# Effective Rotation-invariant Point CNN with Spherical Harmonics kernels

## TL;DR

This paper introduces a rotation-invariant point cloud neural network architecture using spherical harmonics kernels, enabling accurate shape analysis without data augmentation.

## Contribution

It integrates spherical harmonics based kernels into point cloud CNNs to achieve rotation invariance at all layers, including local patches.

## Key findings

- Achieves rotation invariance for global and local transformations.
- Outperforms non-invariant methods on shape classification and segmentation.
- Uses efficient space-partitioning pooling for improved performance.

## Abstract

We present a novel rotation invariant architecture operating directly on point cloud data. We demonstrate how rotation invariance can be injected into a recently proposed point-based PCNN architecture, at all layers of the network, achieving invariance to both global shape transformations, and to local rotations on the level of patches or parts, useful when dealing with non-rigid objects. We achieve this by employing a spherical harmonics based kernel at different layers of the network, which is guaranteed to be invariant to rigid motions. We also introduce a more efficient pooling operation for PCNN using space-partitioning data-structures. This results in a flexible, simple and efficient architecture that achieves accurate results on challenging shape analysis tasks including classification and segmentation, without requiring data-augmentation, typically employed by non-invariant approaches.