[Paper Review] PIE-NET: Parametric Inference of Point Cloud Edges

Xiaogang Wang, Yuelang Xu+5 more|arXiv (Cornell University)|Jul 9, 2020

3D Shape Modeling and AnalysisEngineering47 references43 citations

TL;DR

PIE-Net presents an end-to-end learnable pipeline that detects edge and corner points in 3D point clouds and infers a set of parametric curves (lines, circles, and B-splines) representing edges, outperforming traditional and prior learning methods.

ABSTRACT

We introduce an end-to-end learnable technique to robustly identify feature edges in 3D point cloud data. We represent these edges as a collection of parametric curves (i.e.,lines, circles, and B-splines). Accordingly, our deep neural network, coined PIE-NET, is trained for parametric inference of edges. The network relies on a "region proposal" architecture, where a first module proposes an over-complete collection of edge and corner points, and a second module ranks each proposal to decide whether it should be considered. We train and evaluate our method on the ABC dataset, a large dataset of CAD models, and compare our results to those produced by traditional (non-learning) processing pipelines, as well as a recent deep learning based edge detector (EC-NET). Our results significantly improve over the state-of-the-art from both a quantitative and qualitative standpoint.

Motivation & Objective

• Motivate a data-driven, robust edge detection approach for 3D point clouds under noise and sparse sampling.
• Propose PIE-Net to output parametric edge curves (lines, circles, and B-splines) rather than pointwise edge labels.
• Develop a region-proposal framework: first detect edge/corner points, then generate and select curve proposals.
• Train and evaluate on the ABC CAD model dataset to demonstrate accuracy and generalization.
• Show that end-to-end learning improves over traditional pipelines and EC-Net in both quantitative and qualitative metrics.

Proposed method

• Two-stage pipeline: (i) point classification to identify edge and corner points with offsets to project onto edges/corners; (ii) curve proposal and selection to produce open and closed parametric curves.
• Parameterizations for circles and B-splines are differentiable; circles use three non-collinear points to derive (n, c, r) and sample points on the circle; B-splines use four control points and uniform sampling with residuals regressed for intermediate points.
• Open-curve proposals: generate all corner pairs from N corners, search within a sphere around the pair midpoint, sample a subset of edge points, and jointly predict curve type and parameters via multi-head PointNet-like networks.
• Closed-curve proposals: cluster edge points by feature similarity, fit circles to each cluster, and predict circle parameters with confidence; use Chamfer distance for parameter regression.
• Training losses: L_detection combining focal loss for edge/corner classification and smooth L1 for offsets; L_proposal combining mask, type classification, and parameter regression losses with Chamfer-based terms; L_closed for similarity, score, and parameter regression; non-maximal suppression and IoU-based clustering to select final curves.
• Computational aspects: approximate runtimes ~0.5s for classification and ~3s for curve generation per cloud; training times on a Titan X GPU for multiple components.

Experimental results

Research questions

• RQ1 Can a region-proposal based learning framework accurately detect and represent 3D edge features as parametric curves from point clouds?
• RQ2 How do edge and corner detection, curve-type classification, and parameter regression components interact to produce robust edge reconstructions under noise and varying sampling densities?
• RQ3 Do parametric edge representations (lines, circles, B-splines) generalize well to novel CAD shapes and non-CAD object categories?
• RQ4 How does PIE-Net perform relative to classical (VCM, EAR) and learning-based (EC-Net) baselines in both edge detection accuracy and geometric fidelity of inferred curves?
• RQ5 What is the impact of sampling, thresholds, and sphere-based heuristics on the quality and efficiency of open/closed curve proposals?

Key findings

• PIE-Net significantly outperforms traditional edge detectors and EC-Net on the ABC dataset in both edge Chamfer Distance and IoU metrics.
• The method generalizes well to novel object categories beyond the training CAD models, as shown in qualitative results on tables, chairs, vases, etc.
• A fully end-to-end pipeline combining edge/corner detection with open/closed curve proposals yields superior geometric fidelity and robustness to noise and sampling density changes.
• Ablation studies demonstrate stability across sphere radius, corner/edge thresholds, and the impact of including residual offsets D_e, D_c in the final curve accuracy.
• Compared to VCM, EAR, and EC-Net, PIE-Net achieves lower ECD and higher IoU, precision, and recall across varying evaluation settings.
• The approach maintains efficient runtimes (classification ~0.5s, curve generation ~3s per cloud) while delivering higher accuracy than baselines.