2.1 Vehicle-mounted LiDAR PC segmentation method based on improved EC algorithm

The PC data obtained from vehicle-mounted LiDAR possesses advantages such as high precision and high resolution, but it also faces issues like excessive noise, uneven density, and significant ground interference, directly impacting the accuracy and efficiency of subsequent target detection. Although traditional EC algorithms are widely applied in PC segmentation, they exhibit limitations when dealing with large-scale, high-noise PCs, such as low computational efficiency, sensitivity to parameters, and susceptibility to ground point interference [20]. Therefore, this study proposes a vehicle-mounted LiDAR PC segmentation method based on an improved EC algorithm. By introducing a ground point filtering strategy and an efficient neighbor search mechanism, the robustness and real-time performance of PC segmentation are enhanced. The robustness of PC segmentation is defined as the performance retention rate of the model under changes in PC density and noise level; Real time is defined as the single frame processing time satisfying the sensor frame period constraint. Its expression is shown in Eq (1).

(1)

In Eq (1), represents robustness. and represent PC density and noise level, respectively. represents the benchmark performance indicator. represents the time required for the system to process a single frame PC. represents the upper limit of the sensor frame period. The CSF algorithm divides PCs into ground points and non-ground points by simulating the interaction between cloth and the ground. This algorithm treats the PC as a series of cloth particles, with each particle subjected to the combined effects of gravity and ground reaction force. By iteratively calculating the position changes of each particle, the final stable height of the particles corresponds to the simulated ground height, thus achieving precise filtering of ground points [21]. The force model and position update of cloth particles are presented in Eq (2).

(2)

In Eq (2), is the external resultant force; and are gravity and ground reaction respectively; is the 3D position of particle at the next time ; is the 3D position of particle at the current time ; and are particle mass and time step, respectively; is the acceleration of the particle. After the cloth simulation is stable, the study compares the height of each point in the original PC with the height of the cloth particle at the corresponding position, and calculates its absolute height difference, as shown in Eq (3).

(3)

In Eq (3), is the height difference; is the elevation value of the midpoint of the original PC; is the simulated ground height of the cloth particles at the corresponding position. To improve the nearest neighbor (NN) search efficiency in European clustering, the study constructed a KD-Tree structure to divide the PC space. The KD-Tree is a specialized binary tree structure tailored for arranging points in a k-dimensional space. It recursively partitions the space into two distinct sub-spaces by selecting different dimensions as the segmentation axis and taking the median point on the dimension as the segmentation hyperplane [22]. The node division is presented in Eq (4).

(4)

In Eq (4), is the value of the split point; is the point set of nodes; indicates partition dimension; indicates the point in the point set; is the coordinate value of the point on dimension ; is the median function. CSF is a terrain-following algorithm that simulates the physical interaction between a piece of cloth and the ground surface. By treating the PC as a set of cloth nodes influenced by gravity and internal forces, CSF iteratively fits a cloth mesh to the terrain, effectively separating ground points from non-ground objects, thereby providing a cleaner input for subsequent clustering and detection stages. The schematic diagram of CSF and KD-Tree structure is presented in Fig 1.

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Fig 1. Diagrammatic representation of CSF and KD-Tree structures.

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Fig 1 illustrates the principle of the key preprocessing techniques used in this study. Fig 1(a) is a schematic diagram of CSF, which simulates the process of fabric particles adhering to ground laser points under the action of gravity, achieving precise filtering of ground points. Fig 1(b) is a schematic diagram of the KD tree structure, which shows the organization of PC data by recursively dividing space according to different coordinate axes, forming a binary tree to accelerate nearest neighbor search. The root node, child nodes, and left and right branches clearly reflect the spatial segmentation logic. When conducting neighbor search based on the KD-Tree structure, a fast and accurate method is required to calculate the distance between two points to determine whether they belong to the same cluster. The KD-Tree structure can quickly retrieve all candidate points near a given point, avoiding global traversal and improving clustering efficiency. The calculation of the NN search distance is presented in Eq (5) [23].

(5)

In Eq (5), is the Euclidean distance between points and ; and denote points in 3D space; , and are the 3D coordinates of point ; , and are the 3D coordinates of point . On the basis of traditional EC, adaptive distance threshold and minimum number of points are introduced [24]. To adapt to the change of PC density in different scenes, an adaptive distance threshold calculation method is proposed. This method is based on the average NN distance of the PC to dynamically adjust the clustering radius, as shown in Eq (6).

(6)

In Eq (6), is adaptive distance threshold; is the adjustment coefficient; is the number of non ground PCs; is the NN of point ; is the distance of the NN between two points. adjusts the distance threshold based on local point density; Larger allows merging of sparser regions, while smaller preserves fine structure. In addition, the minimum number of points threshold also needs to be adjusted adaptively according to the size of the PC [25]. In this study, logarithmic function is used to balance clustering sensitivity and computational efficiency, as shown in Eq (7).

