Point Convolutional Neural Networks by Extension Operators

Matan Atzmon, Haggai Maron, Yaron Lipman

Research output: Contribution to journalArticlepeer-review


This paper presents Point Convolutional Neural Networks (PCNN): a novel framework for applying convolutional neural networks to point clouds. The framework consists of two operators: extension and restriction, mapping point cloud functions to volumetric functions and vise-versa. A point cloud convolution is defined by pull-back of the Euclidean volumetric convolution via an extension-restriction mechanism.

The point cloud convolution is computationally efficient, invariant to the order of points in the point cloud, robust to different samplings and varying densities, and translation invariant, that is the same convolution kernel is used at all points. PCNN generalizes image CNNs and allows readily adapting their architectures to the point cloud setting.

Evaluation of PCNN on three central point cloud learning benchmarks convincingly outperform competing point cloud learning methods, and the vast majority of methods working with more informative shape representations such as surfaces and/or normals.

Original languageEnglish
Article number71
Number of pages12
JournalACM Transactions on Graphics
Issue number4
StatePublished - Jul 2018


  • Geometric Deep Learning
  • Normal Estimation
  • Shape Analysis
  • Shape Classiffication
  • Shape Segmentation

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design


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