# BFS-Based Weighted Late Fusion for 3D Object LiDAR Detection in V2X Systems

Selma Oubouabdellah, Elwan Héry, Julien Moreau, Vincent Frémont

► To cite this version:

Selma Oubouabdellah, Elwan Héry, Julien Moreau, Vincent Frémont. BFS-Based Weighted Late Fusion for 3D Object LiDAR Detection in V2X Systems. International Conference on the AI Revolution: Research, Ethics, and Society (AIR-RES 2025), American Council on Science and Education, Apr 2025, Las Vegas, United States. 10.1007/978-3-032-12930-7_26. hal-05280517

HAL Id: hal-05280517

https://hal.science/hal-05280517v1

Submitted on 24 Sep 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
BFS-Based Weighted Late Fusion for 3D Object
LiDAR Detection in V2X Systems

Selma Nourhane OUBOUABDELLAH¹,², Elwan HERY¹, Julien MOREAU²,
and Vincent FREMONT¹

1 École Centrale de Nantes, LS2N (UMR CNRS 6004), France
{selma.oubouabdellah,elwan.hery,vincent.fremont}@ls2n.fr

² Université de technologie de Compiègne, HEUDIASYC (UMR CNRS 7253), France
julien.moreau@hds.utc.fr

**Abstract.** In urban environments, Autonomous Vehicles (AVs) face various challenges, particularly in dealing with occlusions. This work delves into vehicle-to-everything (V2X) cooperation to enhance AVs’ perception in the 3D object detection task. Collaboration combines fields of view from various agents to enable AVs to ‘see’ through occlusions and detect objects that are either poorly visible or completely outside their range. This enhancement is crucial to ensure safer and more efficient urban navigation. We specifically focus on the late fusion of LiDAR data streams, using a Breadth-First Search (BFS) algorithm to group bounding boxes with high Intersection-over-Union (IoU). The resulting clusters are then fused via a weighted averaging scheme, producing more accurate and robust 3D detections. This BFS-based weighted method is straightforward, computationally efficient, and requires minimal communication overhead, making it well-suited for real-time urban driving scenarios.

**Keywords:** Autonomous vehicles · Late V2X fusion · 3D object detection · Lidar · Breadth First Search algorithm.

Short Research Paper

# 1 INTRODUCTION

In urban settings, Autonomous Vehicles (AVs) navigate environments filled with obstacles and occlusions, making moving objects a real danger. They can suddenly appear and disappear from the vehicle's view, posing challenges to the trajectory planning and control modules. To ensure the safe navigation of AVs in this setting, the first step is to enhance their perception module, enabling them to detect what lies beyond obstacles and react as soon as possible. To achieve this, data from intelligent vehicles and Road Side Units (RSU) can be combined. The varied perspectives of each agent offers help to reveal what is concealed behind occlusions. Such collaborative perception is known as V2X (vehicle-to-everything) [1].
In this work, we focus on 3D object detection using LiDAR data, chosen for its 360° coverage and precise metric information [2]. Although LiDAR suffers from reduced point density at longer ranges, V2X fusion helps compensate this limitation. We propose a late-fusion strategy (Figure 1) that is model-agnostic and computationally efficient. The main contribution lies in optimizing bounding-box clustering via a heading-penalized 3D Intersection over Union (IoU) and the Breadth First Search (BFS) algorithm. Evaluations on the V2X-Sim dataset [3] show that our approach achieves superior detection performance with a very low added computational cost compared to single-vehicle baselines.

<figure><img src="image_2.png" /><figcaption>Fig. 1: The proposed Late Fusion architecture.</figcaption></figure>

In the following section, we provide an overview of the current state of the art in V2X LiDAR perception. This is followed by a detailed explanation of the method we propose. Subsequently, we present the experimental setup and results, accompanied by a discussion. Finally, we conclude with a summary and an outlook on future perspectives.

