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PCEDNet : A Lightweight Neural Network for Fast and Interactive Edge Detection in 3D Point Clouds

Chems-Eddine Himeur, Thibault Lejemble, Thomas Pellegrini, Mathias Paulin, Loic Barthe, Nicolas Mellado

arXiv:2011.01630v4cs.GR

TL;DR

Point-cloud edge detection is difficult because edge definitions can be subjective and acquired clouds are unstructured. The paper combines multi-scale geometric parameterization with a lightweight classifier, reporting that PCEDNet outperforms prior methods and baselines while supporting fast processing. Its stated limitations include SSM precomputation as a current bottleneck and a surface-only scope.

  • Problem

    Edge detection in point clouds remains challenging, and what counts as an edge can vary with observer and observation scale.

    Source: §1 · p. 1

  • Method

    The paper encodes multi-scale geometric information around each point in a Scale-Space Matrix and uses it with a lightweight neural classifier.

    Source: §1 · p. 2

  • Results

    PCEDNet outperforms prior methods and CNN and fully connected baselines, with efficiency demonstrated on CAD and real-world point clouds.

    Source: §1 · p. 2, §7 · p. 25

  • Takeaways & Limitations

    The compact network can be specialized to user-defined edge definitions and classify millions of points in seconds.

    Source: §1 · p. 2

    SSM precomputation is currently the bottleneck, and SSM is theoretically limited to surfaces.

    Source: §7 · p. 26

Abstract

from arXiv · show

In recent years, Convolutional Neural Networks (CNN) have proven to be efficient analysis tools for processing point clouds, e.g., for reconstruction, segmentation and classification. In this paper, we focus on the classification of edges in point clouds, where both edges and their surrounding are described. We propose a new parameterization adding to each point a set of differential information on its surrounding shape reconstructed at different scales. These parameters, stored in a Scale-Space Matrix (SSM), provide a well suited information from which an adequate neural network can learn the description of edges and use it to efficiently detect them in acquired point clouds. After successfully applying a multi-scale CNN on SSMs for the efficient classification of edges and their neighborhood, we propose a new lightweight neural network architecture outperforming the CNN in learning time, processing time and classification capabilities. Our architecture is compact, requires small learning sets, is very fast to train and classifies millions of points in seconds.

1 Introduction

Point-cloud edge detection remains challenging because edges can be interpreted differently across observers and scales, while acquired clouds are large and unstructured. The paper introduces PCEDNet, pairing a multi-scale point parameterization with a lightweight classifier and reporting advantages over prior methods across varied data.

1 Introduction

  • Edge interpretation is subjective: sharpness depends on observation scale, and different users may draw feature lines differently.The paper notes this ambiguity for real-world models with edges ranging from sharp to smooth and rounded.Source: §1 · p. 1
  • A Scale-Space Matrix encodes multi-scale geometric properties around each point for a compact neural classifier that trains quickly on small datasets.The paper reports average processing of 500,000 points per second on its current CPU implementation.Source: §1 · p. 2
  • PCEDNet outperforms previous works, with efficiency demonstrated on CAD models and real-world examples containing tens of millions of points.The reported comparisons include geometric and point-based methods, a CNN, and a fully connected network.Source: §1 · p. 2
  • The authors position the lightweight design against deep end-to-end point-cloud networks, arguing that multi-scale geometric descriptors support a simpler architecture.They present compactness, speed, scalability, and resource requirements as relevant to interactive adaptation and low-resource processing.Source: §1 · p. 2

2 Related Work

The related work covers point-cloud representations, point-based learning architectures, and geometric edge detectors. It motivates a specialized approach using multi-scale geometric descriptors with a compact network.

