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REVNET: Rotation-Equivariant Point Cloud Completion via Vector Neuron Anchor Transformer

Zhifan Ni, Eckehard Steinbach

TL;DR

REVNET tackles the challenge of completing partial 3D point clouds under arbitrary rotations by introducing a rotation-equivariant Vector Neuron (VN) Anchor Transformer. The framework encodes input geometry into a set of VN anchors, predicts missing anchors with a VN-MATr, and decodes densely around anchors using a rotation-invariant fine decoder, all while maintaining equivariance through a rotation-aware bias and ZCA-based normalization. The approach achieves state-of-the-art equivariant completion on the synthetic MVP dataset and delivers competitive results on real-world KITTI data without input pose alignment, highlighting robustness to pose variations in practical deployments. The work advances rotation-equivariant 3D vision by integrating local anchor-based reasoning with equivariant-to-invariant conversions, enabling stable coordinate generation and improved preservation of local geometry in completions.

Abstract

Incomplete point clouds captured by 3D sensors often result in the loss of both geometric and semantic information. Most existing point cloud completion methods are built on rotation-variant frameworks trained with data in canonical poses, limiting their applicability in real-world scenarios. While data augmentation with random rotations can partially mitigate this issue, it significantly increases the learning burden and still fails to guarantee robust performance under arbitrary poses. To address this challenge, we propose the Rotation-Equivariant Anchor Transformer (REVNET), a novel framework built upon the Vector Neuron (VN) network for robust point cloud completion under arbitrary rotations. To preserve local details, we represent partial point clouds as sets of equivariant anchors and design a VN Missing Anchor Transformer to predict the positions and features of missing anchors. Furthermore, we extend VN networks with a rotation-equivariant bias formulation and a ZCA-based layer normalization to improve feature expressiveness. Leveraging the flexible conversion between equivariant and invariant VN features, our model can generate point coordinates with greater stability. Experimental results show that our method outperforms state-of-the-art approaches on the synthetic MVP dataset in the equivariant setting. On the real-world KITTI dataset, REVNET delivers competitive results compared to non-equivariant networks, without requiring input pose alignment. The source code will be released on GitHub under URL: https://github.com/nizhf/REVNET.

REVNET: Rotation-Equivariant Point Cloud Completion via Vector Neuron Anchor Transformer

TL;DR

REVNET tackles the challenge of completing partial 3D point clouds under arbitrary rotations by introducing a rotation-equivariant Vector Neuron (VN) Anchor Transformer. The framework encodes input geometry into a set of VN anchors, predicts missing anchors with a VN-MATr, and decodes densely around anchors using a rotation-invariant fine decoder, all while maintaining equivariance through a rotation-aware bias and ZCA-based normalization. The approach achieves state-of-the-art equivariant completion on the synthetic MVP dataset and delivers competitive results on real-world KITTI data without input pose alignment, highlighting robustness to pose variations in practical deployments. The work advances rotation-equivariant 3D vision by integrating local anchor-based reasoning with equivariant-to-invariant conversions, enabling stable coordinate generation and improved preservation of local geometry in completions.

Abstract

Incomplete point clouds captured by 3D sensors often result in the loss of both geometric and semantic information. Most existing point cloud completion methods are built on rotation-variant frameworks trained with data in canonical poses, limiting their applicability in real-world scenarios. While data augmentation with random rotations can partially mitigate this issue, it significantly increases the learning burden and still fails to guarantee robust performance under arbitrary poses. To address this challenge, we propose the Rotation-Equivariant Anchor Transformer (REVNET), a novel framework built upon the Vector Neuron (VN) network for robust point cloud completion under arbitrary rotations. To preserve local details, we represent partial point clouds as sets of equivariant anchors and design a VN Missing Anchor Transformer to predict the positions and features of missing anchors. Furthermore, we extend VN networks with a rotation-equivariant bias formulation and a ZCA-based layer normalization to improve feature expressiveness. Leveraging the flexible conversion between equivariant and invariant VN features, our model can generate point coordinates with greater stability. Experimental results show that our method outperforms state-of-the-art approaches on the synthetic MVP dataset in the equivariant setting. On the real-world KITTI dataset, REVNET delivers competitive results compared to non-equivariant networks, without requiring input pose alignment. The source code will be released on GitHub under URL: https://github.com/nizhf/REVNET.
Paper Structure (36 sections, 18 equations, 7 figures, 7 tables)

This paper contains 36 sections, 18 equations, 7 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Rotation-Aware Point Cloud Analysis.
  4. Point Cloud Completion.
  5. Methodology
  6. Vector Neuron Network
  7. Rotation-Equivariant Bias Formulation.
  8. ZCA-based Layer Normalization.
  9. VN Feature Backbone
  10. Missing Anchor Position Predictor
  11. VN Missing Anchor Transformer
  12. Local Rotation-Invariant Fine Decoder
  13. Loss Function
  14. Experiments
  15. Datasets and Baselines
  16. ...and 21 more sections

Figures (7)

  • Figure 1: (a) Conventional point cloud completion methods are trained with data in canonical poses and cannot handle observation under pose changes. (b) Our proposed REVNET can consistently recover shapes under arbitrary poses.
  • Figure 1: Failure cases on MVP dataset.
  • Figure 2: The overview of our REVNET framework.
  • Figure 3: The architecture of our VN feature backbone.
  • Figure 4: The architecture of VN Missing Anchor Transformer.
  • ...and 2 more figures