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End-to-End Vectorized HD-map Construction with Piecewise Bezier Curve

Limeng Qiao, Wenjie Ding, Xi Qiu, Chi Zhang

arXiv:2306.09700v1cs.CV

TL;DR

Combining conventional and learning-based approaches offers multi-scenario scalability while reducing the demand for annotated data. BeMapNet predicts vectorized maps end-to-end with a unified piecewise Bézier representation, using geometric-prior alignment, a curve-output head, and progressive curve-restoration loss. BeMapNet is reported as remarkably superior to state-of-the-art approaches on existing benchmarks.

  • Problem

    Combining conventional and learning-based approaches offers multi-scenario scalability while reducing the demand for annotated data.

    Source: §1 · p. 2

  • Method

    BeMapNet predicts vectorized maps end-to-end with a unified piecewise Bézier representation, using geometric-prior alignment, a curve-output head, and progressive curve-restoration loss.

    Source: §1 · p. 2

  • Results

    BeMapNet is reported as remarkably superior to state-of-the-art approaches on existing benchmarks.

    Source: §1 · p. 2, §5 · p. 8

  • Takeaways & Limitations

    The paper presents postprocessing-free piecewise Bézier modeling as a new perspective for future HD-map research.

    Source: §5 · p. 8

    IPM position calculation assumes a pinhole camera model and a flat ground surface at fixed height.

    Source: §3.2.2 · p. 5

Abstract

from arXiv · show

Vectorized high-definition map (HD-map) construction, which focuses on the perception of centimeter-level environmental information, has attracted significant research interest in the autonomous driving community. Most existing approaches first obtain rasterized map with the segmentation-based pipeline and then conduct heavy post-processing for downstream-friendly vectorization. In this paper, by delving into parameterization-based methods, we pioneer a concise and elegant scheme that adopts unified piecewise Bezier curve. In order to vectorize changeful map elements end-to-end, we elaborate a simple yet effective architecture, named Piecewise Bezier HD-map Network (BeMapNet), which is formulated as a direct set prediction paradigm and postprocessing-free. Concretely, we first introduce a novel IPM-PE Align module to inject 3D geometry prior into BEV features through common position encoding in Transformer. Then a well-designed Piecewise Bezier Head is proposed to output the details of each map element, including the coordinate of control points and the segment number of curves. In addition, based on the progressively restoration of Bezier curve, we also present an efficient Point-Curve-Region Loss for supervising more robust and precise HD-map modeling. Extensive comparisons show that our method is remarkably superior to other existing SOTAs by 18.0 mAP at least.

1. Introduction

Online HD-map construction must model varied map elements as vectorized instances without relying on raster segmentation and heavy post-processing. BeMapNet uses a unified piecewise Bézier representation and an end-to-end set-prediction architecture for this task.

1. Introduction

  • Raster segmentation lacks instance-level detail and requires heavy post-processing for vectorization, while lane-focused methods do not directly suit HD-maps’ more shape-variable elements.Online HD-map construction also faces challenges in 2D-to-3D perspective transformation.Source: §1 · p. 1
  • Piecewise Bézier curves represent each map curve as k segments of degree n, enabling more compact parameterization with fewer control points and higher capacity.The paper presents this as a scalable and robust approach for practice.Source: §1 · p. 2
  • BeMapNet formulates vectorized HD-map construction as sparse set prediction with bipartite matching, making the end-to-end architecture postprocessing-free.Its four modules progress from shared image features through semantic BEV and instance curve representations to point-level parameterization.Source: §1 · p. 2
  • IPM-PE Align injects inverse-perspective geometric priors into BEV features through position encoding, while the Piecewise Bézier Head predicts segment count and control-point coordinates.Point-Curve-Region Loss supervises curve restoration progressively.Source: §1 · p. 2
  • BeMapNet is reported as remarkably superior to state-of-the-art methods on existing benchmarks.The introduction attributes this result to the proposed approach without giving a benchmark metric there.Source: §1 · p. 2

2. Related Work

Prior HD-map work includes segmentation-based representations that require vectorization or remain semantic, alongside methods for modeling geometric structures as points or curves. BeMapNet is positioned as an end-to-end, parameterization-based alternative for varied map geometry.

