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3D Parametric Wireframe Extraction Based on Distance Fields

Albert Matveev, Alexey Artemov, Denis Zorin, Evgeny Burnaev

arXiv:2107.06165v2cs.CVcs.GR

TL;DR

Sharp feature curves are important in CAD, but extracting them from point clouds as parametric entities remains a challenge. This paper processes per-point distance-to-feature estimates through corner detection, curve segmentation, graph construction, and spline fitting. Across its evaluation, the method produces more robust and meaningful results than the recent learning-based alternative.

  • Problem

    Sharp feature curves are essential to CAD and computer graphics, yet they must be reconstructed as parametric entities from 3D geometry.

    Source: §1 · p. 2

  • Method

    The pipeline uses per-point distance-to-feature estimates for corner detection, curve segmentation, topological graph construction, and spline fitting.

    Source: §1 · p. 2, §3.1 · p. 2

  • Results

    The method is more robust and produces more meaningful results than the recent learning-based alternative, with meaningful outputs in most cases.

    Source: §5 · p. 5

  • Takeaways & Limitations

    Extracted curves generally correspond to separate smooth curves, avoid overestimating curve count, and can be edited and sampled at arbitrary resolution.

    Source: §5 · p. 5

    Evaluation used densely sampled clean point clouds; real-world scan evaluation remains future work, and results depend on distance estimates and parameter choices.

    Source: §4.3 · p. 5, §5 · p. 5

Abstract

from arXiv · show

We present a pipeline for parametric wireframe extraction from densely sampled point clouds. Our approach processes a scalar distance field that represents proximity to the nearest sharp feature curve. In intermediate stages, it detects corners, constructs curve segmentation, and builds a topological graph fitted to the wireframe. As an output, we produce parametric spline curves that can be edited and sampled arbitrarily. We evaluate our method on 50 complex 3D shapes and compare it to the novel deep learning-based technique, demonstrating superior quality.

1 INTRODUCTION

Growing access to 3D scans increases the need for efficient geometry processing, while reconstructing sharp feature curves as parametric entities is essential in CAD and computer graphics. The paper introduces a distance-field-based pipeline that converts sharp-feature predictions into parametric splines.

  • CAD models represent 3D geometry with parametric curves and surfaces, making them useful ground truth for geometry-processing tasks.Source: §1 · p. 1
  • Sharp feature curves, where surface normals are discontinuous, are essential to reconstruct as parametric entities for CAD and computer graphics.Source: §1 · p. 2
  • DEF regresses a scalar distance field for sharp features rather than the segmentation masks used by earlier neural networks, and the authors argue this suits parametric curve extraction.Source: §1 · p. 2
  • The proposed pipeline uses distance estimates for corner detection, curve-instance clustering, topological graph construction, and spline fitting; tests on 50 shapes report robust curve detection and accurate parametric wireframes.Source: §1 · p. 2

2 RELATED WORK

Prior work spans geometric datasets, analytical and learning-based sharp-feature detection, and parametric curve extraction. The paper identifies PIE-Net as its most direct competitor and limits comparisons to it because PC2WF supports only straight segments.

Datasets

  • ABC provides over 1,000,000 high-quality CAD models with geometric, topological, and semantic annotations, including parametric curves for quantitative wireframe evaluation.Source: §2 · p. 2

Sharp Feature Curves Estimation

  • Analytical sharp-edge methods use local normals or covariance analysis to classify points, but their extracted features can be noisy and unstable and require per-model parameter tuning.Source: §2 · p. 2
  • Hard-label point classifications are limited for curve inference because imprecise detections do not locate curves precisely.Source: §2 · p. 2

Deep Learning for Sharp Feature Detection

  • Earlier learning-based sharp-feature methods also classify points, whereas DEF represents features with distance fields that provide soft detections suitable for curve inference.Source: §2 · p. 2

Parametric Curve Extraction

  • PIE-Net derives splines from sharp-edge segmentation and detected corners; PC2WF infers wireframes from corners but supports only straight segments, so the paper compares only with PIE-Net.Source: §2 · p. 2

3 3D WIREFRAME EXTRACTION

The pipeline turns DEF distance estimates into editable parametric splines through corner detection, curve segmentation, topological graph construction, and distance-aware spline fitting. Its stages use the estimated field to select feature-near points and guide the geometry of extracted curves.