(7)

In Eq (7), is the minimum number of points threshold; is the adjustment coefficient; is the logarithm of the number of PCs. performs logarithmic scaling on the minimum point threshold to prevent over segmentation in dense PCs and under segmentation in sparse PCs. Eq (7) constructs an efficiency model through the logarithmic point number adaptive mechanism MinPts, transforming the control of computational complexity into a scaling problem of logarithmic functions. Its parameter β directly balances the risks of over segmentation and under segmentation. In the process of clustering, it is essential to clearly define the judgment criteria of whether two points belong to the same cluster. This standard comprehensively considers the distance constraint and density requirements to ensure the rationality of the clustering outcomes. The clustering merging conditions are presented in Eq (8).

(8)

In Eq (8), is the point set in the neighborhood of point ; indicates the number of points in the neighborhood of a point. To further improve the clustering quality, the preliminary clustering results are post processed, including eliminating clusters with too few points and merging clusters with close spatial distance [26]. The final cluster merging decision needs to comprehensively consider the distance between clusters and the scale of clusters. The study is based on the merging criterion of relative distance to ensure the rationality and effectiveness of the merging operation, as shown in Eq (9).

(9)

In Eq (9), is the distance between the center points of two clusters; and are the diameters of cluster and cluster , respectively; is the merge threshold coefficient. controls inter cluster merging based on relative clustering diameter to avoid erroneous fusion of different objects. Finally, the label of each cluster and its BB are output to complete the task of PC segmentation. To rigorously handle sparsity and improve feature representation in 3D detection, the improved PointNet incorporates the following mathematical formulations. In complex dynamic scenes, the robustness of PC segmentation directly determines the stability of subsequent detection tasks. To improve the ability to suppress noise and outliers, the segmentation process is formalized as an optimization problem with regular constraints, and its calculation is shown in Eq (10).

(10)

In Eq (10), represents the segmentation objective function value, which measures the clustering quality. represents the total number of clusters. represents the th cluster. represents the th point in the PC. represents the center point of the th cluster. represents the regularization coefficient. represents the indicator function. represents the threshold for cluster size. Traditional fixed thresholds are difficult to adapt to the changing PC density distribution in road scenes. Therefore, the study introduces an adaptive distance threshold based on local statistics, as shown in Eq (11).

(11)

In Eq (11), represents the adaptive distance threshold at point . represents the scaling factor. represents the set of neighboring points of point within radius . represents a point in the neighborhood. The mathematical logic for clustering distance lies in introducing local statistics to enable the threshold to adaptively change with PC density. This essentially solves the problem of segmentation robustness under density changes by dynamically adjusting similarity measures. The above Eq (11) establishes a robustness model based on an adaptive threshold using local statistics, transforming the density change problem into local neighborhood statistical analysis, and achieving global optimization by adjusting the alpha parameter. The flow diagram of the improved EC algorithm is presented in Fig 2.

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Fig 2. Flow diagram of improved EC algorithm.

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In Fig 2, the improved EC algorithm first performs CSF ground point filtering on the input raw PC to separate out non-ground PCs. Subsequently, a KD-Tree structure is constructed to accelerate neighbor search, and adaptive distance thresholds and minimum point counts are calculated. Based on these parameters, EC is performed, and after traversing all points, the initial clustering clusters are output. Finally, through post-processing steps such as eliminating too small clusters, the final high-quality clustering results are output.

2.2 3D OD method based on improved PointNet

After efficiently segmenting the PC, it is essential to further accurately identify and detect 3D objects from the segmented PC clusters. However, existing 3D OD methods exhibit poor real-time performance, and traditional PointNets tend to ignore detailed information when performing fine detection on complex 3D objects, leading to a decrease in detection accuracy [27]. Therefore, a 3D OD method based on an improved PointNet is proposed. This method extracts local features of 3D objects through MSG and MRG. To enhance the network’s feature integration capability, a skip connection mechanism is incorporated into the convolutional layer structure, the prediction of the affine transformation matrix is eliminated, and random point sampling is adopted to reduce computational complexity. The reason for removing the affine transformation matrix prediction module is that the T-Net structure requires an independent sub network for affine transformation prediction, which introduces additional computational overhead and parameter count [28].

The PointNet extracts features point by point through a Multi-Layer Perceptron (MLP) with shared weights and a symmetry function, and aggregates global information to achieve the detection task of 3D objects for vehicle-mounted lidar [29]. This network utilizes a Transform Network (T-Net) to align the coordinates of the input PC, reducing external transformation interference [30]. Then, multiple MLP layers with shared weights are independently applied to each point for feature extraction, gradually increasing the feature dimension of each point, and using max pooling as the symmetry function to aggregate the features of all points, as shown in Eq (12).

