TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis
This work addresses rotation invariance in 3D point cloud analysis for applications like object classification and segmentation, representing an incremental improvement by integrating steerable neurons into an existing framework.
The paper tackled the problem of 3D point cloud analysis requiring rotation invariance by proposing TetraSphere, a learnable descriptor invariant under 3D rotations and reflections, which achieved state-of-the-art performance on challenging subsets of ScanObjectNN and outperformed all equivariant methods on ModelNet40 and ShapeNet.
In many practical applications, 3D point cloud analysis 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 introduced 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 extract 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 practical value of steerable 3D spherical neurons for learning in 3D Euclidean space. The code is available at https://github.com/pavlo-melnyk/tetrasphere.