2.1 Point cloud parameterization

  • Grid-based point-cloud parameterizations use regular structures but can require enough memory to limit scalability, especially for large models and thin details such as edges.The related-work overview distinguishes these methods from approaches that process points and their neighborhoods directly.Source: §2.1 · p. 3

2.2 Network architectures

  • Point-based convolutions learn multi-scale features from point locations, but real-data sampling variation, noise, outliers, and missing data must also be learned.The network-architecture review notes that many existing systems target semantic analysis and use deep, large architectures that are unnecessarily complex for this specialized geometric task.Source: §2.1 · p. 3, §2.2 · p. 3

2.3 Edge detection

  • Geometric edge detectors based on covariance descriptors can be sensitive to noise and thresholds, while global analysis may improve robustness but limit scalability.The cited methods include multi-scale curvature ratios and graph-based structuring of classified points.Source: §2.3 · pp. 3–4
  • Deep edge-detection networks such as ECNet and PIENet require substantial resources, and ECNet is also limited in scalability by up-sampling.PIENet combines several networks for edge and corner classification, filtering, clustering, and curve generation.Source: §2.3 · p. 4
  • The paper proposes stable multi-scale descriptors with scale derivatives and a compact network that recursively combines features learned at different analysis scales.The approach is intended to improve robustness to noise and adapt to different feature sizes and shapes.Source: §2.3 · p. 4

3 Method

The method addresses sparse, rounded, and scale-dependent edges by learning from multiscale surface descriptors rather than relying on a single sharp-edge definition. It organizes those descriptors in an SSM and processes them with a compact network that merges scales pairwise.

3.1 Problem statement

  • Sparse sampling and edge rounding challenge sharp-edge definitions, so points are labeled sharp-edge, smooth-edge when near or on rounded edges, or non-edge.The authors propose learning the edge definition from examples; PCEDNet uses three classes, while PCEDNet-2C uses two.Source: §3.1 · pp. 4–5

3.2 Scale-Space Matrix

  • The SSM organizes differential surface descriptors across scales, using GLS to distinguish geometric features from noise and describe features defined at different scales.Surface reconstruction uses APSS, while descriptors include scale-space and spatial variation properties selected for rigid-transform invariance and nonredundancy.Source: §3.2 · p. 5

3.3 Our network: PCEDNet

  • PCEDNet successively merges scale pairs before classification, forming a compact tree-like network intended to reduce scale bias and sensitivity to scale-dependent noise.Inputs comprise 16 six-dimensional vectors per point; the final feature vector feeds an MLP with a three-neuron output layer.Source: §3.3 · pp. 6–7

3.4 Baseline models

  • The FC baseline combines all scales in dense layers, whereas the CNN baseline applies 1D convolutions before fully connected classification layers.FC uses about 6,663 weights and CNN about 8.7k; both receive the sixteen six-dimensional scale vectors used by PCEDNet.Source: §3.4 · pp. 7–8

4 Experimental setup

Experiments use labeled point-cloud datasets spanning acquisition artifacts, CAD sharp edges, and human-annotated curves, alongside visual tests on acquired models. Training uses balanced batches to address class imbalance and evaluates network learning under a shared validation setup.

4 Experimental setup

  • Evaluation covers Default, ABC, and SHREC datasets, plus visual assessments on nine acquired point clouds, including a 35-million-vertex scan.The datasets target acquisition artifacts, CAD sharp edges, and human-annotated curves, respectively.Source: §4.1 · pp. 8–9

4.1 Point cloud dataset

  • PCEDNet can also be learned from a small set of user-annotated data to classify point clouds without additional predefined training data.The authors describe this as an additional evaluation of interactive annotation.Source: §4.1 · p. 8
  • Default uses a small synthetic training set with varied shapes and Gaussian noise; ABC labels sharp edges only, while SHREC uses human-annotated curves and heterogeneous model splits.The Default validation subset balances three classes, and its evaluation set tests noise and sharp angles on models not used for training.Source: §4.1 · pp. 8–9

4.2 Networks training

  • Balanced batches replicate edge samples to counter training-set imbalance; all networks reach 98% validation accuracy, while PCEDNet training usually takes minutes versus over an hour for CNN.CNN, FC, and PCEDNet train for 200, 200, and 40 epochs, respectively.Source: §4.2 · p. 10

5 Results

Section 5 evaluates PCEDNet across datasets and validates its input parameterization and output classes. The ablation study finds that the six-parameter input and three-class output improve classification quality.