(12)

In Eq (12), is the output characteristics of the MLP at layer ; and are the weight matrix and bias vector of MLP; means activation function; is the global eigenvector obtained after the maximum pool; is the eigenvector of all points; is the total number of layers of MLP. The algorithm architecture diagram of PointNet is shown in Fig 3.

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Fig 3. Algorithm architecture diagram of PointNet.

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Fig 3 shows the overall architecture of the PointNet algorithm. The network first performs spatial transformation alignment on N input 3D PCs to improve rotation invariance. Subsequently, high-dimensional features are extracted point by point using an MLP with shared weights, and the features of all points are aggregated using a max pooling function to generate a global feature vector. The entire process achieves end-to-end processing from raw PC input to global feature output, balancing point level feature learning and global information integration. To significantly improve processing efficiency while retaining key geometric information, the study first performs random point sampling on the input PC, uniformly downsampling it to a fixed number of points. The sampling process is presented in Eq (13).

(13)

In Eq (13), is the output PC after sampling; means random point sampling function; indicates the input PC; indicates the fixed number of points after sampling. The traditional PointNet lacks explicit modeling of local neighborhood structure. To overcome this defect and enable the network to perceive the local geometric context in different ranges, the study introduces an MSG strategy [31]. By querying the neighborhood of each point in multiple different radius ranges, the strategy can capture the local structural features at different scales from fine to coarse, as shown in Eq (14).

(14)

In Eq (14), is the neighborhood point set with point as the center and radius as; and are the center point and any other point in the PC respectively; is the search radius at the th scale; f^(k)_local is the local aggregation characteristics of point under scale ; is the input characteristics of the point . The selection of MSG radius aims to capture hierarchical geometric features from fine-grained details to broader contextual structures. Capture local curvature and edges with a small radius (0.1 m). The medium radius (0.2 m) covers the component level structure. Large radius (0.4 m) covers object level context and partial occlusion. In addition, the density change of PC in different regions also serves as a crucial determinant influencing the effect of feature extraction. To enhance the adaptability of the network to sparse and dense areas, the study uses the MRG strategy to group the PCs, ensuring that the structural information can be effectively captured regardless of the point density [32], as shown in Eq (15).

(15)

In Eq (15), is the multi-resolution aggregation feature; indicates feature splicing operation; is the number of sampling points under scale ; is the farthest point sampling function; means traversing different scales. To avoid gradient vanishing and information decay in deep networks, and to fully utilize geometric details in shallow layers and semantic information in deep layers, a skip connection mechanism is introduced. This mechanism directly fuses shallow and deep features through channel concatenation, forming composite feature vectors with richer information. The fusion method is presented in Eq (16).

(16)

In Eq (16), is the composite feature vector after fusion; is the global eigenvector. Eq (16) establishes a sparse data feature fusion model through skip connections, transforming the information flow optimization problem into direct connections and concatenation operations in the feature space. These formulaic expressions not only define specific algorithm steps, but more importantly, transform abstract scientific goals such as robustness, efficiency, and sparse data processing capabilities into computable problems with clear objective functions, parameter spaces, and assessable indicators, thus establishing a solid bridge between theoretical rigor and practical effectiveness. Considering the uneven density of LiDAR PCs, a density weighted multi-resolution grouping strategy is proposed, as shown in Eq (17).

(17)

In Eq (17), represents the aggregated feature vector of point after density weighted multi-resolution grouping. represents the local point density of point at the th scale. represents the farthest sampling function. represents the collection of the entire input PC. represents the number of sampling points at the th scale. In the detection header part, the network outputs the category probability and BB parameters of each candidate target. The boundary box regression needs to precisely forecast the location and dimensions of the target. The smooth L1 loss function can effectively balance the advantages of the loss and provide a more stable gradient at the initial stage of training [33]. The expression is presented in Eq (18).

(18)

In Eq (18), is the smooth L1 loss function; refers to sample index; and are the predicted BB parameters and the real BB parameters of the th target, respectively. Category prediction uses cross entropy loss, which can accurately assess the discrepancy between the predicted probability distribution and the actual label, and promote the network to learn the correct category discrimination characteristics [34]. Finally, through the weighted combination of regression loss and classification loss, the network can simultaneously optimize the target positioning and classification performance, and realize end-to-end training, as shown in Eq (19).

(19)

In Eq (19), is classification loss; indicates category index; and are the category probability of the real label and prediction respectively; is the total loss function; indicates the balance superparameter. For the loss function, its mathematical logic is reflected in balancing classification and localization losses, so that the model can maintain detection accuracy while satisfying real-time constraints. The illustrative schematic of the improved PointNet is presented in Fig 4.

