SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table S1: LET-BEV-AP results with different longitudinal tolerance  $T_{l}$ . The performances of different modality combinations of our algorithm on RADial Dataset test split are presented, using refined 3D bounding box annotations. C, L, and RT respectively refer to the camera, LiDAR, and range-time data. The results with LiDAR are on gray background.
Modality	\(T_l=0.1, LET-BEV-AP@0.7\% \)↑	\(T_l=0.3, LET-BEV-AP@0.7\% \)↑
C	RT	L	Overall	0 - 50m	50 - 100m	Overall	0 - 50m	50 - 100m
✓	56.92±3.91	78.98±1.41	36.20±5.81	81.36±1.15	83.30±2.01	77.00±0.43
✓	55.04±1.25	68.56±4.11	52.30±1.82	55.34±1.91	69.79±4.59	51.02±0.07
✓	86.07±0.44	88.55±0.79	93.17±0.10	86.41±0.47	89.72±0.03	93.22±0.04
✓	✓	88.86±0.62	92.81±1.37	94.81±0.52	88.56±0.53	92.58±0.70	94.57±0.29
Table S2: Recall with different IoU thresholds. The performances of different modality combinations of our algorithm on RADIal Dataset test split are presented, using refined 3D bounding box annotations. C, L, and RT respectively refer to the camera, LiDAR, and range-time data. The results with LiDAR are on gray background.
Modality	BEV recall@0.7(%)↑	BEV recall@0.3(%)↑
C	RT	L	Overall	0 - 50m	50 - 100m	Overall	0 - 50m	50 - 100m
✓	62.73±1.24	73.89±2.11	61.21±0.82	86.27±0.43	92.13±0.71	93.40±0.54
✓	86.38±0.00	89.11±0.08	93.35±0.08	91.40±0.08	96.13±0.17	96.95±0.16
✓	✓	86.18±0.13	89.13±0.6	92.53±0.56	91.78±0.85	95.82±0.50	97.67±1.05
Table S3: BEV detection performances of different modality combinations of our algorithm on RADIal Dataset test split. Refined 3D bounding box annotations are applied. C, L, ADC, RD, RT, RA, RP respectively refer to the camera, LiDAR, ADC data, 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	ADC	RT	RD	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
✓	49.64±0.43	61.37±1.57	47.92±1.48	56.52±2.36	68.93±1.87	54.68±1.76
✓	48.26±0.92	62.33±4.00	45.05±0.98	55.04±1.25	68.56±4.11	52.30±1.82
✓	47.34±0.73	59.31±1.64	42.53±1.98	54.96±0.67	67.02±1.67	50.59±0.26
✓	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
✓	✓	84.85±0.22	87.68±1.54	91.46±1.08	88.66±0.63	92.43±1.15	94.99±0.66
✓	✓	84.92±0.98	87.56±1.58	91.06±1.18	88.86±0.62	92.81±1.37	94.81±0.52
✓	✓	83.31±0.39	87.26±0.56	89.16±0.44	88.24±0.06	92.18±0.43	93.26±0.73
✓	✓	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
Table S4: Ablation on the coordinate system. Experiments are carried on RADIal dataset, with RT data and image as input.
Coordinate	BEV AP@0.7(%)↑	LET-BEV-AP@0.7(%)↑
Overall	0 - 50m	50 - 100m	Overall	0 - 50m	50 - 100m
Polar	84.92±0.98	87.56±1.58	91.06±1.18	88.86±0.62	92.81±1.37	94.81±0.52
Sphere	85.02±0.60	88.02±0.59	91.76±0.98	89.97±0.61	93.35±0.32	96.41±1.21
Figure S2: Visualization of ground truths and predictions from RT and image fusion. The ground truth bounding boxes are in pink, while the predicted bounding boxes are in green with the confidence score on its upper right. The LiDAR points and the radar points are respectively in blue and red. The rear edge of each car is in cyan. We recommend readers to zoom in for better detail.
(c)
Figure S3: Statistics of RADial dataset. Image (a) corresponds to sample distribution over range, while images (b) and (c) correspond to yaw distribution over the range of train and test data splits.
