PIE-NET: Parametric Inference of Point Cloud Edges

1 Introduction

• Point-cloud edge estimators remain sensitive to parameter settings and often underperform near soft edges, noise, and sparse data.The authors attribute this to decisions based on manually designed local surface features.Source: §1 · p. 1
• PIE-NET proposes potentially invalid or redundant parametric curves, then suppresses proposals using learned confidence scores and curve fit to the data.Its output represents edge features as parametric curves; Figure 1 contrasts this with a deep method that only classifies edge points.Source: §1 · p. 1, Figure 1 · p. 2
• PIE-NET significantly outperforms traditional edge detectors and recent learnable variants on the ABC dataset, quantitatively and qualitatively.The dataset contains more than one million feature-rich CAD models with parametric edge representations.Source: §1 · p. 2

2 Related work

• Primitive-inference work includes least-squares and RANSAC fitting, data-driven priors, and end-to-end models for cuboids, super-quadrics, and convexes.Li et al. predict per-point properties before estimating primitives.Source: §2 · p. 2
• Consolidation and reconstruction methods use detected or preserved edges to support point-cloud, implicit-surface, and RGBD reconstruction.EC-Net regresses upsampled points and point-to-edge distances, while PU-Net expands learned per-point features for upsampling.Source: §2 · p. 2
• Traditional edge detectors use local geometric properties such as normals, curvatures, and feature anisotropy, with MLS-based analysis or segmentation.Fleishman et al. use robust estimators with MLS neighborhoods; Daniels et al. extend this approach to noisy point clouds.Source: §2 · pp. 2–3
• PIE-NET first detects edges and corners, then generates and selects curve proposals for corner pairs.The paper treats this as a region-proposal process.Source: Figure 2 · p. 3
• EC-Net classifies points and regresses their distances to edges, whereas PIE-NET estimates parametric edge curves with an end-to-end trainable network.The authors identify EC-Net as the only prior deep-learning method for feature-edge estimation to their knowledge.Source: §2 · p. 3

3 Method

• The method focuses on lines, circles, and B-splines; circles use three points for parameterization, while B-splines use four control points.ABC dataset edges largely fall into these three types, which account for more than 95% of edges; other types are filtered out.Source: §3 · p. 3

3.1 Point classification

• Point classification predicts edge and corner probabilities and offsets, then applies point-level NMS to consolidate nearby corner detections.The method uses separate edge-versus-null and corner-versus-null classifiers; NMS selects the highest-probability corner within each cluster.Source: §3.1 · pp. 3–4, Figure 3 · p. 4

3.2 Open Curve proposal

• For open curves, PIE-NET proposes a curve for each corner pair and predicts its point membership, curve type, and parameters.Candidate edge points are localized to a sphere around the corner pair; curve fitting uses Chamfer-distance losses based on sampled curves.Source: §3.2 · pp. 4–5, Figure 4 · p. 5

3.3 Closed curve proposal

• For closed curves, feature-based clustering forms point proposals, and a network fits circular curves while predicting confidence scores.The feature-distance matrix supplies a proposal from each row; the fitting network regresses circle parameters and confidence.Source: Clustering · p. 5, §3.3 · p. 5, Figure 5 · p. 6

3.4 Curve proposal selection

• The final selection stage filters redundant or invalid proposals using separate rules for open and closed curves.Overlapping open-curve candidates are merged while retaining the larger segmentation; closed-curve candidates are clustered and the highest-confidence proposal is kept.Source: §3.4 · p. 6, Figure 6 · p. 6

4.2 Comparisons to the state-of-the-art

• PIE-NET outperforms VCM, EAR, and EC-Net in the reported comparisons.Figure 9 presents qualitative and quantitative comparisons; the text reports an order-of-magnitude ECD difference between EAR and PIE-NET.Source: Figure 9 · p. 7, §4.2 · pp. 7–8

4.1 Ablation studies

• Increasing the sampling radius makes the correct curve subset harder to identify, while higher corner and edge thresholds trade precision against recall and can omit curves.The sphere heuristic also hints which curve to sample; overly high corner thresholds filter out points needed for some feature curves.Source: §4.1 · p. 7

4.2 Comparisons to the state-of-the-art

• On novel object categories absent from training, Figure 10 shows PIE-NET applied to general 3D objects, although no ground-truth edges were available for those shapes.The caption reports consistent outperformance over VCM, EAR, and EC-Net.Source: §4.2 · p. 8, Figure 10 · p. 8

4.3 Stress tests

• With random sampling, PIE-NET remains comparable to its original performance and outperforms the baselines except for VCM at τ=0.12 recall, paired with precision 0.3063.The exception has recall 0.8385; the point clouds were subsampled to 8,096 points.Source: §4.3 · p. 8
• When trained with noisy data, PIE-NET still outperforms VCM, EAR, and EC-Net tested on or trained with clean data.The tested normal-direction noise scales were X={0, 0.01, 0.02, 0.05}.Source: §4.3 · p. 8, Figure 11 · p. 9
• When trained on point clouds reduced to as few as 1,024 points, PIE-NET still outperforms the baselines evaluated at full resolution of 8,096 points.The tested densities were P={8,096, 4,096, 2,048, 1,024}.Source: §4.3 · p. 9

4.4 Timing

• Per point cloud, PIE-NET takes about 0.5 seconds for point classification and 3 seconds for curve generation; baseline classification times are all slower.VCM, EAR, and EC-Net classification average 5.5, 4.0, and 0.8 seconds, respectively.Source: §4.4 · p. 9

• PIE-NET uses a region-proposal architecture to extract parametric curves from point clouds and significantly outperforms traditional methods and the recent deep model EC-Net.Source: §5 · p. 9
• The paper defines parametric edge estimation as a new learning problem and says its only domain-knowledge assumption is simple curve parameterization.It also defines a corresponding challenge for the ABC dataset.Source: §5 · p. 9

• The authors describe the work as largely academic and identify no foreseeable risks in defense, security, or other sensitive fields.Source: Broader impact · p. 10