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Fig 4. Schematic diagram of improved PointNet.

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In Fig 4, the improved PointNet first performs random sampling and grouping on the input PC, and then extracts high-dimensional features layer by layer through a series of MLPs with shared weights. The network aggregates global features using the max pooling function and integrates multi-level information through skip connections, ultimately outputting detection results through a fully connected layer and a Softmax classifier. The flowchart of 3D object detection using vehicle mounted LiDAR is shown in Fig 5.

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Fig 5. The flowchart of 3D object detection using vehicle mounted LiDAR.

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In Fig 5, firstly, the original point cloud data is input, and after preprocessing, an improved Euclidean clustering algorithm is used for ground filtering and adaptive threshold clustering, and KD Tree is used to accelerate neighborhood search. Then perform random sampling, multi-scale grouping, and multi-resolution grouping on the point cloud. Subsequently, feature extraction and fusion are carried out through point by point feature extraction and global feature pooling, and a skip connection mechanism is introduced. Finally, the 3D object detection head completes bounding box regression and category prediction, and outputs the detection results. The entire process has achieved end-to-end processing from point cloud input to object detection.

3.1 Evaluation of PC segmentation performance for improved EC algorithm

To verify the performance of the proposed improved EC algorithm in the task of PC segmentation for vehicle-mounted LiDAR, a systematic evaluation was conducted on two public datasets: KITTI and NuScenes. The KITTI dataset contains PC data from urban road scenes, with annotations covering categories such as vehicles, pedestrians, and bicycles. The NuScenes dataset includes PC data under more complex multi-scene and multi-weather conditions. The experimental evaluation was conducted using publicly available datasets, ensuring reproducibility and comparability. For the KITTI dataset, data were collected with a vehicle-mounted Velodyne HDL-64E LiDAR, which has a maximum range of ~120 m, a 360° horizontal field of view, and 64 laser channels. The NuScenes dataset employs a 32-beam LiDAR with comparable horizontal coverage and an effective detection range of up to 100 m for object-level perception.

Four representative clustering algorithms were selected as benchmark comparisons. Traditional EC serves as a baseline reference using fixed distance thresholds [14]. Fast Channel Clustering (FCC) represents the hardware-accelerated approach for extreme speed optimization [10]. Mask-based Panoptic LiDAR Segmentation (MaskPLS) embodies advanced segmentation methods incorporating semantic information [11]. The Real-Time Point Cloud Clustering algorithm for Roadside LiDAR (RTPCC-RL) demonstrates application-specific optimization [12]. By systematically comparing with these four types of methods covering different technical routes, the comprehensive advantages of the proposed improved algorithm in accuracy, speed, and adaptability were fully validated. The experimental environment and parameter settings are shown in Table 1.

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Table 1. Experimental setup and parameter configurations.

https://doi.org/10.1371/journal.pone.0348581.t001

To verify the rationality of the keyword parameter settings in the proposed algorithm, sensitivity analysis was conducted on the coefficients α, β, and γ on the KITTI and NuScenes datasets, and the Intersection over Union (IoU) and processing time of the proposed algorithm were evaluated. α, β, and γ were mainly determined through iterative grid search process, and their selection was based on achieving the best balance between segmentation accuracy and computational efficiency. The purpose of this search is to find parameter values that can generalize well under different scene complexities and point cloud densities inherent in these benchmark datasets. The sensitivity analysis results are shown in Table 2. In Table 2, in the KITTI dataset, when the coefficient α is set to 1.2, the IoU reaches the highest value of 92.12% with a processing time of 15.63 ms. On the NuScenes dataset, the optimal IoU is also obtained when α is set to 1.2, which is 90.89% with a processing time of 17.24 ms. For the coefficient β, when it is set to 0.5, the optimal IoU is obtained on both datasets with corresponding processing times of 15.63 ms and 17.24 ms. The coefficient γ performs best when it is set to 0.8, with IoUs of 92.12% and 90.89% on the KITTI and NuScenes datasets, respectively. Comprehensive analysis shows that α is 1.2, β is 0.5, and γ is 0.8, which can achieve low processing delay while maintaining high segmentation accuracy, verifying the effectiveness and robustness of this parameter setting on different datasets.

