the camera frame using extrinsic parameters:
$$
\left( \begin{array}{l} x _ {C} \\ y _ {C} \\ z _ {C} \end{array} \right) = R \left( \begin{array}{l} x _ {R} \\ y _ {R} \\ z _ {R} \end{array} \right) + T = \left( \begin{array}{l} a _ {1} r _ {b e v} \cos \phi_ {b e v} + b _ {1} r _ {b e v} \sin \phi_ {b e v} + c _ {1} z + d _ {1} \\ a _ {2} r _ {b e v} \cos \phi_ {b e v} + b _ {2} r _ {b e v} \sin \phi_ {b e v} + c _ {2} z + d _ {2} \\ a _ {3} r _ {b e v} \cos \phi_ {b e v} + b _ {3} r _ {b e v} \sin \phi_ {b e v} + c _ {3} z + d _ {3} \end{array} \right). \tag {S3}
$$
Using the intrinsic parameters, the camera coordinate  $(x_{C},y_{C},z_{C})$  can be correlated with image pixel position  $(x_{I},y_{I})$  using:
$$
\frac {x _ {I} - u _ {0}}{f _ {x}} = \frac {x _ {C}}{z _ {C}}, \frac {y _ {I} - v _ {0}}{f _ {y}} = \frac {y _ {C}}{z _ {C}}, \tag {S4}
$$
where  $f_{x}, f_{y}, u_{0}$ , and  $v_{0}$  are intrinsic parameters. Our goal is to find a situation that the pillar is projected as a column on the image plane. Under this condition,  $x_{I}$  should be irrelevant with  $z$ , i.e. in the equation below:
$$
\frac {x _ {I} - u _ {0}}{f _ {x}} = \frac {x _ {C}}{z _ {C}} = \frac {a _ {1} r _ {b e v} \cos \phi_ {b e v} + b _ {1} r _ {b e v} \sin \phi_ {b e v} + c _ {1} z + d _ {1}}{a _ {3} r _ {b e v} \cos \phi_ {b e v} + b _ {3} r _ {b e v} \sin \phi_ {b e v} + c _ {3} z + d _ {3}}. \tag {S5}
$$
The coefficients of  $z$  should be 0, which means by combining the relationship between rotation matrix  $R$  with roll  $\alpha$ , pitch  $\beta$ , and yaw  $\gamma$  [30], we can derive:
$$
\left\{ \begin{array}{l} c _ {1} = \sin \gamma \sin \alpha + \cos \gamma \sin \beta \cos \alpha = 0 \\ c _ {3} = \cos \beta \cos \alpha = 0. \end{array} \right. \tag {S6}
$$
Considering second row of Eq. (S6), there are two solutions  $\beta = \pm \frac{\pi}{2}$  or  $\alpha = \pm \frac{\pi}{2}$ . Considering the first solution  $\beta = \pm \frac{\pi}{2}$ , the first row of Eq. (S6) is transformed to:
$$
\sin \gamma \sin \alpha \pm \cos \gamma \cos \alpha = 0, \tag {S7}
$$
which means:
$$
\cos (\gamma \mp \alpha) = 0. \tag {S8}
$$
$$
\beta = \frac {\pi}{2}, \gamma = \alpha \pm \frac {\pi}{2}, \alpha \in [ - \pi , \pi ], \tag {S9}
$$
$$
o r, \beta = - \frac {\pi}{2}, \gamma = - \alpha \pm \frac {\pi}{2}, \alpha \in [ - \pi , \pi ].
$$
For another solution  $\alpha = \pm \frac{\pi}{2}$ , the first row of Eq. (S6) is transformed to:
$$
\sin \gamma \sin \alpha + \cos \gamma \sin \beta \cos \alpha = \pm \sin \gamma = 0. \tag {S10}
$$
$$
\alpha = \pm \frac {\pi}{2}, \gamma = 0 o r \pi , \beta \in [ - \pi , \pi ]. \tag {S11}
$$
As a result, the final solution is:
$$
\beta = \frac {\pi}{2}, \gamma = \alpha \pm \frac {\pi}{2}, \alpha \in [ - \pi , \pi ],
$$
$$
o r, \beta = - \frac {\pi}{2}, \gamma = - \alpha \pm \frac {\pi}{2}, \alpha \in [ - \pi , \pi ], \tag {S12}
$$
$$
o r, \alpha = \pm \frac {\pi}{2}, \gamma = 0 o r \pi , \beta \in [ - \pi , \pi ].
