Stable and efficient differential estimators on oriented point clouds

Stable and efficient differential estimators on oriented point clouds

Thibault Lejemble (1), David Coeurjolly (2), Loïc Barthe (1), Nicolas Mellado (1).
(1) CNRS, IRIT, Université de Toulouse, France.
(2) CNRS, LIRIS, Université de Lyon, France.

Computer Graphics Forum.
Eurographics Symposium on Geometry Processing (SGP)

Point clouds are now ubiquitous in computer graphics and computer vision. Differential properties of the point-sampled surface,such as principal curvatures, are important to estimate in order to locally characterize the scanned shape. To approximate the surface from unstructured points equipped with normal vectors, we rely on the Algebraic Point Set Surfaces (APSS) [GG07] for which we provide convergence and stability proofs for the mean curvature estimator. Using an integral invariant viewpoint, this first contribution links the algebraic sphere regression involved in the APSS algorithm to several surface derivatives of different orders. As a second contribution, we propose an analytic method to compute the shape operator and its principal curvatures from the fitted algebraic sphere. We compare our method to the state-of-the-art with several convergence and robustness tests performed on a synthetic sampled surface. Experiments show that our curvature estimations are more accurate and stable while being faster to compute compared to previous methods. Our differential estimators are easy to implement with little memory footprint and only require a unique range neighbors query per estimation. Its highly parallelizable nature makes it appropriate for processing large acquired data, as we show in several real-world experiments

Differential estimations computed with our stable estimators on a large point cloud with normals (2.5M points). Zoom on: (a) the initial point cloud, (b) our corrected normal vectors, (c) mean curvature, (d,e) principal curvatures, and (f) principal curvature directions.
PCEDNet : A Lightweight Neural Network for Fast and Interactive Edge Detection in 3D Point Clouds

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. CNRS, IRIT, Université de Toulouse, France.

ACM Transactions on Graphics, Volume 41, Issue 1 February 2022, Article No.: 10, pp 1–21

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 light-weight 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.


Three examples of edge detection in point clouds by our PCEDNet neural network. It handles both:
(a) the imperfect edges of large scale scans (here 12million vertices) subject to irregular sampling and noise while detecting both sharp (in red) and smoother (in yellow) edges in few minutes (here less than6) -and –
(b) accurate CAD data on which it can focus on sharp edges if desired, in a few seconds for this model.
(c) Our network can also be trained in a fewseconds to detect edges following the edge definition provided by a user in an interactive model annotation. We show two annotations corresponding todifferent user expectations. Most of the processing is precomputed and at runtime edges of this model are classified in less than a second.


    author = {Himeur, Chems-Eddine and Lejemble, Thibault and Pellegrini, Thomas and Paulin, Mathias and Barthe, Loic and Mellado, Nicolas}, 
    title = {PCEDNet: A Lightweight Neural Network for Fast and Interactive Edge Detection in 3D Point Clouds}, 
    year = {2021}, 
    issue_date = {February 2022}, 
    publisher = {Association for Computing Machinery}, 
    address = {New York, NY, USA}, 
    volume = {41}, 
    number = {1}, 
    issn = {0730-0301}, 
    url = {}, 
    doi = {10.1145/3481804}, 
    journal = {ACM Trans. Graph.}, 
    month = nov, 
    articleno = {10}, 
    numpages = {21}, 
    keywords = {Point clouds processing, neural networks, edge detection, datasets, energy efficiency, low resource computing}