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Table 2. Sensitivity analysis of coefficients α, β, and γ on two datasets.

https://doi.org/10.1371/journal.pone.0348581.t002

The study first analyzed the segmentation accuracy of the proposed improved EC algorithm on PCs in the KITTI and NuScenes datasets, and compared it with other mainstream clustering algorithms. The outcomes are presented in Fig 6. In Fig 6(a), in the KITTI dataset, when the iteration count was 120, the accuracies of EC, FCC, MaskPLS, and RTPCC-RL algorithms were 71.63%, 78.76%, 85.09%, and 89.31%, respectively, while the accuracy of the introduced algorithm was 94.26%. When the iteration count reached 240, the accuracies of EC, FCC, MaskPLS, RTPCC-RL, and the introduced algorithm were 81.76%, 85.23%, 88.39%, 91.26%, and 94.96%. In Fig 6(b), when the iteration count was 120, the accuracies of the five clustering algorithms in the NuScenes dataset were 69.89%, 76.02%, 80.05%, 87.92%, and 92.24%. When the iteration count increased to 240, the accuracies of EC, FCC, MaskPLS, and RTPCC-RL algorithms were 79.27%, 82.86%, 86.37%, and 89.12%, respectively, while the accuracy of the introduced algorithm was 93.12%. The outcomes showed that the introduced algorithm had superior segmentation accuracy and robustness in both datasets.

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Fig 6. The accuracy of various algorithms in the KITTI and NuScenes datasets.

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To confirm the convergence performance of the introduced algorithm, a comparison of the losses of different clustering algorithms was carried out on the KITTI and NuScenes datasets, with the results shown in Fig 7. In Fig 7(a), on the KITTI dataset, at an iteration count of 60, the losses of EC, FCC, and MaskPLS algorithms were 1.22, 1.77, and 0.74, while the losses of RTPCC-RL and the introduced algorithm were 0.38 and 0.23, respectively. When the iteration count reached 200, the losses of EC, FCC, MaskPLS, RTPCC-RL, and the introduced algorithm were 0.89, 0.77, 0.38, 0.28, and 0.20, respectively. In Fig 7(b), on the NuScenes dataset, at an iteration count of 60, the losses of the five algorithms were 1.26, 1.23, 0.86, 0.54, and 0.38, respectively. When the iteration count increased to 200, the losses of EC, FCC, MaskPLS, and RTPCC-RL algorithms were 0.97, 0.88, 0.48, and 0.37. Compared to these, the loss of the introduced algorithm was 0.26, representing reductions of 73.20%, 70.79%, 46.94%, and 31.58%. The outcomes indicated that the introduced algorithm exhibited superior convergence and stability in both datasets, effectively enhancing clustering efficiency.

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Fig 7. The loss values of different algorithms in KITTI and NuScenes datasets.

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The study further analyzed the comprehensive performance of different clustering algorithms on two datasets, with assessment criteria encompassing precision, recall, F1 score, and IoU. The results are presented in Table 3. In Table 3, the precision, recall, and F1 score of the introduced algorithm on the KITTI dataset were 0.943, 0.935, and 0.939, respectively, with an IoU of 92.12%, all of which were superior to other comparative algorithms. On the NuScenes dataset, the precision, recall, F1 score, and IoU of the introduced algorithm were 0.928, 0.914, 0.921, and 90.89%, respectively. Specifically, the precision of the introduced algorithm was 10.02%, 8.9%, 4.95%, and 2.16% higher than that of EC, FCC, MaskPLS, and RTPCC-RL algorithms, respectively, and the IoU was 14.47%, 12.26%, 8.04%, and 3.68% higher, respectively. The outcomes demonstrated that the introduced algorithm could effectively balance the accuracy and completeness of segmentation, achieving more precise and robust PC segmentation effects in different scenarios.

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Table 3. Performance comparison of various clustering algorithms.

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To confirm the efficacy of the introduced algorithm, the study compared the processing time of single-frame PCs and the speed of PC segmentation among different algorithms on two datasets. The outcomes are presented in Fig 8. In Fig 8(a), the processing times of single-frame PCs for the EC, FCC, MaskPLS, and RTPCC-RL algorithms on the KITTI dataset were 22.52ms, 98.36ms, 12.34ms, and 120.56ms, respectively, while on the NuScenes dataset, they were 25.84ms, 135.72ms, 14.85ms, and 147.92ms, respectively. The processing times of the introduced algorithm on the two datasets were 15.63ms and 17.24ms, respectively. In Fig 8(b), on the KITTI dataset, the PC segmentation speeds of EC, FCC, MaskPLS, RTPCC-RL, and the introduced algorithm were 44.42 Hz, 10.26Hz, 82.04Hz, 4.96Hz, and 67.13 Hz, respectively. The segmentation speeds of these five algorithms on the NuScenes dataset were 38.82 Hz, 7.43 Hz, 67.68 Hz, 5.36 Hz, and 58.06 Hz. The outcomes demonstrated that the introduced algorithm could effectively improve computational efficiency while ensuring segmentation accuracy. Compared with FCC and RTPCC-RL algorithms, the processing time of single frames and the speed of PC segmentation were improved by nearly 10 times, meeting the real-time PC processing requirements of auto drive systems.

