FA-KPConv: Introducing Euclidean Symmetries to KPConv via Frame Averaging

TL;DR

FA-KPConv introduces a frame-averaging technique to make KPConv-based neural networks exactly invariant or equivariant to Euclidean transformations, improving performance in 3D point cloud tasks under challenging conditions.

Contribution

It presents a novel frame-averaging method that enforces exact Euclidean invariance/equivariance in KPConv networks without increasing parameters.

Findings

Enhanced invariance leads to better classification accuracy.

Improved registration performance in scarce data scenarios.

Robustness to random rotations demonstrated.

Abstract

We present Frame-Averaging Kernel-Point Convolution (FA-KPConv), a neural network architecture built on top of the well-known KPConv, a widely adopted backbone for 3D point cloud analysis. Even though invariance and/or equivariance to Euclidean transformations are required for many common tasks, KPConv-based networks can only approximately achieve such properties when training on large datasets or with significant data augmentations. Using Frame Averaging, we allow to flexibly customize point cloud neural networks built with KPConv layers, by making them exactly invariant and/or equivariant to translations, rotations and/or reflections of the input point clouds. By simply wrapping around an existing KPConv-based network, FA-KPConv embeds geometrical prior knowledge into it while preserving the number of learnable parameters and not compromising any input information. We showcase the benefit of such an introduced bias for point cloud classification and point cloud registration, especially in challenging cases such as scarce training data or randomly rotated test data.