2018

Point Convolutional Neural Networks by Extension Operators

Atzmon, Matan, Maron, Haggai, Lipman, Yaron

Understand

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.

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