3.1 Description of Distance Field

  • Distance estimates identify points near feature curves, and the field’s zero level set marks the feature line while avoiding a fixed segmentation width.DEF processes patches separately, then combines them and aggregates predictions for global field consistency; the patch design supports large point sets.Source: §3.1 · p. 2

3.2 Extracting Parametric Curves

  • The pipeline thresholds points by distance to form a feature skeleton, then detects corners, segments curves, constructs a topological graph, and fits splines.Corner detection supports both curve clustering and construction of graph segments between corners.Source: §3.2 · p. 3

3.2.1 Corner Detection.

  • Farthest-point sampling selects 10% of skeleton points as query centers; PCA on their neighborhoods supplies explained-variance ratios for corner detection.The method uses the middle ordered ratio, σ2, to decide whether a local set is near a corner, then bounds detected sets to form corner clusters.Source: §3.2.1 · p. 3

3.2.2 Shape Curve Segmentation.

  • After removing corner clusters, the method connects curve-skeleton points within the estimated sampling distance and treats each connected component as a curve cluster.Removing corner neighborhoods is intended to keep separate curve clusters disconnected in the constructed graph.Source: §3.2.2 · p. 3

3.2.3 Extraction of Topological Graph.

  • Each curve cluster is approximated by a recursively subdivided polyline, splitting where predicted distance and the point-to-segment gap differ beyond T_split.Closed curves without endpoints start from three sampled points joined as a triangle; polyline endpoints connect to nearest corner-cluster centers, and graph nodes with more than two incident segments are corners.Source: §3.2.3 · p. 3

3.2.4 Spline Fitting.

  • Graph paths between nodes of degree other than two serve as curve proxies, and fitted spline control points are optimized to match field-indicated distances while preserving endpoints.For closed curves, spline endpoints must coincide and endpoint tangents must match.Source: §3.2.4 · pp. 3–4

4 EXPERIMENTS

The evaluation compares the pipeline with PIE-Net on 50 diverse CAD models, using curve-distance metrics and failure rates. Tests used densely sampled clean point clouds; the authors identify parameter choices, distance-estimate dependence, and real-world scans as limitations.

4.1 Dataset and Implementation Details

  • Evaluation used 50 diverse ABC CAD models sampled following the DEF paper, with DEF predictions supplying distance-field inputs.The selected shapes varied in surface types, feature-curve types, and sharpness angles.Source: §4.1 · p. 4
  • The implementation relates parameters to average pairwise sampling distance r = 0.02, including T_dist = 1.5r and R_corner = T_split = 4r.T_dist balances having enough skeleton samples against keeping lines thin for robust corner detection; T_split is chosen above T_dist to prevent overfitting while reflecting curve geometry.Source: §4.1 · p. 4

4.2 Numerical Evaluation

  • The pipeline’s Chamfer distance was 0.07, and its Hausdorff error was smaller than PIE-Net’s.The reported Chamfer distance is about four average sampling distances; the paper says PIE-Net’s Chamfer error is an order of magnitude larger.Source: §4.2 · p. 4, Table 1 · p. 5
  • The pipeline failed on 12% of shapes, compared with PIE-Net’s 66% failure rate; most pipeline failures arose from numerical instabilities in spline fitting.The authors say PIE-Net’s remaining outputs commonly fit shapes inaccurately and suggest its training on small 8,192-point shapes may be related.Source: §4.2 · pp. 4–5, Table 1 · p. 5

4.3 Limitations

  • The pipeline requires several parameters, depends on predicted distance estimates that can cause faulty curve connections, and was evaluated on densely sampled clean point clouds rather than real-world scans.The authors suggest careful parameter choice can reduce noise effects and leave real-world scan evaluation for future work.Source: §4.3 · p. 5

5 CONCLUSION

The pipeline converts per-point distance-to-feature estimates into a parametric wireframe through corner detection, curve segmentation, graph construction, and spline fitting. Tests report more robust, meaningful results and better quality measures than a recent learning-based alternative, while real-scan evaluation remains future work.

5 CONCLUSION

  • The four-stage pipeline processes per-point distance-to-feature estimates through distance-based corner detection, curve segmentation, graph construction, and spline fitting.The topological graph describes connectivity, and splines are fitted to paths in that graph.Source: §5 · p. 5
  • On geometrically complex shapes, extracted curves generally correspond to separate smooth shape curves, avoiding overestimation of curve count.Source: §5 · p. 5
  • The parametric output supports CAD and graphics workflows, analytical differential queries, and sampling at arbitrary resolution.Source: §5 · p. 5
  • The method is more robust and produces more meaningful results than a recent learning-based alternative, with better quality measures.The pipeline produces meaningful results in most cases.Source: §5 · p. 5
  • Real-scan evaluation remains future work; proposed learning-based corner detection and segmentation could reduce parameters and improve robustness and generality.Source: §5 · p. 5

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