Point Convolutional Neural Networks by Extension Operators

TL;DR

This paper introduces Point Convolutional Neural Networks (PCNN), a new framework for applying CNNs to point clouds using extension and restriction operators, achieving invariance, robustness, and superior performance on benchmarks.

Contribution

The paper proposes a novel extension-restriction framework for point cloud convolution, enabling CNN application with invariance and robustness, and demonstrates superior benchmark results.

Findings

PCNN is computationally efficient and invariant to point order.

PCNN is robust to sampling density variations.

PCNN outperforms existing methods on key benchmarks.

Abstract

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.