## 2 RELATED WORKS

Several methods have been developed to address 3D object detection in autonomous vehicles [2], overcoming challenges such as real-time processing constraints and data sparsity in LiDAR-based techniques [4]. Persistent limitations of single-vehicle approaches are occlusions, and the inherent inability of sensors to detect objects outside their field of view. Some studies have explored indirect occlusion management through path planning based on scene semantics for safe navigation [5]. However, a more direct approach to this physical constraint is multi-agent collaboration. Multiple viewpoints of the same scene
can effectively reveal areas that are otherwise obscured. In our research, we utilize vehicle-to-everything (V2X) collaboration. Employing RSUs, typically positioned at elevated points within infrastructure such as intersections, enhancing scene visibility and reducing occlusions occurrences, especially in complex urban environments.

In collaborative data fusion, achieving an optimal balance between accuracy and communication bandwidth is essential. We categorize four types of collaboration networks [1]:

- Early Fusion: Exchanges raw sensor data, offering high accuracy but requiring substantial bandwidth and computing power, limiting its suitability for real-time applications [6].

- Late Fusion: Shares processed results, advantageous for real-time applications due to reduced computational demands and minimal bandwidth needs, but possibly less accurate due to information loss. Despite this limitation, late fusion remains flexible in accommodating heterogeneous sensors and model configurations [7].

- Intermediate Fusion: A compromise between early and late fusion, this method shares pre-processed data to effectively balance communication efficiency with accuracy [8] [9] [10]. The difficulty to succeed is to be able to keep most of the relevant data in the encoding step. However, this approach typically requires each agent to use an identical detection algorithm, limiting flexibility, modularity, and the potential for future upgrades.

- Hybrid Fusion: Intelligently combines aspects of both early and late fusion to align with specific research objectives. This could involve sharing processed results, akin to late fusion, but integrating them earlier in the data processing sequence [11] [12].

In this work, we adopt a late-fusion strategy to ensure real-time responsiveness to fast moving objects and unforeseen events. Furthermore, this approach remains flexible for different detection models, since real-world multi-generational intelligent vehicles will use varying architectures.

Standard bounding box fusion techniques, such as Non-Maximum Suppression (NMS) or soft-NMS [13], effectively remove overlapping boxes from a single model's predictions by selecting the one with the highest confidence score. However, they are often suboptimal in multi-agent scenarios, where low-confidence boxes might still contain valuable information. In contrast, Weighted Boxes Fusion (WBF) [14] combines boxes according to their confidence scores, producing a final consensus box that more accurately represents multiple model outputs. Although WBF has shown improved performance for LiDAR-based detection, most notably in WBF-ODAL [15], it also has a higher computational cost due to its sequential matching and fusion steps. Building on WBF, our approach employs a heading-penalized 3D IoU metric and a Breadth First Search (BFS) clustering algorithm to ensure that overlapping boxes truly represent the same real-world object. This strategy improves both fusion accuracy and computational efficiency while preserving detections that traditional methods might discard.
## 3 BFS-BASED WEIGHTED LATE FUSION

In multi-agent perception, different sensors may generate overlapping detections of the same object. To consolidate these redundant bounding boxes, we propose a BFS-based Weighted Late Fusion framework as shown in Figure 2. This procedure fuses detections from various agents into a single bounding box per physical object, while taking into consideration both 3D overlap and heading alignment.

<figure><img src="image_3.png" /><figcaption>Fig. 2: BFS-based Weighted Late Fusion.</figcaption></figure>

Let each 3D bounding box be represented by:

$$ \mathbf{b}_i = [x_i, y_i, z_i, dx_i, dy_i, dz_i, \theta_i] $$

where $(x_i, y_i, z_i)$ is the box center, $(dx_i, dy_i, dz_i)$ are the box dimensions, and $\theta_i$ is the yaw angle.

### 3.1 3D IoU with Heading Penalty

We first compute a penalized 3D Intersection over Union (IoU) that incorporates both spatial overlap and yaw-angle alignment. Denote two bounding boxes as $\mathbf{b}_1$
and $\mathbf{b}_2$, with volumes $V_1$ and $V_2$, and let $V_{\text{int}}$ be the intersection volume. Then the union volume is given by:

$$V_{\text{union}} = V_1 + V_2 - V_{\text{int}} \qquad (1)$$

To compute $V_{\text{int}}$, we assume that both bounding boxes share the same orientation, making their intersection a cuboid.

