TopoCurve: Geometry-Aware Topology Reasoning via Bézier Curves in Autonomous Driving

Mihai Bogdan Deaconu; Laura Dioşan

cs.CVOct 6, 2026

TopoCurve: Geometry-Aware Topology Reasoning via Bézier Curves in Autonomous Driving

Authors: Mihai Bogdan Deaconu, Laura Dioşan

Organizations: Bosch Engineering Center Cluj, Cluj-Napoca, Romania · Faculty of Mathematics and Computer Science Babes,-Bolyai University, Cluj-Napoca, Romania

Abstract

Topology reasoning jointly detects 3D lanes and traffic elements from multi-view images and infers their structural connectivity. Current methods model lanes as discrete polylines, lacking smoothness, analytical tangent directions, and global spatial support for attention, while providing sparse topology supervision. We propose TopoCurve, a geometry-driven architecture for 3D topology reasoning grounded in a structured parametric lane representation. Lanes are modeled as endpoint-fixed cubic Bézier curves, enabling continuous geometry with exact endpoints and analytically defined directionality. We exploit this shared curve geometry across the entire pipeline. Endpoint distance and tangent alignment are encoded with multi-scale Fourier features and injected into the topology head. Sampled curve points serve as geometry-aligned references for deformable cross-attention spanning the full lane. Parallel curve-anchored attention branches provide diverse predictions for one-to-many topology supervision. These components form a tightly coupled cascade where representation enables geometric reasoning, guides feature aggregation, and supports denser supervision. TopoCurve achieves 50.6 OLS on the OpenLane-V2 benchmark without any post-processing, establishing a new state-of-the-art among end-to-end camera-only methods, and outperforms all existing approaches on endpoint detection (56.8 vs. 52.6 on DET_p).

Figures & tables

Figure 1 : TopoCurve architecture. (a) The point-lane decoder processes queries through 6 layers, each containing 4 parallel BDDA blocks for lanes and standard deformable attention for points, alongside a standard Deformable DETR head for traffic elements. (b) FourierGeoBias injects Fourier-encoded distance and tangent into the lane-lane topology head. (c) During training, CARS extracts pre-fusion queries for O2M topology supervision. (d) Topology heads produce predictions.

Data	Method	Venue	DET l $\uparrow$	DET t $\uparrow$	TOP ll $\uparrow$	TOP lt $\uparrow$	OLS $\uparrow$	DET p $\uparrow$
sub-A	TopoNet Li et al. [2023]	arXiv’23	28.6	48.6	10.9	23.8	39.8	43.8
	TopoMLP Wu et al. [2024]	ICLR’24	28.3	49.5	21.6	26.9	44.1	43.4
	TopoLogic Fu et al. [2024]	NeurIPS’24	29.9	47.2	23.9	25.4	44.1	45.2
	TopoFormer † Lv et al. [2025]	CVPR’25	34.7	48.2	24.1	29.5	46.3	–
	TopoPoint Fu et al. [2025]	NeurIPS’25	31.4	55.3	28.7	30.0	48.8	52.6
	TopoCurve	–	33.9	55.6	30.7	33.0	50.6	56.8

Table 1 : Results on OpenLane-V2. All methods use ResNet-50 backbone and are trained for 24 epochs. TopoFormer † uses a pretrained lane detector. The DET p scores for TopoNet, TopoMLP, and TopoLogic are computed using their official codebases. “–” denotes the absence of relevant data.

Table 3

Table 4

Table 5

Figure 2 : Qualitative comparison between TopoPoint and TopoCurve. We showcase multi-view inputs, BEV lane detections, and the corresponding lane-lane topology graphs. TopoCurve consistently produces smoother curves, precise endpoint alignment, and more accurate topology.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 3 : Additional qualitative comparison between TopoCurve and TopoPoint. The visualization illustrates lane-to-traffic element topology in the front-view camera alongside lane-lane connectivity in the Bird’s-eye view. TopoCurve consistently produces cleaner, smoother predictions, eliminating the jagged, self-intersecting artifacts prevalent in TopoPoint. Moreover, our continuous parametric representation achieves superior endpoint alignment and more accurate topological reasoning across both lane-lane and lane-traffic interactions.

Figure 4 : Additional qualitative comparison between TopoCurve and TopoPoint. The visualization illustrates lane-to-traffic element topology in the front-view camera alongside lane-lane connectivity in the bird’s-eye view. TopoCurve consistently produces cleaner, smoother predictions, eliminating the jagged, self-intersecting artifacts prevalent in TopoPoint. Moreover, our continuous parametric representation achieves superior endpoint alignment and more accurate topological reasoning across both lane-lane and lane-traffic interactions.

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Unified Modeling of Lane and Lane Topology for Driving Scene Reasoning

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Autonomous vehicles need to perceive not only physical elements in the driving scene, such as lane lines and traffic lights, but also logical elements like lane centerlines and their topology. Existing lane topology reasoning methods typically follow a reasoning-by-detection paradigm, where lane topological relationships are primarily derived from lane detection results. In this paper, we propose an innovative method called Unified Modeling of Lane and Lane Topology (UniTopo), which represents the topological relationships between lanes as connected lanes, encompassing predecessor lanes, successor lanes, and their interconnections. This unified representation of lanes and lane topology allows us to simultaneously obtain both the positions and topological information of lanes within a shared perception pipeline, establishing a new paradigm for directly perceiving lane topology from original image features. We validate our method on the driving scene reasoning benchmark OpenLane-V2, which consists of two subsets, built based on Argoverse2 and nuScenes, respectively. Our method achieves TOP_ll of 30.1% and 31.8% on the two subsets, significantly surpassing the existing state-of-the-art method T^2SG by 6.0% and 8.6%.

Abstract

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