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Fig 8. Single frame PC processing time and PC segmentation speed of different algorithms in KITTI and NuScenes datasets.

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3.2 Verification of improved 3D OD performance of PointNet

To confirm the capability of the proposed improved PointNet for 3D OD, the study analyzed its detection accuracy and efficiency on two datasets, KITTI and NuScenes, and compared it with existing popular 3D OD methods. The comparative methods encompassed mainstream 3D detection technical approaches: traditional PointNet served as the baseline method for direct PC processing [29]. PointNet++ served as a representative PC network for hierarchical feature extraction [30]. PointPillars represented the efficient pillar-based encoding detection approach [35]. Voxel RCNN reflected the balanced design of voxel-based methods [36]. PV-RCNN stood as the current performance benchmark for point-voxel fusion frameworks [37]. Through systematic comparison with these methods based on different design philosophies, the significant improvements of the improved PointNet in detection accuracy, inference speed, and overall performance were conclusively demonstrated.

The study first conducted sensitivity analysis on the MSG radius in the KITTI and NuScenes datasets, using mAP and NuScenes Detection Score (NDS) as evaluation metrics. The results are shown in Table 4. In Table 4, the radius combinations (0.1, 0.2, 0.4) achieved optimal results on both the KITTI and NuScenes datasets, with mAP of 90.36% and NDS of 81.07% on KITTI. On NuScenes, mAP was 89.03% and NDS was 80.15%. The results indicated that the selected combination achieved the best balance between capturing local details and contextual information, and had strong cross dataset generalization ability. The selected radius corresponded to a typical physical scale in urban driving scenarios, with a radius of 0.1m being the width of pedestrian limbs or vehicle edges. A radius of 0.2m was half the width of a compact car door. A radius of 0.3m was a typical distance between objects in congested traffic. This geometric alignment ensured that the features learned by the network were semantically meaningful and could be extended across object categories.

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Table 4. Sensitivity analysis of MSG radii on detection performance.

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The study compared the average detection accuracy and average Frames Per Second (FPS) of different 3D OD methods on the KITTI and NuScenes datasets, aiming to investigate the detection accuracy and instantaneous processing capability of the introduced approach. The outcomes are presented in Fig 9. In Fig 9(a), the average detection accuracy of PointNet, PointPillars, and PointRCNN on the KITTI dataset was 79.65%, 82.47%, and 88.58%, while the average detection accuracy of sparse depth-based single shot detector and the proposed method EC PointNet++ was 85.78% and 94.36%, respectively. On the NuScenes dataset, the average detection accuracy of PointNet, PointPillars, PV-RCNN, and Voxel RCNN was 75.84%, 80.05%, 85.97%, and 81.26%, while the accuracy of the proposed method EC PointNet++ was 92.68%. In Fig 9(b), the FPS of PointNet, PointPillars, PV-RCNN, Voxel RCNN, and the introduced approach on the KITTI dataset were 19fps, 31fps, 14fps, 24fps, and 34fps, respectively, while on the NuScenes dataset, they were 16fps, 23fps, 12fps, 21fps, and 31fps, respectively. The outcomes indicated that the proposed 3D OD method achieved high detection precision while enhancing processing speed, achieving a balance between accuracy and speed.

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Fig 9. The average detection accuracy and FPS of different 3D OD methods.

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To confirm the detection capability of the proposed detection method under different categories and difficulty levels, the study analyzed the average detection accuracy of different detection methods for three types of targets: vehicles, pedestrians, and bicycles, in the KITTI dataset. The difficulty levels were categorized as easy, medium, and hard. The outcomes are presented in Fig 10. In Fig 10(a), the detection accuracy of PointNet, PointPillars, PV-RCNN, Voxel RCNN, and the introduced approach for vehicles under the easy level were 88.92%, 92.13%, 94.80%, 94.24%, and 97.21%, while the accuracy under the hard level were 76.35%, 85.24%, 86.78%, 86.52%, and 90.89%. In Fig 10(b), for pedestrian detection, the detection accuracy of the five methods under the easy level were 75.68%, 82.23%, 83.81%, 82.86%, and 89.24%, respectively, while the accuracy under the hard level were 62.13%, 68.37%, 73.26%, 72.89%, and 76.61%, respectively. In Fig 10(c), for bicycle detection, the detection accuracy of PointNet, PointPillars, PV-RCNN, and Voxel RCNN under the hard level were 65.13%, 72.01%, 73.04%, and 74.09%, respectively, while the detection accuracy of the proposed method EC PointNet++ was 79.06%. The outcomes indicated that the introduced approach could effectively enhance the feature representation ability for multi-category and multi-difficulty targets, achieving superior detection accuracy and improving the 3D detection performance in complex scenes.

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Fig 10. The average detection accuracy of three types of targets using different 3D OD methods.