2.1. Vectorized HD-map Construction

  • Segmentation-based HD-map methods produce rasterized semantic maps, with some approaches using heuristic post-processing for vectorized results and others stopping at semantic representations.BeMapNet is described as constructing instance-level vectorized maps end-to-end from multi-view camera input.Source: §2.1 · p. 2

2.2. Structure Modeling of Geometric Data

  • Geometric modeling methods include point-based representations and curve-based polynomial or Bézier forms, while BeMapNet uses piecewise Bézier curves for arbitrary-shape HD-map geometry without complicated geometric assumptions.The cited examples include point proposals, keypoints, polynomial coefficients, and query-based poly-parameter prediction.Source: §2.2 · p. 2

Piecewise Bézier Output Head

The architecture depicts a staged progression from image and BEV features to curve descriptors and Bézier control points. The related camera-to-BEV literature motivates aligning position embeddings with world coordinates when introducing 3D geometry priors.

Piecewise Bézier Output Head

  • The architecture’s four stages progress from multi-scale image features through semantic BEV features and instance curve descriptors to point-level Bézier control sequences.The head’s diagram distinguishes explicit control points from implicit control offsets.Source: Figure 2 · p. 3

2.3. Multi-view Camera-to-BEV Transformation

  • Prior camera-to-BEV methods introduce geometry through camera poses, depth distributions, 3D positions, or position embeddings; the paper additionally aligns position embeddings in world coordinates.The cited approaches include VPN, LSS, BEVDet, DETR3D, and PETR.Source: §2.3 · p. 3

3. Method

BeMapNet parameterizes map elements as piecewise Bézier curves with degree fixed by semantic class and segment count chosen per instance. Its architecture aligns camera and BEV features, predicts curve parameters, and uses point-, curve-, and region-level supervision.

3.1. Problem Formulation

  • The method represents map elements as piecewise Bézier curves, keeping degree fixed by semantic class while selecting segment count dynamically per instance.Implicit control points are modeled as offsets from the centers of explicit control points.Source: §3.1 · p. 4, Figure 3 · p. 4

3.2.1 Overall Architecture

  • BeMapNet combines shared multi-camera feature extraction, semantic BEV decoding, instance-level Bézier decoding, and a piecewise Bézier output head for vectorized map prediction.The feature extractor uses a shared CNN backbone and FPN; the decoders produce semantic and instance-level map representations.Source: §3.2.1 · p. 4

3.2.3 Piecewise B´ezier Output Head

  • The output head regresses Bézier control-point coordinates and predicts curve length as an N-class termination-index classification, where N is the map class’s maximum piece count.Split Coordinate Regression produces the coordinates; Dynamic End-index Classification scores each position as a possible termination point.Source: §3.2.1 · p. 4, §3.2.3 · p. 5

3.2.2 IPM-PE Align Layer

  • IPM-PE Align encodes 2D–3D geometry priors through positional embeddings to align camera-view and BEV coordinate systems, assuming flat ground at a fixed height for its IPM branch.A shared fully connected layer further aligns the position embeddings because the flat-ground, known-height assumption may not hold in practice.Source: §3.2.2 · p. 5

3.3. End-to-End Training

  • Ground truth converts annotated points into k segments modeled by n-order Bézier curves, while auxiliary semantic and instance mask losses supervise intermediate decoders.Curve reconstruction uses matrix multiplication with a Bernstein matrix, and the auxiliary compound loss combines cross-entropy and Dice losses.Source: §3.3 · pp. 5–6
  • PCR-Loss supervises control points, reconstructed curves, and dilated curve regions, combining point, curve, and region losses as a weighted sum.Region supervision samples the ground-truth and predicted masks at dilated predicted-curve coordinates.Source: §3.3 · p. 6

4. Experiments

On NuScenes, BeMapNet outperforms prior SOTAs, and ablations report gains associated with position encoding, PCR supervision, auxiliary tasks, and Bezier vectorization.

4.1. Experimental Settings

  • NuScenes evaluation covers three static map categories, uses instance-level AP at three Chamfer-distance thresholds, and includes lighting and weather subsets.The dataset evaluation focuses on lane-divider, pedestrian-crossing, and road-boundary; perception range is [30, 30, 15, 15]m at 0.15 m/pixel.Source: §4.1 · p. 6

4.2. Comparisons with State-of-the-art Methods

  • Up to 18.0 improvement over existing SOTAs is reported for BeMapNet with EfficientNet-B0 and 30 epochs.The comparison uses the same setting; Table 1 also presents results under two distance-threshold protocols.Source: Table 1 · p. 7, §4.2 · p. 7
  • BeMapNet gains 0.6 and 3.0 AP with ResNet-50 and SwinTiny, at least 5.4 more with 110 epochs, and 13.2 and 16.9 AP for night and rainy scenes.The reported night and rainy values are respectively 13.2 and 16.9 AP.Source: §4.2 · p. 7