Define $\Delta\theta$ as the absolute difference in yaw angles, normalized so that $\Delta\theta \in [0, \pi]$. To penalize large heading mismatches, we introduce a linear function:

$$p(\Delta\theta) = \max(0, 1 - \frac{\Delta\theta}{\pi}) \qquad (2)$$

This function equals 1 when the bounding boxes share the same orientation ($\Delta\theta = 0$) and decreases linearly to 0 as $\Delta\theta$ approaches $\pi$. Hence, the penalized 3D IoU is:

$$\text{IoU}_{\text{penalized}}(\mathbf{b}_1, \mathbf{b}_2) = \frac{V_{\text{int}}}{V_{\text{union}}} \times p(\Delta\theta) \qquad (3)$$

This ensures that boxes with similar orientation receive higher IoU than those whose yaw angles differ significantly.

## 3.2 BFS Clustering

Next, we construct a graph in which each node represents a bounding box. We connect two nodes by an edge if their heading-penalized IoU exceeds a threshold $\tau$ (we achieved the optimal performance with $\tau = 0.7$). We then apply a breadth-first search (BFS) to identify connected components:

$$C = \{ \mathbf{c}_1, \dots, \mathbf{c}_K \}$$

where each $\mathbf{c}_k$ is a cluster of indices corresponding to boxes that should be fused. The BFS ensures that all boxes within a cluster have high mutual overlap, either directly or through a chain of intermediate boxes. It avoids redundant visits to the same node which makes it computationally efficient. It can be represented by Algorithm 1:
<caption>**Algorithm 1:** BFS Clustering of Bounding Boxes</caption>

Input: $B \in R^{N \times 7}$; // All bounding boxes: each row
[x, y, z, dx, dy, dz, θ]
IoU<sub>penalized</sub>(·, ·); // 3D IoU with heading penalty
τ; // IoU threshold (e.g., 0.5)
Output: $C = \{c_1, ..., c_K\}$; // List of clusters, each is a set
of box indices

iouMatrix ← PairwiseIoU3D(B, IoU<sub>penalized</sub>);
visited ← ∅;
C ← ∅;

for i ← 1 to N do
    if i ∉ visited then
        Q ← {i}; // Initialize BFS queue
        c ← ∅; // Current cluster
        while Q ≠ ∅ do
            u ← PopFront(Q);
            if u ∉ visited then
                visited ← visited ∪ {u};
                c ← c ∪ {u};
                // Find all neighbors whose IoU exceeds τ
                N ← {v | iouMatrix[u, v] > τ};
                foreach v ∈ N do
                    if v ∉ visited then
                        PushBack(Q, v);
                    end
                end
                end
            end
            C ← C ∪ {c}; // Add new cluster
        end
    end
    return C;

3.3 Weighted Fusion

Consider one cluster **c**<sub>k</sub> containing *l* bounding boxes {**b**<sub>1</sub>, ..., **b**<sub>*l*</sub>} with
detection scores {s<sub>1</sub>, ..., s<sub>*l*</sub>} and labels {l<sub>1</sub>, ..., l<sub>*l*</sub>}.

We define weights:

$$
w_i = \begin{cases} \frac{s_i}{\sum_{j=1}^{\ell} s_j} & \text{if } \sum_{j=1}^{\ell} s_j > 0, \\ \frac{1}{\ell} & \text{otherwise.} \end{cases} \qquad (4)
$$
Each box $\mathbf{b}_i$ has parameters $[x_i, y_i, z_i, dx_i, dy_i, dz_i, \theta_i]^T$. We obtain the fused bounding box $\bar{\mathbf{b}}$ via:

**Center and Dimensions:** We compute the weighted averages for $\{x, y, z, dx, dy, dz\}$:

$$ \bar{x} = \sum_{i=1}^{\ell} w_i x_i, \quad \bar{y} = \sum_{i=1}^{\ell} w_i y_i, \quad \bar{z} = \sum_{i=1}^{\ell} w_i z_i, \qquad (5) $$

$$ \bar{dx} = \sum_{i=1}^{\ell} w_i dx_i, \quad \bar{dy} = \sum_{i=1}^{\ell} w_i dy_i, \quad \bar{dz} = \sum_{i=1}^{\ell} w_i dz_i. \qquad (6) $$

**Heading:** To avoid discontinuities in yaw, we aggregate angles using sine and cosine:

$$ \bar{\theta} = \arctan2\left(\sum_{i=1}^{\ell} w_i \sin(\theta_i), \sum_{i=1}^{\ell} w_i \cos(\theta_i)\right). \qquad (7) $$

**Score:** We define the fused detection confidence as the average:

$$ \bar{s} = \frac{1}{\ell} \sum_{i=1}^{\ell} s_i. \qquad (8) $$

**Label:** Finally, we assign the class label with the highest cumulative score:

$$ \bar{l} = \arg\max_{l \in \{l_1, \dots, l_\ell\}} \left( \sum_{i \mid l_i = l} s_i \right). \qquad (9) $$

This BFS-based weighted late-fusion framework generates a single bounding box per cluster. If a cluster contains only one bounding box, it is retained as is. By reducing overlapping detections and leveraging multi-view data to handle occlusions, the framework achieves efficient and robust performance. Moreover, its low computational cost and minimal communication overhead make it well-suited for real-time collaborative perception in autonomous driving applications.

# 4 EXPERIMENTATION

## 4.1 Implementation details

In order to evaluate the proposed method, we utilized the V2X-Sim dataset [3], which provides multi-agent (V2X) collaborative perception data. We based our 3D object detection pipeline and our evaluation metrics on the OpenPCDet library [16], employing PointPillars [17] for the encoding step and a CenterPoint [18] detection head. We evaluated the model using the JeanZay supercomputer which provides a cluster of V100 GPUs.
## 4.2 Results

Figure 3 illustrates that the fused detection results (blue boxes) enable the ego vehicle (orange point cloud) to detect objects that may be out of its sensor range or obscured by occlusions.

<figure><img src="image_4.png" /><figcaption>Fig. 3: Multi-Agent 3D Object Detection: Grey points represent data from different agents, while the ego agent's point cloud appears in orange. Ground truth bounding boxes are shown in green, and fused detection results in blue.</figcaption></figure>

To evaluate the proposed method, we employ the standard NuScenes evaluation metrics [19]. Table 1 shows the 3D object detection performance using mean Average Precision (mAP) at different distance thresholds, while Table 2 lists the average translation (ATE), and scale (ASE) errors. We compare three methods: single-vehicle detection, V2X detection using a BFS-based fusion that clusters bounding boxes based on their center distances, and our proposed approach that clusters bounding boxes based on a heading-penalized IoU.

<table><caption>Table 1: Detection Performance Metrics (mAP at various distances)</caption><thead><tr><th></th><th>mAP (0.5 m) ↑</th><th>mAP (1 m) ↑</th><th>mAP (2 m) ↑</th><th>mAP (4 m) ↑</th></tr></thead><tbody><tr><td>Single vehicle</td><td>0.036</td><td>0.059</td><td>0.082</td><td>0.090</td></tr><tr><td>V2X (center distance)</td><td>0.120</td><td><strong>0.173</strong></td><td><strong>0.224</strong></td><td><strong>0.246</strong></td></tr><tr><td><strong>V2X (3D IoU)</strong></td><td><strong>0.121</strong></td><td>0.167</td><td>0.206</td><td>0.226</td></tr></tbody></table>