5 Results

  • The results section compares PCEDNet with geometric methods, point-processing networks, and CNN and fully connected baselines across several datasets.The evaluation includes training and classification times as well as quantitative and visual comparisons.Source: §5 · pp. 10–11

5.1 Ablation study

  • The ablation compares five input sets, from 28 to 3 parameters per scale, by adjusting the first four layers and their connection to the fifth.The selected six parameters remove k2, which is linearly dependent on k1 and κ; alternatives remove scale or curvature information.Source: §5.1 · pp. 11–12
  • The six-parameter input has the highest Recall, F1 and MCC, while maintaining good Precision against the tested alternatives.The comparison uses the Default evaluation set and combines sharp-edge and smooth-edge labels as positives.Source: §5.1 · pp. 11–12
  • Adding the smooth-edge class gives PCEDNet higher scores than PCEDNet-2C across all metrics on the Default evaluation set.The authors suggest the third class enables more conservative labeling amid uneven sampling and tedious edge annotation.Source: §5.1 · p. 12, Table 4 · p. 12

5.2 Different number of input scales

PCEDNet’s performance depends on scale count and evaluation setting: 16 scales are the default compromise, while training and classification comparisons show both efficiency and dataset-specific differences.

5.2 Different number of input scales

  • Sixteen scales are the default speed-and-detection compromise; 8 to 32 may suit the feature scales in a model, while 64 and 128 add time without improving over 32.Eight scales may suffice for ABC’s similarly scaled, sharp edges, whereas 32 may improve results on large models with features at several scales.Source: §5.2 · p. 13, Table 5 · p. 14

5.3 Training and classification times

  • PCPNet and PIENet require more than 500 times longer training than PCEDNet on ABC; classification comparisons also show PCEDNet’s compact architecture is fast.Scale-space calculation takes longer than classification for PCEDNet, FC and CNN, and PCPNet and ECNet need more than 24 GB of GPU memory for large point clouds.Source: §5.3 · p. 14

5.4 Quantitative evaluation

  • On Default, PCEDNet (Default) achieves the best balance of precision and recall, with the highest F1 and MCC scores among compared methods.The passage reports significantly higher indicators than other approaches on this dataset.Source: §5.4 · p. 15
  • On ABC, all PCEDNet variants have F1 scores above 0.7, and PCEDNet-2C (ABC) has MCC and F1 above 0.8.PCEDNet (Default) has MCC = 0.688 but lower recall; PCPNet-2C (ABC) takes 3 days to process the dataset versus 3 hours for PCEDNet-2C (ABC).Source: §5.4 · p. 17
  • On SHREC, CNN (Default) scores best on MCC and F1, while PCEDNet variants are more stable across training sets at MCC ≈0.4.The dataset is challenging because annotations appear to reflect semantics as well as geometric features.Source: §5.4 · p. 17

5.5 Visual evaluation

Visual evaluations on acquired point clouds favor PCEDNet’s handling of fine detail and acquisition artifacts. The noisy-data and interactive-learning sections show how its classification behavior changes with noise and user annotations.

5.5 Visual evaluation

  • On the Lans example, PCEDNet detects fine details that CNN misses, while FC and FEE leave out finer details.The authors highlight scale-separation layers in PCEDNet as important to this behavior.Source: §5.5 · pp. 17–18
  • On noisy models with outliers, CNN and PCEDNet retain high edge recall, with PCEDNet reported as the least sensitive to noise.Other compared methods are weakened by outliers or classify flat areas and outliers as edges.Source: §5.5 · p. 18
  • On the 6M-point Munich cloud, PCEDNet (Default) produces cleaner detection and is less affected by acquisition artifacts than CA and FEE.The cloud has variable densities, large gaps, scan noise and volumetric objects; other approaches required too much memory or time for comparison.Source: §5.5 · p. 19

5.6 Behavior on noisy data

  • For ABC data with Gaussian noise σ = 0.04, PCEDNet (Default)+ has the best Recall, MCC and F1, slightly exceeding ECNet, but detects smoother edges.The plus setting counts both sharp- and smooth-edge classes as positive; PCEDNet (Default)+ is trained on a smaller dataset and takes 3 hours versus 20 days for ECNet.Source: Table 11 · p. 19, §5.6 · p. 20

5.7 Interactive learning

  • Interactive training lets users shape edge definitions through annotations, from sharp edges to larger-scale features that include chamfers.The network is trained on user-labeled points and can be refined with additional annotations.Source: §5.7 · pp. 20–21

5.8 Energy efficiency

The paper estimates energy use for training and classification because energy matters for embedded deployment and environmental impact. It also tests how classification responds to changes in point-cloud density, scale range, and surface reconstruction.