$$
In standard ADS, the LiDAR or radar coordinate system usually has a  $z$ -axis pointing up, while the camera coordinate system has a  $y$ -axis pointing up or down. So a widely adopted practice first exchanges the  $y$  and  $z$  axes, which means a roll  $\alpha = \pm \frac{\pi}{2}$ . After that, a pitch  $\beta$  around the vertical  $y$ -axis is executed, while further rotation around the  $z$ -axis is not required, as shown in Figure S1. In other words, the roll  $\beta$  can be any value between  $-\pi$  and  $\pi$ , while yaw  $\gamma$  is set to 0. This is exactly the situation of the third solution of Eq. (S12). And under this condition, we have expression of  $R$  according to [30]:
Figure S1: Illustration of coordinate system transformation.
$$
R = \left( \begin{array}{c c c} \cos \beta & \pm \sin \beta & 0 \\ 0 & 0 & \mp 1 \\ - \sin \beta & \pm \cos \beta & 0 \end{array} \right), T = \left( \begin{array}{c} d _ {1} \\ d _ {2} \\ d _ {3} \end{array} \right). \tag {S13}
$$
Thus, using Eq. (S3) and Eq. (S5), we can get the expression of column index  $x_{I}$ . If  $\alpha = \frac{\pi}{2}$ , we have:
$$
x _ {I} = u _ {0} + f _ {x} \frac {r _ {b e v} \cos (\beta - \phi_ {b e v}) + d _ {1}}{- r _ {b e v} \sin (\beta - \phi_ {b e v}) + d _ {3}}. \tag {S14}
$$
If  $\alpha = -\frac{\pi}{2}$ , we have:
$$
x _ {I} = u _ {0} + f _ {x} \frac {r _ {b e v} \cos (\beta + \phi_ {b e v}) + d _ {1}}{- r _ {b e v} \sin (\beta + \phi_ {b e v}) + d _ {3}}. \tag {S15}
$$
For RADIal, the rotation matrix from the radar coordinate system to the camera coordinate system is:
$$
R = \left( \begin{array}{c c c} 0. 0 4 6 5 & - 0. 9 9 8 9 & - 0. 0 0 5 1 \\ - 0. 0 4 7 6 & 0. 0 0 2 9 & - 0. 9 9 8 9 \\ 0. 9 9 7 8 & 0. 0 4 6 7 & - 0. 0 4 7 4 \end{array} \right), \tag {S16}
$$
which is the approximation of  $(\alpha, \beta, \gamma) = (\pi/2, -\pi/2, 0)$ . And thus we approximately have:
$$
x _ {I} \approx u _ {0} + f _ {x} \frac {- r _ {b e v} \sin \phi_ {b e v} + d _ {1}}{r _ {b e v} \cos \phi_ {b e v} + d _ {3}}. \tag {S17}
$$
It can be inferred that  $x_{I}$  is almost irrelevant to  $z$ , which means one pillar in the polar coordinate of radar corresponds to a column in the image.
B Visualization and Dataset Statistics
To better illustrate the performance of our method, we visualize the predictions and ground truths in Figure S2. As can be seen from the cases in the first and the second column, our method can accurately predict the position of vehicles. But there are several cases in which the accurate prediction does not get high confidence, as shown in the upper case in the third column. On the other hand, the orientation estimation error may be significant when the yaw of the vehicle is large, shown in the inferior case in the third column. The main reason is that the samples with large yaw are relatively rare in the dataset, as shown in Figure S3 (b) and (c).
As shown in Figure S3 (a), the samples of test data are rather rare within 30 meters and out of 80 meters. To comprehensively explore the detection performance of objects, we divide the range into  $0 - 50\mathrm{m}$  and  $50 - 100\mathrm{m}$ , which correspond to short-range and long-range detection performance respectively.
We further visualize scenarios that are corrected by our new labels. It is worth noting that the original annotation and prediction of previous methods are centers of objects' visible faces, and they assign a fixed scale and zero orientation when calculating Average Precision (AP). But vehicles of large angles and scales are normal in daily scenarios, as shown in Figure S4. Our new annotations based on dense LiDAR points correct this, helping a more comprehensive evaluation of existing methods. We also annotate other traffic participants such as pedestrians and cyclists. But due to their limited numbers (4 cyclists, 23 pedestrians in training split, and 17 cyclists, 0 pedestrians in test split), we don't add more fine-grained class labels.