We first preprocess the point cloud obtained from 4D mmWave radar to extract point-wise features for the road boundary segmentation task while reducing noisy points and mitigating the sparsity of the point cloud.

The point-wise road boundary segmentation module aims to distinguish road boundary points from noisy points. The segmentation is based on the PointNet++ framework, which efficiently captures the spatial distribution of point clouds and point-wise features Qi et al. (2017). The main innovations of our method are: 1) we reduce the false positive detections (i.e., falsely detecting non-road boundary points) by incorporating a distance-based loss, which penalizes detected points far away from the road boundary as road boundaries into the PointNet++ segmentation network and 2) we capture the temporal dynamics of the point cloud sequences by adding the vector representing point’s deviation from the motion-compensated road boundary detection result obtained from the previous frame into the point-wise features.

To reduce false positive detections of noisy points, we incorporate a distance-based loss into the PointNet++ segmentation network to penalize such false positive detections. The PointNet++ network is selected as the basic structure of the point segmentation module due to its effectiveness in extracting hierarchical features and its adaptability to various spatial scales Qi et al. (2017). The original PointNet++ network uses only binary cross-entropy loss for point segmentation, which is inadequate for our task. This limitation arises because, after point cloud preprocessing, most noisy points are filtered out, leaving only a small fraction of distant noisy points compared to road boundary points. Consequently, their influence on the loss function is minimal. However, if these distant noisy points are misclassified as road boundary points (false positive detections), they can significantly degrade the boundary fitting process. To this end, we calculate the average Euclidean distance between each detected road boundary point and its nearest actual road boundary point as the distance loss (see Figure 3a). The distance loss is defined in Equation 1. Here, P denotes the set of points classified as road boundaries by the model, Q represents the ground truth boundary points, and | P | is the number of points in P . The distance loss is particularly high for these false positive points, which helps mitigate the false positive detections. L dist = ∑ p i ∈ P m i n q j ∈ Q ‖ p i − q j ‖ 2 | P | (1) L total = L BCE + α   L dist (2)

To capture the temporal dynamics of the point cloud sequences, we augment each point’s feature representation with a deviation vector, which encodes its direction and distance relative to the road boundary points detected in the previous frame. For each point in the current frame, this deviation vector is defined as the shortest vector originating from a motion-compensated road boundary point in the previous frame and terminating at the current point (see Figure 3b). P1, P2, and P3, along with their respective deviation vectors a 1 , a 2 , a 3 , illustrate three typical cases in the point cloud data (1) newly observed road boundary points (e.g., P1, a 1 ): that appear in the current frame but were absent in the previous frame due to the vehicle’s forward motion, (2) noisy points that only appear in the current frame (e.g., P2, a 2 ), and (3) consistent road boundary points that appear in both the current and previous frames (e.g., P3, a 3 ). The deviation vectors exhibit different patterns for each of these three point types. For newly appearing points (e.g., P1), the deviation vector typically points in the direction of the road boundary line. For noisy points (e.g., P2), the deviation vector usually points perpendicular to the general road boundary direction. For the nearby road boundary points (e.g., P3), the vector is usually small in magnitude since the road boundary tends to be static and continuous. These deviation vectors ( a 1 , a 2 , a 3 in Figure 3b) provide crucial spatial and temporal information, aiding in consistent road boundary segmentation. Existing point-based methods for processing point cloud sequences often capture temporal dynamics by grouping points or aggregating information from neighboring points to track movements across frames Liu et al. (2019); Wei et al. (2022); Fan et al. (2021). However, in autonomous driving scenarios focused on road boundary detection, temporal changes in point clouds are primarily due to the continuous appearance of new points at the edge of the sensor’s range as the vehicle moves forward, rather than the movement of individual points, since road boundaries are static. Consequently, these methods may struggle to effectively handle newly appeared points, making them less suitable for this specific application.

Additionally, we incorporate the road boundary probability of the closest detected road boundary point from the previous frame (the starting point of the deviation vector) as a point-wise feature. This probability serves as a confidence measure in road boundary segmentation process. Without this confidence information, if a noisy point far away from the road boundaries is mistakenly detected as a road boundary point in one frame, it can lead to error propagation in subsequent frames. However, we observe that in such cases, incorrectly detected points generally have a lower road boundary probability than actual boundary points, indicating lower confidence in the segmentation result. By incorporating this probability, the model gains confidence awareness, effectively suppressing the propagation of false detections across frames.