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The study conducted ablation experiments on the proposed 3D OD method in two datasets, with evaluation metrics including accuracy and training time. The results are shown in Table 5. In Table 5, the combination of modules produced significant synergistic effects. The combination of MSG and MRG resulted in mAPs of 85.10% and 82.95% on the KITTI and NuScenes datasets, respectively. The mAP of MSG+Skip and MRG+Skip, which contain skip connections, further increased to 86.33 and 86.89% on the KITTI dataset, and 84.12 and 84.67% on the NuScenes dataset, respectively. Introducing only a dynamic distance threshold could increase the mAP of the KITTI dataset from 75.52% to 80.15%, and the mAP of the NuScenes dataset from 73.81% to 78.40%, with only a slight increase in training time. This confirmed that adaptive thresholding based on local PC density could significantly improve segmentation accuracy, especially in areas where PC density changes. The logarithmic point adaptive mechanism further increased the mAP of KITTI dataset to 81.33% and NuScenes dataset to 79.88%. This indicated its role in balancing clustering sensitivity and computational efficiency, effectively preventing over segmentation in dense PCs and under segmentation in sparse PCs. Only adding skip connections could increase the mAP of KITTI dataset to 83.44% and NuScenes dataset to 81.28%. In theory, skip connections alleviated the problem of gradient vanishing and promote better gradient flow during backpropagation. More importantly, they achieved direct feature reuse by concatenating shallow geometric details with deep semantic features. This multi-level feature fusion enhanced the model’s ability to simultaneously represent fine-grained local structures and high-level contextual information, thereby improving detection accuracy and stability, especially in complex and occluded scenes. The full model achieved the best detection accuracy, with mAPs of 88.96% and 86.27% on KITTI and NuScenes, respectively, which were 13.44 and 12.46 percentage points higher than the baseline model. It is worth noting that the training time for the complete model was 12.32 minutes and 12.81 minutes respectively, indicating that collaborative optimization between modules improved training efficiency.

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Table 5. Ablation study of the proposed improved PointNet on KITTI and NuScenes datasets.

https://doi.org/10.1371/journal.pone.0348581.t005

To explore the actual detection performance of the introduced approach, a comparison was carried out regarding the average detection accuracy and detection speed of different 3D OD methods in real-world urban road scenes. The testing of traffic flow is conducted in a high-density mixed traffic flow simulation scenario. This scenario covers various dynamic traffic participants, such as passenger cars, buses, and pedestrians, and includes complex interactive scenarios such as intersection queuing and lane changing games. In this test, the traffic flow was set at approximately 2500–3200 vehicles per hour, with passenger cars accounting for about 75%, buses accounting for about 10%, and other participants such as pedestrians and cyclists accounting for about 15%. Data collection is conducted under various lighting conditions, including sunny, cloudy, and nighttime. To focus on the perceptual stability of the model under standard operating conditions, all tests were conducted without precipitation or extreme weather events. The research and testing routes cover various structured types of urban roads, including main roads, secondary roads, and intersections with traffic lights. The real-world test data was collected using a vehicle platform on selected urban roads in Nanjing, Jiangsu Province, China. The test vehicle is equipped with Velodyne HDL-64E LiDAR, which is consistent with the main sensor of KITTI benchmark test, to ensure the fairness of point cloud feature comparison. The collected dataset consists of continuous LiDAR point cloud frames that record the defined urban scenes. At the same time, corresponding high-precision GPS/INS data was recorded as trajectory truth values, and manual 3D bounding box annotation was performed on the main targets (vehicles, pedestrians, cyclists) in some keyframes for quantitative evaluation. Due to the current stage of the project and institutional data policies, this specific real-world dataset has not yet been publicly released. However, the evaluation process and detailed annotation specifications (including definitions of target category, occlusion level, truncation degree, and bounding box specifications) follow the established standards of the publicly available KITTI 3D object detection benchmark.

The outcomes are presented in Fig 11. In Fig 11(a), the average detection accuracies of PointNet, PointPillars, and PV-RCNN in actual urban road scenes were 72.31%, 84.57%, and 90.01%, respectively. The average detection accuracies of Voxel RCNN and the introduced approach were 87.21% and 93.86%. Compared with the other four approaches, the detection accuracy of the introduced approach was improved by 21.55%, 9.29%, 3.84%, and 6.64%, respectively. In Fig 11(b), the average FPS of PointNet, PointPillars, PV-RCNN, Voxel RCNN, and the introduced approach were 28fps, 42fps, 25fps, 35fps, and 38fps, respectively. The outcomes indicated that the proposed 3D OD method exhibited superior detection accuracy and efficiency in real-world scenes, outperforming other comparative methods and validating its superiority.