4.3. Ablation Study

  • IPM-PE improves AP by 3.9/5.7 over sine/learned positional encoding, while shared-FC alignment adds 2.6 points.The authors attribute the shared alignment layer's role to mitigating performance decline from an unreasonable IPM assumption.Source: §4.3 · p. 7, Table 2 · p. 7
  • Using point, curve, and region supervision together achieves the optimal reported AP of 43.7; region-only supervision performs poorly.Among single-supervision variants, the reported trend is curve > point > region.Source: §4.3 · p. 8, Table 3 · p. 8
  • Average AP rises from 20.0 without auxiliary loss to 34.5 with semantic supervision, 38.4 with instance supervision, and 43.7 with both.Source: §4.3 · p. 8, Table 4 · p. 8
  • Bezier-based vectorization achieves 4.5 AP more than the polyline variant, with larger gains as map-element shape complexity increases.The polyline variant sets the degree to 1 for all elements.Source: §4.3 · p. 8, Table 5 · p. 8
  • Qualitative comparisons show BeMapNet constructing varied HD-map elements more compactly and robustly while avoiding complex vectorized post-processing.Figure 5 compares HDMapNet, BeMapNet, and ground truth across scenarios.Source: §4.3 · p. 8, Figure 5 · p. 8

5. Conclusion

The conclusion presents BeMapNet as an end-to-end, postprocessing-free approach to online vectorized HD-map construction using unified piecewise Bezier curves.

5. Conclusion

  • BeMapNet combines an IPM-PE Align Module, Piecewise Bezier Head, and Point-Curve-Region Loss and reaches state-of-the-art performance.The conclusion describes the framework as a new perspective for future HD-map research.Source: §5 · p. 8

Supplementary Material

The supplementary material adds architecture details, further map-construction experiments, benchmark-extension statistics, and qualitative visualizations.

Supplementary Material

  • Supplementary contents include architecture details, additional map-construction results, benchmark-extension statistics, and qualitative visualizations.Source: Supplementary Material · p. 9

A. Additional Details of Architecture Design

The appendix explains IPM-PE's geometric motivation: camera and BEV grids are mapped into a shared world space to model their positional relationships.

A.1. The Motivation of IPM-PE

  • IPM-PE maps camera-coordinate grids with IPM and transforms BEV grids into the same world space using a scale coefficient.The shared-space representation models positional relationships across multiple views and spaces; Figure 6 illustrates the motivation.Source: §A.1 · p. 9, Figure 6 · p. 9

A.2. Alignment Method of IPM-PE

Shared camera–BEV alignment improves IPM-PE performance, while single or exclusive alignment declines. The section also reports that the proposed dynamic coordinate-regression head outperforms direct FC projection.

A.2. Alignment Method of IPM-PE

  • Shared camera–BEV alignment improves performance by 2.6 AP, whereas single or exclusive alignment causes a decline.The authors attribute the shared-alignment improvement to mutual alignment between the two positional-embedding branches.Source: §A.2 · p. 9, Table 7 · p. 9

A.3. Coordinate Regression Head Design

  • The proposed dynamic Split Coordinate Regression Head is more advantageous than direct FC projection for coordinate regression.The comparison is summarized in Table 8.Source: §A.3 · p. 9, Table 8 · p. 9, Figure 8 · p. 9

B. More Experimental Results

These experiments examine BeMapNet’s efficiency, architecture and representation choices, and the reliability of generated Bézier ground truths. They report favorable speed and model-size comparisons, design-dependent performance trends, and high reconstruction agreement with annotations.

B.1. The running time and model size.

  • 0.4× fewer parameters (69.8 →27.6) and 6.9× higher speed (0.7 →4.8) are reported for BeMapNet versus HDMapNet under the same EfficientNet-B0 backbone.Measurements used one RTX 2080Ti GPU with batch size 1; inference time includes network forwarding and post-processing but excludes data loading.Source: Table 9 · p. 10, §B.1 · p. 10

B.2. The Number of Transformer Layers.

  • 30.9 AP is reached with one transformer layer in each of the three modules, while overall AP tends to saturate at six layers.The reported trend is that AP improves gradually as the number of layers increases.Source: Table 10 · p. 10, §B.2 · p. 10

B.3. The Number of BEV Queries.; B.4. The Number of B´ezier Queries.