Point-wise road boundary segmentation only provides discrete points representing road boundaries. However, control and planning tasks in autonomous driving usually require continuous road boundary curves. To this end, we first identify the continuous curves from the detected road boundary points by clustering, and then fit the road boundary curves for each of the identified point cloud clusters.

We employ the DBSCAN clustering method Ester et al. (1996) to identify continuous road boundary curves from the detected road boundary points. DBSCAN is chosen because it does not require a predefined number of clusters, which is suitable for situations where the number of road boundaries is uncertain. It is also capable of clustering road boundaries of various shapes, which is crucial in complex driving scenarios. Due to the short Euclidean distance between the left and right road boundaries, the algorithm often incorrectly clusters them into one cluster. To solve this problem, we divide the y-coordinate (representing the forward direction of vehicle motion) of the point cloud by a factor before clustering. This scaling factor is set to 5 based on empirical analysis of point cloud sparsity, which balances the trade-off between boundary fragmentation and over-merging. Smaller factors result in over-segmentation due to point sparsity, while factors exceeding 5 cause incorrect merging of opposite-side boundaries at intersections. Since road boundaries usually follow the direction of vehicle motion, this scaling helps the algorithm better cluster the road boundary curves. Without this scaling, the algorithm may incorrectly cluster left- and right-parallel road boundary curves into a single cluster due to their close Euclidean distance or split a single road boundary into multiple clusters due to the variation in the distance along the y-axis.

We take subsamples from each cluster identified by the DBSCAN algorithm and use Gaussian Process Regression (GPR) to fit road boundary curves and provide 95 % confidence intervals for each curve Williams and Rasmussen (1995). The subsampling step aims to reduce the GPR fitting time. GPR is a nonparametric method that does not assume a specific functional form and is therefore suitable for modeling road boundaries with various shapes. We use a Matérn kernel with a ν value of 10 to avoid fitting unrealistic road boundary curves with large gradients. To prevent misconnections at intersections, where two boundary curves on opposite sides of an intersection are mistaken for a single cluster, we introduce a condition that if the point cloud data is missing along the y-axis (the forward direction of vehicle movement) for a gap of more than 6 m (approximately the width of an urban intersection), the fitted curves will be split into two segments. In addition, if the 95% confidence interval exceeds 2 m, indicating uncertain identification of road boundary curves, we re-cluster the points within this cluster and fit each new cluster independently. This strategy effectively reduces the number of nearby road boundaries that are grouped into a single curve.

The real-world driving dataset consists of 50 data clips, each approximately 40 s in duration, totaling 30,424 frames. During the driving tests, RGB cameras, 4D millimeter-wave (mmWave) radar, LiDAR, GPS, and IMU sensors are used to capture detailed driving scenario information. The 4D mmWave radar used in this study operates in a dual-band mode covering 76–79 GHz, comprising both long-range (76–77 GHz) and short-range (77–79 GHz) channels. The long-range channel provides extended detection capability with a narrower bandwidth, while the short-range channel offers higher resolution for near-field sensing. The horizontal field of view (FoV) of the radar is ± 60°, and the vertical FoV is ± 12°. The angular resolutions are 2° in the horizontal plane and 4° in the vertical plane, enabling fine spatial discrimination of detected targets. The radar achieves a range resolution of 0.4 m and a Doppler velocity resolution of 1 km/h, allowing precise estimation of target distance and radial velocity. RGB cameras and LiDAR capture detailed road scenarios for ground truth information. The GPS and IMU sensors provide the vehicle location, velocity, and yaw rate. For point-wise road boundary segmentation training, the training set includes 40 data clips, with 24,291 point cloud frames. To enhance model performance, data augmentation is applied by horizontally flipping the frames along the x-axis based on the left-right symmetry of the vehicle. With the data augmentation, the training set is expanded to 48,582 frames. Both the validation and test sets contain 5 data clips each, with 3,076 frames in the validation set and 3,057 frames in the test set. The dataset covers diverse driving scenarios, including highways, urban areas, and winding roads. The ground truth labels of road boundaries are inferred from LiDAR point clouds using the PointPillars method Lang et al. (2019).

