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Bezier Everywhere All at Once: Learning Drivable Lanes as Bezier Graphs
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Proposes Bézier Graphs, a shared parameterisation of cubic Bézier curves over lane graphs, and BGFormer, a Relationformer-based transformer that predicts them end-to-end from aerial images, evaluated on UrbanLaneGraph.
Problem
Extracting drivable lane topology and geometry from aerial imagery; existing node-based lane graph predictions are noisy, non-physical, and need heavy downstream processing.
Approach
Represent a lane graph as a graph of cubic Bézier curves whose node positions and direction vectors are shared across connected edges, enforcing direction continuity, and predict this graph end-to-end with a DETR-style transformer (BGFormer) plus a tile-based aggregation with Hungarian matching.
Key results
- On Succ-LGP, BGFormer reaches APLS 0.772 vs 0.202 for LaneGNN and SDA20 0.492 vs 0.227, but lower Graph IoU (0.312 vs 0.347) and lower recall.
- On Full-LGP, BGFormer achieves APLS up to 0.229 vs 0.065 for LaneGNN and inference time of ~101-108 s vs 9784 s, a >95% reduction.
- Average curvature KL divergence is 0.04 ± 0.02 for BGFormer vs 0.12 ± 0.03 for LaneGNN across 11 evaluation images.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| predict lane graphs with BGFormer rather than LaneGNN | Succ-LGP · Succ-LGP | APLS: 0.202 -> 0.772 | Helped |
| predict lane graphs with BGFormer rather than LaneGNN | Succ-LGP · Succ-LGP | SDA20: 0.227 -> 0.492 | Helped |
| predict lane graphs with BGFormer rather than LaneGNN | Succ-LGP · Succ-LGP | Graph IoU: 0.347 -> 0.312 | Hurt |
| predict lane graphs with BGFormer rather than LaneGNN | Succ-LGP · Succ-LGP | TOPO F1: 0.646 -> 0.547 | No clear effect |
| predict full lane graphs with BGFormer rather than LaneGNN | Full-LGP · Full-LGP | APLS: 0.065 -> 0.187 | Helped |
| apply rotation to each tile (ablation) | BGFormer Full-LGP · Full-LGP, high thresholds | APLS: 0.187 -> 0.208 | Helped |
| apply rotation to each tile (ablation) | BGFormer Full-LGP · Full-LGP, low thresholds | APLS: 0.212 -> 0.229 | Helped |
| apply rotation to each tile (ablation) | BGFormer Full-LGP · Full-LGP | inference time (s): 108.15 -> 401.87; 101.42 -> 416.49 | Hurt |
| use low rather than high node and edge detection thresholds (ablation) | BGFormer Full-LGP · Full-LGP, no rotation | APLS: 0.187 -> 0.212 | Helped |
| use low rather than high node and edge detection thresholds (ablation) | BGFormer Full-LGP · Full-LGP, rotation | APLS: 0.208 -> 0.229 | Helped |
| use BGFormer rather than LaneGNN to predict curvature | Full-LGP · Full-LGP evaluation graphs | curvature-distribution KL divergence: 0.12 ± 0.03 -> 0.04 ± 0.02 | Helped |
Surprising findings
- On Full-LGP, BGFormer scores higher on recall metrics but lower on precision compared with LaneGNN, reversing the Succ-LGP trend.
- BGFormer's Succ-LGP recall is worse than LaneGNN because it frequently omits entire lanes when a single node is missed.
Limitations
- Predictions omit entire lanes when a single node is missed, hurting recall on Succ-LGP.
- Edges that cut corners require a hand-designed post-processing step to remove.
- Evaluated only on aerial imagery from UrbanLaneGraph; combination with onboard sensors is future work.
Experimental setup
Datasets: UrbanLaneGraph
Benchmarks: UrbanLaneGraph Succ-LGP UrbanLaneGraph Full-LGP
Metrics: APLS SDA20 SDA50 Graph IoU TOPO GEO KL divergence of curvature inference time
Baselines: LaneGNN LaneGraphNet
Builds on: Relationformer Deformable DETR LaneGNN DETR
Closest papers by meaning
- GLane3D: Detecting Lanes with Graph of 3D Keypoints (CVPR 2025 · similarity 0.88)
- TopoCurve: Geometry-Aware Topology Reasoning via Bézier Curves in Autonomous Driving (NeurIPS 2026 · similarity 0.88)
- Sketch and Refine: Towards Fast and Accurate Lane Detection (AAAI 2024 · similarity 0.88)
- LaneSegNet: Map Learning with Lane Segment Perception for Autonomous Driving (ICLR 2024 · similarity 0.88)
- Rethinking Lanes and Points in Complex Scenarios for Monocular 3D Lane Detection (CVPR 2025 · similarity 0.87)
- LaneCPP: Continuous 3D Lane Detection using Physical Priors (CVPR 2024 · similarity 0.87)
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