mlsanityData to 14 Oct 2026

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

arXiv 2211.14456 ↗First posted 26 Nov 2022cs.CVcited by 2

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Abstract (arXiv)

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.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 37 of its 54 references that are in the map. First posted on arXiv 26 Nov 2022.

Builds on

37 of 54 references.

References · 37

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25 more
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Cited by year

Citing papers per year: 2023: 1; 2024: 0; 2025: 1.

2 papers.

  1. 2023On Learning Deep O(n)-Equivariant Hyperspherescited by 1
  2. 2025Towards Training-Free Open-World Classification with 3D Generative Modelscited by 0