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Fig 11. Average detection accuracy and speed of different methods in practical scenarios.

https://doi.org/10.1371/journal.pone.0348581.g011

In Table 6, the study further analyzed the detection performance of the proposed method on the KITTI dataset at different difficulty levels. It should be noted that the detection difficulty of the KITTI dataset was divided into three levels based on the degree of target occlusion, truncation, and bounding box size: Easy, Moderate, and Hard. This grading standard provided an important benchmark for evaluating the robustness of the model in different challenging scenarios. The proposed method significantly outperformed mainstream methods in terms of overall performance and difficulty levels. Specifically, the mAP of the proposed method was as high as 91.04%, which was 16.64%, 13.19%, 9.34%, and 6.59% higher than PointNet, PointNet++, PointPillars, Voxel RCNN, and PV-RCNN, respectively. In simple, moderate, and difficult difficulty scenarios, the AP values of the proposed method were 94.36%, 91.24%, and 87.52%, respectively, which were significantly ahead of other methods, especially in difficult scenarios. The results fully demonstrated the effectiveness of the proposed method in improving detection accuracy and scene robustness.

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Table 6. Performance comparison of different 3D OD methods on the KITTI dataset.

https://doi.org/10.1371/journal.pone.0348581.t006

This study compared and analyzed the average accuracy, Average Translation Error (ATE), Average Scale Error (ASE), and NDS of different 3D OD methods on the NuScenes dataset. The results are shown in Table 7. In Table 7, the proposed method achieved optimal results in all key indicators. Specifically, the average accuracy mAP of the proposed method was 92.68%, significantly higher than PointNet, PointNet++, PointPillars, Voxel RCNN, and PV-RCNN. In terms of positioning accuracy, the proposed method had ATE and ASE as low as 0.298m and 0.218m, respectively, which were superior to all compared methods. In the end, the NDS of the proposed method reached 83.45%, which was significantly improved compared to other methods. These data fully demonstrated the excellent detection performance and accuracy advantages of the proposed method in complex multi scene scenarios.

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Table 7. Comprehensive performance comparison of different 3D OD methods on the NuScenes dataset.

https://doi.org/10.1371/journal.pone.0348581.t007

To evaluate the robustness of the proposed method in challenging environments, the sparsity of PCs was simulated by randomly downsampling the original LiDAR frames to 10%, 20%, and 50% of their original points under sparse PC conditions. The mAP and FPS of different methods were compared and analyzed, and the results are shown in Table 8. In Table 8, the proposed method achieved mAP of 84.37% and 82.15% on the KITTI and NuScenes datasets, respectively, which was over 16 percentage points higher than PointNet. When the density increased to 50%, the mAP of the proposed method reached 91.85% and 90.03%, respectively, maintaining a leading advantage. In terms of real-time performance, the proposed method maintained a stable frame rate of 31 FPS-33 FPS, slightly lower than PointPillars’ maximum of 38 FPS, but achieved a better balance between accuracy and speed. The results indicated that the proposed method significantly enhances the robustness to sparse PCs through improved clustering strategies and feature extraction mechanisms.

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Table 8. Performance under sparse PC conditions.

https://doi.org/10.1371/journal.pone.0348581.t008

Further comparative analysis was conducted on the mAP, Precision, Recall, F1 score, and FPS of different methods in real-world urban driving scenarios. The results are shown in Table 9. In Table 9, the proposed method ranked first with a mAP of 91.42%, which was 1.3 percentage points higher than the second place PV-RCNN. In terms of quality indicators, the proposed method achieved the best performance with an accuracy of 0.928, a recall of 0.912, and an F1 score of 0.920. In terms of real-time performance, the proposed method significantly outperformed PV-RCNN and PointNet++ with a processing speed of 36 FPS, second only to PointPillars which focused on speed optimization. These data proved that the method in this paper could maintain high precision detection and good real-time performance at the same time in complex real scenes, and meet the actual deployment requirements of auto drive system.

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Table 9. Performance in real-world urban driving scenarios.

https://doi.org/10.1371/journal.pone.0348581.t009

To further investigate the actual detection performance of the proposed improved PointNet network for 3D objects, the study conducted tests in a real urban scene, and the results are shown in Fig 12. In Fig 12, it was found that the improved PointNet network could achieve stable and accurate detection of vehicles, and the generated 3D bounding boxes were highly consistent with the true shape of the target. In complex environments with dense targets and partial occlusion, the improved network still exhibited strong robustness, reducing missed and false detections. The results indicated that the proposed method could achieve more complete and accurate 3D OD in complex environments, improving the robustness and practicality of the model.

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Fig 12. Improving the 3D OD performance of PointNet network.

(Taken in Nanjing, Jiangsu, China, October 2024).

https://doi.org/10.1371/journal.pone.0348581.g012