**Discussion** Table 1 and Table 2 demonstrate that both fusion methods significantly improve detection performance over the single-vehicle baseline.
<table><caption>Table 2: Error Metrics : Average Translation Error, Average Scale, Orientation Error</caption><thead><tr><th></th><th>ATE (m) ↓</th><th>ASE ↓</th></tr></thead><tbody><tr><td>Single vehicle</td><td>0.529</td><td>0.418</td></tr><tr><td>V2X (center distance)</td><td>0.416</td><td>0.292</td></tr><tr><td><b>V2X (3D IoU)</b></td><td><b>0.391</b></td><td><b>0.278</b></td></tr></tbody></table>

At the tightest matching threshold (0.5 m center distance), mean Average Precision (mAP) jumps from 0.036 for a single vehicle to 0.120 with center-distance fusion and to 0.121 when using 3D IoU fusion. This improvement holds at longer ranges: at 1 m, mAP increases from 0.059 to 0.173 (center distance) and 0.167 (3D IoU); at 2 m from 0.082 to 0.224 and 0.206; and at 4 m from 0.090 to 0.246 and 0.226. Although the used mAP metric is based on center-distance thresholds and does not reflect bounding-box shape, both fusion schemes markedly outperform the single-vehicle case.

Looking at the error metrics, our 3D IoU fusion achieves the lowest Average Translation Error (ATE) of 0.391 m, an improvement over 0.416 m for center-distance fusion, and 0.529 m for the single-vehicle system. Similarly, Average Scale Error (ASE) falls to 0.278 with our fusion, compared to 0.292 for center-distance fusion and 0.418 for the baseline. These reductions in translation and scale errors indicate that incorporating heading-penalized 3D IoU more accurately captures object geometry than purely distance-based fusion.

In summary, although both fusion approaches substantially boost detection accuracy, the 3D IoU-based method provides the most precise localization and sizing of objects. This enhanced geometric fidelity is crucial for multi-agent 3D object detection, directly supporting safer navigation and collision avoidance.

**Limitations** While the proposed method demonstrates promising efficiency, two noteworthy limitations remain. First, the current framework does not incorporate agent-specific information during the weighted fusion step, even though each agent may rely on a different detection model with distinct performance. As a result, it is not always valid to treat confidence scores from different models as directly comparable. Furthermore, although the BFS-based clustering ensures that all boxes within a cluster maintain high mutual overlap, either directly or through a chain of intermediate boxes, this property can unintentionally cause the algorithm to merge two distinct physical objects into a single cluster.

# 5 CONCLUSIONS AND PERSPECTIVES

In this paper, we introduced a BFS-based weighted late fusion framework for 3D object detection in V2X systems. Our approach leverages a heading-penalized 3D IoU metric and a BFS clustering algorithm to group overlapping bounding boxes from multiple agents, which are then fused through a confidence-weighted averaging scheme. Experimental results on the V2XSim dataset demonstrate that our
method significantly enhances detection performance compared to single-vehicle baselines. Despite these promising results, our method has two key limitations: it does not currently incorporate agent-specific information during the fusion process, and the BFS clustering may occasionally merge boxes corresponding to distinct physical objects. Future work will focus on improving the clustering strategy and integrating agent-specific performance metrics.

**Acknowledgments.** This work is a part of the ANNAPOLIS ANR project. This work was granted access to the HPC resources of IDRIS under the allocation 2024-AD011012128R4 made by GENCI.

## References

1. Huang, T., Liu, J., Zhou, X., Nguyen, D.C., Azghadi, M.R., Xia, Y., Han, Q.-L., Sun, S.: V2X Cooperative Perception for Autonomous Driving: Recent Advances and Challenges. arXiv preprint arXiv:2310.03525 (2023)

2. Mao, J., Shi, S., Wang, X., Li, H.: 3D Object Detection for Autonomous Driving: A Review and New Outlooks. arXiv preprint arXiv:2206.09474 (2022)

3. Li, Y., Ma, D., An, Z., et al.: V2X-Sim: Multi-Agent Collaborative Perception Dataset and Benchmark for Autonomous Driving. IEEE Robotics and Automation Letters. 7(4), 10914–10921 (2022)

4. Dao, M.-Q., Héry, E., Frémont, V.: Attention-Based Proposals Refinement for 3D Object Detection. In: 2022 IEEE Intelligent Vehicles Symposium (IV), pp. 197–205. IEEE, Aachen (2022)