We evaluate the 4DRadarRBD system using point-wise road boundary segmentation accuracy, Chamfer distance (CD) error, and Hausdorff distance (HD) error between the detected and actual road boundaries. Chamfer distance and Hausdorff distance are calculated as the average and maximum closest point distance, respectively, between the sets of detected and actual road boundary points Borgefors (1986); Rockafellar and Wets (2009).

4DRadarRBD achieves 93 % accuracy for point-wise road boundary segmentation, with a median Chamfer distance error of 0.023 m and a median Hausdorff distance error of 2.34 m (see Figure 4). The confusion matrix for road boundary point segmentation is shown in Figure 4A. For comparison, state-of-the-art mmWave radar-based methods achieve approximately 80 % accuracy with a 0.11 m estimation error Kingery and Song (2024); Xu et al. (2020). LiDAR-based approaches attain around 90 % accuracy but rely on more expensive sensors Xu et al. (2025); Wang et al. (2020); Suleymanoglu et al. (2024). Additionally, fusion methods combining cameras with mmWave radar report a precision of about 80 % Patel and Elgazzar (2022). In contrast, our 4DRadarRBD system achieves higher accuracy and lower distance error for road boundary detection while relying on lower-cost sensors compared to LiDAR and offering greater robustness to adverse weather and lighting conditions than RGB camera-based methods.

To evaluate the effectiveness of 4DRadarRBD, two ablation tests are conducted, including: 1) using the model without updating with the deviation vector obtained from the previous frame’s detection results (baseline model) and 2) using the model trained without the incorporation of distance loss. All model architectures, training procedures, and hyperparameters remain identical to our method except for the specified ablations. By updating the model with the deviation vector, 4DRadarRBD reduces the median Chamfer distance error by 92.6 % and the Hausdorff distance error by 62.2 % (see Figure 4B). 4DRadarRBD reduces the median Chamfer distance error by 30.3 % and the Hausdorff distance error by 13.0 % by incorporating a distance loss to penalize false detections of points away from the road boundary (see Figure 4C). These results show that the proposed method of distance loss and updating the model with deviation vectors is effective.

In this section, we evaluate the robustness of the 4DRadarRBD system to varying numbers of road boundary curves, varying types of noisy points, varying road boundary curve shapes, and the system’s temporal stability over driving time.

4DRadarRBD is robust to varying numbers of road boundary curves. Figure 5 shows the road boundary detection results for three typical complex driving scenarios, including a highway situation with 2 road boundary curves (top), a fork road situation with 3 road boundary curves (middle), and a complex urban area situation with multiple road boundary curves (bottom). The left figures show the top view of the point cloud and the corresponding detection results, with the red dots representing the detected road boundary points and the blue dots representing the detected non-road boundary points. The right figures represent the corresponding RGB images. The 4DRadarRBD system can automatically detect varying numbers of road boundary curves and accurately fit the road boundary curves. Notably, in the third scenario, 4DRadarRBD successfully separates the two road boundary curves at the intersection instead of connecting them.

The 4DRadarRBD system successfully achieves robust road boundary detection with various environmental noisy points. On a highway with multiple overpasses and moving vehicles, we achieve up to 94 % accuracy for point-wise road boundary segmentation and a median Chamfer distance as low as 0.025 m (see examples in Figure 6).

4DRadarRBD is robust to various shapes of road boundary curves. Under the twisting driving conditions of mountainous roads, we achieve a point-wise road boundary segmentation accuracy as high as 91.2 % and successfully fit various shapes of the road boundaries with a median Chamfer distance of 0.11 m (see an example in Figure 7).

Overall, 4DRadarRBD is robust with consistently high accuracy and low Chamfer and Hausdorff distance errors over continuous driving time. As illustrated in Figure 8, during approximately 20 min of continuous monitoring, the method achieves stable low error metrics for most of the duration. Around frame 85, a temporary drop in accuracy and an increase in distance errors occur due to the ground truth system (based on a LiDAR sensor) failing to capture the right-hand road boundary, as confirmed by manual inspection of the corresponding RGB images and point clouds. Notably, even under these circumstances, 4DRadarRBD correctly identifies the road boundaries.