  • The experiments vary BEV-query and Bézier-query counts; the text says BEV-query count represents BEV-feature resolution and that Table 11 verifies this relation.Tables 11 and 12 report the impacts of different BEV-query and Bézier-query counts, respectively.Source: §B.3 · p. 10, Table 11 · p. 10, §B.4 · p. 10

B.5. The Impact of Different B´ezier Setup

  • With fixed control-point count, too many pieces and too large a degree both degrade performance; at fixed degree, adding pieces improves performance until saturation.At fixed piece count, larger degree increases fitting ability but also learning difficulty.Source: Table 15 · p. 10, Table 14 · p. 10, Table 13 · p. 10

B.6. The Impact of Input Resolution; B.7. The Impact of Different FPN-Output Shape

  • 8.4× higher input resolution improves performance by 4.5 AP, while increasing the FPN output shape improves AP until it tends to saturate at 30×70.The experiments adopt input resolution 896×512 and report saturation as FPN output shape reaches 30×70.Source: Table 16 · p. 11, §B.6 · p. 11, Table 17 · p. 11

B.8. The Impact of Different Curve Length

  • Table 18 compares performance across different lengths of restored Bézier curves, with curve length linked to the curve-supervision part of PCR-Loss.The passage provides no comparative values for the tested lengths.Source: Table 18 · p. 11, §B.8 · p. 11

B.9. More details of the proposed GenGT

  • The GenGT procedure interpolates a sub-curve, fits control points by least squares, restores its Bézier curve, and updates segment bounds based on fitting error.The described algorithm initializes Bernstein coefficients and their pseudo-inverse using the selected degree and point count.Source: §B.9 · p. 11

B.10. Verification of the Generated B´ezier GTs

  • 99.94 mAP or higher at τ = 0.2m, and 97.7–98.7 mAP at τ = 0.1m, are reported when generated curves are evaluated against original annotations.Generated control-point sequences are restored to curves and treated as predictions in the same evaluation protocol.Source: Table 19 · p. 11, §B.10 · p. 11

C.1. Data Split by Different Conditions

The appendix describes condition-based data subsets and examines compactness and parameter choices for piecewise Bézier map elements. It also presents qualitative results across lighting, weather, difficult-road scenarios, and model failure cases.

C.1. Data Split by Different Conditions

  • NuScenes is divided into day, night, sunny, cloudy, and rainy subsets to examine performance under different lighting and weather conditions.Figures 9–10 provide subset distributions and scenario examples.Source: §C.1 · p. 11, Figure 9 · p. 11, Figure 10 · p. 12

C.2. More Compact Map Element Expression

  • Generated Bézier curve ground truth uses at least 81% fewer annotated points than the original point ground truth.The comparison concerns the number of points required to represent map elements.Source: §C.2 · pp. 11–12, Figure 11 · p. 12

C.3. How many pieces are reasonable?

  • The selected configurations are ⟨3, 2⟩ for lane dividers, ⟨1, 1⟩ for pedestrian crossings, and ⟨7, 3⟩ for road boundaries.The passage describes these as reasonable settings for fully representing the respective map instances.Source: Figure 12 · p. 12, §C.3 · p. 12

C.4. How many degree are reasonable?

  • For road boundaries, higher degree requires fewer pieces but makes the curve more difficult to model.Figure 13 shows piece-number and instance-number distributions at different degrees.Source: Figure 13 · p. 12, §C.4 · p. 12

D. Qualitative Visualization

  • Qualitative figures show examples across daytime, nighttime, sunny, cloudy, rainy, and difficult-road conditions, plus some bad cases for future improvement.The cited visualizations include predictions from HDMapNet, BeMapNet, and ground truth for difficult road scenarios.Source: D. Qualitative Visualization · p. 12

D.1. The reason for rounded corner arising

The rounded-corner discussion links curve shape to control-point accuracy, using a right-angle example represented by a piecewise Bézier curve.

D.1. The reason for rounded corner arising

  • Rounded corners are attributed mainly to slightly inaccurate predictions of key control points.The illustrated right-angle example uses ⟨2, 2⟩ with five ground-truth control points.Source: §D.1 · p. 12, Figure 14 · p. 12
  • A small offset at the turn control point can produce a rounded restored curve even when the other control points are accurate.The discussion identifies improving predictions for key control points as future work.Source: §D.1 · p. 12

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