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

NeurIPS 2026 · 3D vision › 3D generation · approach: 3D perception for autonomous driving

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Proposes TopoCurve, which parameterizes 3D lanes as endpoint-fixed cubic Bézier curves and uses them for Fourier-encoded geometric topology bias, curve-anchored deformable attention, and one-to-many redundancy supervision, reaching 50.6 OLS on OpenLane-V2 subset_A without post-processing.

Problem

3D lane topology reasoning from multi-view images relies on discrete polyline lane representations that lack smoothness, analytic tangents, and full-lane attention support, and topology supervision is sparse under one-to-one matching.

Approach

Reparameterize lanes as endpoint-fixed cubic Bézier curves and reuse the same curve geometry across the pipeline: analytic endpoint distance and tangent alignment encoded with multi-scale Fourier features as an additive bias in the lane-lane topology head, curve-sampled references for deformable attention, and parallel curve-anchored attention branches providing one-to-many supervision.

Key results

• TopoCurve reaches 50.6 OLS on OpenLane-V2 subset_A vs 48.8 for TopoPoint (with PLGM), without post-processing.
• On subset_A, DET_p reaches 56.8 vs 52.6 for TopoPoint; subset_B OLS is 51.2 vs 49.2.
• Removing the Bézier parameterization drops OLS from 50.6 to 48.7 in leave-one-out ablation.

Surprising findings

• Applying PLGM post-processing to TopoCurve slightly degrades performance (50.5 vs 50.6 OLS).

Limitations

• Operates on single frames only.
• Single cubic Bézier is theoretically limited for S-shaped curves; relies on segmenting complex lanes.
• Lower FPS (13.1) and higher parameter count than prior baselines.

Experimental setup

Datasets: OpenLane-V2 Argoverse2 nuScenes

Benchmarks: OpenLane-V2 subset_A OpenLane-V2 subset_B

Metrics: OLS DET_l DET_t TOP_ll TOP_lt DET_p FPS GFLOPs Params

Baselines: TopoNet TopoMLP TopoLogic TopoFormer TopoPoint RelTopo

Builds on: TopoPoint TopoLogic BEVFormer Deformable DETR Group DETR RATopo

Closest papers by meaning

• TopoPoint: Enhance Topology Reasoning via Endpoint Detection in Autonomous Driving (NeurIPS 2025 · similarity 0.92)
• TopoMLP: A Simple yet Strong Pipeline for Driving Topology Reasoning (ICLR 2024 · similarity 0.92)
• TopoLogic: An Interpretable Pipeline for Lane Topology Reasoning on Driving Scenes (NeurIPS 2024 · similarity 0.91)
• Topo2Seq: Enhanced Topology Reasoning via Topology Sequence Learning (AAAI 2025 · similarity 0.90)
• T2SG: Traffic Topology Scene Graph for Topology Reasoning in Autonomous Driving (CVPR 2025 · similarity 0.89)
• Bezier Everywhere All at Once: Learning Drivable Lanes as Bezier Graphs (CVPR 2024 · similarity 0.88)