C Complementary property of radar and camera
To highlight the complementary nature of radar and camera properties, we investigated the performance of LET-BEV-AP with varying longitudinal tolerance  $(T_{l})$ , as presented in Table S1. Notably, when using a larger  $T_{l}$  of 0.3, the camera's performance experiences a significant improvement. This suggests that the relatively lower performance of long-range LET-BEV-AP under  $T_{l}$  of 0.1 primarily stems from depth errors. By reducing the impact of longitudinal estimation, the camera's exceptional angular perception accuracy becomes more pronounced. Conversely, the LET-BEV-AP performance of the radar-only variant remains relatively unchanged. This finding indicates that the radar's depth estimation is quite accurate and minimally affected by the value of  $T_{l}$ . Similarly, the highly accurate LiDAR-only variant and camera and RT fusion variant don't suffer from performance fluctuation as well, which supports our conclusion.
To further investigate the primary factor affecting radar performance, we conducted a comparison of BEV recall at IoU thresholds of 0.7 and 0.3, as outlined in Table S2. It can be deduced that by using a
Figure S4: The visualization of the old labels and new labels under Bird's Eye View. The old labels include 3D center points and fixed scale and orientation, denoted as green boxes. The new labels are denoted as red boxes, which we offered real scale and orientation, as well as objects' accurate center position. The rear edge of each bounding box is colored in cyan. The left, middle, and right column respectively denotes the situation of large heading angle, missed traffic participants, and vehicles of large scale. We recommend readers to zoom in for better detail.
Figure S5: The illustration of Doppler Domain Multiplexing(DDM). This figure shows a toy example of how to use DDM to distinguish four transmitters.
less stringent IoU threshold, the recall of the RT-only variant experiences a significant increase. This result suggests that the RT-only variant's limitation mainly lies in its inferior angular localization ability. But by combining the strengths of camera and radar modalities, the model can leverage the advantages of both modalities, leading to a significant performance boost.
D Doppler domain multiplexing and coordinate system
As mentioned in [39], Doppler Domain Multiplexing(DDM) is used to distinguish received radar signals from different transmitters. The mechanism can be best illustrated in Range-Doppler (RD) spectrum format of data, as shown in Figure S5. Without DDM, the valid measurable speed interval is  $[-V_{max}, V_{max}]$ . Suppose we have four transmitters, Tx 1/2/3/4, and one object with speed in  $[0, V_{max}/2]$ . The echo signals from Tx 1/2/3/4 will respectively fall into sections C, D, A, B by using DDM, showing a periodical pattern. But now we can only measure speed in  $[0, V_{max}/2]$ . Similar
Table S5: BEV detection performances of different modality combination on KRadar Dataset test split with KITTI protocol of 40 recall positions. C, RA, RP respectively refer to the camera, range-azimuth map, and radar point cloud. 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-20-train	EchoFusion(RP)	55.74	43.94	20.56	53.40	29.21	2.90
KRadar-20-train	EchoFusion(RA)	54.45	42.28	17.97	51.75	24.65	3.85
KRadar-20-train	EchoFusion(RP+C)	66.46	54.17	26.39	58.62	34.67	3.96
KRadar-20-train	EchoFusion(RA+C)	68.70	55.90	29.65	66.68	34.33	5.34
phenomenon can be observed in the figure of Range Doppler data, i.e. the third image in Figure 2 in the paper.
We also carried out experiments on coordinate system of BEV space. Though the range dimension is under sphere system, we found that a polar system can achieve on par performance, as shown in Table S4. Thus we apply the polar system in the paper.
E More experimental results
Referring to Table S3, we have included the detection performance when our model consumes the ADC data or range-Doppler spectrum as input. It is worth noticing that we add an extra complex linear layer initialized with FFT coefficients for ADC data to replace the range FFT and the side-lobe suppression. In the case of the single modality version, the performance discrepancy between RT and these two modalities remains within the margin of error. When considering the fusion of image data, the performance of RD slightly lags behind that of RT, while that of ADC is almost the same as RT. These findings suggest that the integration of image data significantly mitigates the importance of conventional radar signal processing in accurate radar-based detection.
Besides, we offer ablation of different modality combinations on KRadar. The results are reported in Table S5. Here, we train all models with training split. The RA map shows considerable superiority over radar point cloud when fusing with the monocular image, which aligns with our research motivation and results on RADial dataset.