5. Drouilly, R., Rives, P., Morisset, B.: Semantic Representation for Navigation in Large-Scale Environments. In: 2015 IEEE International Conference on Robotics and Automation (ICRA), pp. 1106–1111. IEEE, Seattle (2015)

6. Chen, Q., Tang, S., Yang, Q., et al.: Cooper: Cooperative Perception for Connected Autonomous Vehicles Based on 3D Point Clouds. In: 2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS), pp. 514–524. IEEE (2019)

7. Xu, R., Chen, W., Xiang, H., et al.: Model-Agnostic Multi-Agent Perception Framework. In: 2023 IEEE International Conference on Robotics and Automation (ICRA), pp. 1471–1478. IEEE (2023)

8. Wang, T.-H., Manivasagam, S., Liang, M., Yang, B., Zeng, W., Urtasun, R.: V2VNet: Vehicle-to-Vehicle Communication for Joint Perception and Prediction. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, J.-M. (eds.) Computer Vision – ECCV 2020, LNCS, vol. 12347, pp. 605–621. Springer, Cham (2020)

9. Li, Y., Ren, S., Wu, P., Chen, S., Feng, C., Zhang, W.: Learning Distilled Collaboration Graph for Multi-Agent Perception. Advances in Neural Information Processing Systems 34, 29541–29552 (2021)

10. Xu, R., Xiang, H., Tu, Z., Xia, X., Yang, M.-H., Ma, J.: V2X-ViT: Vehicle-to-Everything Cooperative Perception with Vision Transformer. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, J.-M. (eds.) Computer Vision – ECCV 2022, LNCS, pp. 107–124. Springer, Cham (2022)

11. Arnold, E., Dianati, M., de Temple, R., Fallah, S.: Cooperative Perception for 3D Object Detection in Driving Scenarios Using Infrastructure Sensors. IEEE Transactions on Intelligent Transportation Systems. 23(3), 1852–1864 (2022)
12. Dao, M.-Q., Berrio, J.S., Frémont, V., Shan, M., Héry, E., Worrall, S.: Practical Collaborative Perception: A Framework for Asynchronous and Multi-Agent 3D Object Detection. arXiv preprint arXiv:2307.01462 (2023)

13. Bodla, N., Singh, B., Chellappa, R., et al.: Soft-NMS – Improving Object Detection with One Line of Code. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp. 5561–5569. (2017)

14. Solovyev, R., Wang, W., Gabruseva, T.: Weighted Boxes Fusion: Ensembling Boxes from Different Object Detection Models. Image and Vision Computing. 107, 104117 (2021)

15. Katkoria, D., Sreevalsan-Nair, J., Sati, M., et al.: WBF-ODAL: Weighted Boxes Fusion for 3D Object Detection from Automotive LiDAR Point Clouds. In: 2024 International Conference on Vehicular Technology and Transportation Systems (ICVTTS), pp. 1–6. IEEE (2024)

16. OD Team: OpenPCDet: An Open-Source Toolbox for 3D Object Detection from Point Clouds. (2020)

17. Lang, A.H., Vora, S., Caesar, H., et al.: PointPillars: Fast Encoders for Object Detection from Point Clouds. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 12697–12705. (2019)

18. Yin, T., Zhou, X., Krahenbuhl, P.: Center-Based 3D Object Detection and Tracking. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 11784–11793. (2021)

19. Caesar, H., Bankiti, V., Lang, A.H., et al.: nuScenes: A Multimodal Dataset for Autonomous Driving. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 11621–11631. (2020)

20. Tsai, D., Berrio, J.S., Shan, M., et al.: MS3D++: Ensemble of Experts for Multi-Source Unsupervised Domain Adaptation in 3D Object Detection. IEEE Transactions on Intelligent Vehicles (2024)

21. Yang, J., Shi, S., Wang, Z., et al.: ST3D: Self-Training for Unsupervised Domain Adaptation on 3D Object Detection. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10368–10378. (2021)