5.8 Energy efficiency

  • Energy per 1K points is estimated from processor TDP and processing time, producing overestimates useful for comparing approaches with large energy differences.The estimate is based on TDP rather than direct measurement during processing.Source: §5.8 · pp. 22–23
  • Training uses one order of magnitude less energy than the baselines and up to two orders less than GPU-based deep networks, by the authors’ estimate.The authors attribute CNN’s lower efficiency to about four times as many weights as PCEDNet and its TensorFlow implementation.Source: §5.8 · pp. 22, 24
  • CA uses very little classification energy, while PCEDNet and its baselines are more efficient than FEE; PIENet was evaluated on models of around 8,000 points.Other approaches were evaluated on larger models, up to several million points, so PIENet’s classification efficiency on larger clouds remains uncertain.Source: §5.8 · p. 24, Table 13 · p. 24

5.9 Complementary experiments

  • On Loudun clouds subsampled from 35 million to 1 million points, classification remains stable and edges remain localized, though reduced resolution thickens them.The minimum scale is estimated automatically from density, with no parameter value required from the user.Source: Figure 25 · p. 23, §5.9 · p. 24
  • Classification remains stable when the maximum scale is divided by 10 or multiplied by 2.5, which the authors relate to logarithmic scale sampling and SSM scale invariance.Figure 26 shows classification results for varied maximum scales.Source: §5.9 · p. 24, Figure 26 · p. 24
  • Sphere fitting improves classification over plane fitting, and the best results are obtained with MLS projection in the surface reconstruction variants tested.The variants include covariance plane fitting, point set surfaces, algebraic sphere fitting, and APSS.Source: §5.9 · p. 24, Figure 27 · p. 25

6 Discussion

The discussion identifies trade-offs in applying the Scale-Space Matrix (SSM) to patch-based networks and in relying on local surface reconstruction. These issues limit where the approach is straightforward to use.

6 Discussion

  • Adding SSM parameters to patch-based networks would create significant memory overhead on architectures that are already resource-demanding.The authors leave open whether the additional parameters would increase efficiency or duplicate features learned from neighboring points.Source: §6 · p. 25
  • The value of SSM descriptors is less clear for patch-based tasks such as style or large-feature recognition, where early layers already learn from neighboring-point organization.The authors note that redundancy versus added efficiency is difficult to predict.Source: §6 · p. 25
  • Local surface reconstruction does not itself reconstruct or detect edges; it supplies SSM shape descriptors that the network uses to label edge points.Source: §6 · p. 25

7 Limitations and conclusion

The conclusion presents PCEDNet as a compact, fast edge classifier whose GLS-based parameterization performs well on synthetic and real scans. The authors also identify constraints involving normals, preprocessing cost, and surface-only representation.

7 Limitations and conclusion

  • PCEDNet has about 2,100 weights, is faster than the tested approaches, and achieves results similar to CNN on synthetic point clouds.The authors report reduced sensitivity to noise on real scans and interactive training and classification from direct user inputs.Source: §7 · p. 25
  • APSS requires oriented normals, which can be tedious to compute accurately; consistent normals estimated with Meshlab gave good results on tested clouds without normals.The authors identify fitting techniques that do not require oriented normals as future work.Source: §7 · p. 26
  • SSM precomputation is currently the approach’s performance bottleneck, and the authors suggest GPU implementation could enable near-real-time classification.Neighborhood queries are identified as the most computationally intensive task.Source: §7 · p. 26
  • SSM is theoretically limited to surfaces, so alternative representations may be needed to handle lines and volumes.Source: §7 · p. 26
  • The authors propose studying other geometric labeling tasks and semantic analysis as future directions.They also mention experimenting with alternative network layouts, including n by n scale concatenation.Source: §7 · p. 26

A GLS Descriptors and Derivatives

The appendix describes how algebraic sphere fitting and GLS reparameterization yield local geometric quantities and scale-space derivatives. These quantities provide shape information used by the paper’s descriptors.

A GLS Descriptors and Derivatives

B Scores used for quantitative comparison

Appendix B defines the classification scores used for quantitative comparison, covering positive identifications, set overlap, agreement, and overall correctness.

B Scores used for quantitative comparison

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