TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis

In many practical applications, 3D point cloud analy-sis requires rotation invariance. In this paper, we present a learnable descriptor invariant under 3D rotations and reflections, i.e., the O(3) actions, utilizing the recently intro-duced steerable 3D spherical neurons and vector neurons. Specifically, we propose an embedding of the 3D spherical neurons into 4D vector neurons, which leverages end-to-end training of the model. In our approach, we perform TetraTransform-an equivariant embedding of the 3D input into 4D, constructed from the steerable neurons-and ex-tract deeper O(3)-equivariant features using vector neurons. This integration of the TetraTransform into the VN-DGCNN framework, termed TetraSphere, negligibly increases the number of parameters by less than 0.0002%. TetraSphere sets a new state-of-the-art performance classifying randomly rotated real-world object scans of the challenging subsets of ScanObjectNN. Additionally, TetraSphere outperforms all equivariant methods on randomly rotated synthetic data: classifying objects from ModelNet40 and segmenting parts of the ShapeNet shapes. Thus, our results reveal the prac-tical value of steerable 3D spherical neurons for learning in 3D Euclidean space. The code is available at https: //github.com/pavlo-melnyk/tetrasphere.