FA-KPConv: Introducing Euclidean Symmetries to KPConv via Frame Averaging
This work addresses the need for robust geometric priors in 3D point cloud processing, particularly for applications with limited data or variable orientations, though it is incremental as it builds on the established KPConv method.
The authors tackled the problem of achieving exact invariance and equivariance to Euclidean transformations in 3D point cloud analysis by introducing FA-KPConv, which modifies KPConv using Frame Averaging, resulting in improved performance in tasks like classification and registration, especially with scarce or rotated data.
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.