FA-KPConv: Introducing Frame Averaging to Kernel Point Convolution to Enforce Euclidean Symmetries

Abstract

3D point cloud analysis has become central to a wide range of real-world applications especially for autonomous vehicles that rely on LiDAR scans to perceive and navigate their surroundings. Yet a basic problem remains: most networks are not genuinely robust to changes in the orientation of their input. Kernel Point Convolution (KPConv) is one of the most widely adopted backbones for point cloud processing, but like most of its counterparts, it can only approximate invariance to rotations and reflections, typically by relying on large amounts of training data or heavy augmentation rather than addressing the problem by design. This work introduces Frame Averaging (FA) to Kernel Point Convolution, producing FA-KPConv, a neural network architecture that extends the widely used KPConv backbone with exact invariance to Euclidean transformations, not just approximate invariance. The method operates as a lightweight wrapper around the existing KPConv backbone: no additional trainable parameters are introduced, no input information is discarded, and the symmetry is enforced at evaluation time by averaging predictions across a set of PCA-derived coordinate frames. We evaluate the approach on ModelNet40 3D object classification across four training data fractions. On the aligned test set, FA-KPConv matches the baseline within half a percentage point at all data scales, confirming that imposing symmetry does not hurt performance when the data is already well-posed. On the rotated test set, the baseline degrades significantly as training data increases - losing 12.4 percentage points at full data while FA-KPConv maintains consistent performance, with a rotation gap of only 2.1 percentage points. These results demonstrate that Frame Averaging is an effective and lightweight strategy for making KPConv genuinely robust to arbitrary 3D rotations.