Learning Generalizable Shape Completion with SIM(3) Equivariance

2025-09-30

AI Summary

Existing 3D shape completion methods rely on pre-aligned scans, causing models to implicitly exploit absolute pose and scale cues—leading to severe performance degradation when generalizing to unaligned real-world data. To address this, we propose the first SIM(3)-equivariant shape completion network, achieving strict invariance to rotation, translation, and uniform scaling via layer-wise feature normalization, geometrically equivariant inference, and coordinate-adaptive reconstruction. Our method introduces a feature-space normalization/denormalization mechanism and is trained and evaluated under a bias-free assessment protocol. Experiments demonstrate state-of-the-art performance: surpassing existing equivariant and data-augmentation baselines on the PCN benchmark; reducing cross-domain matching distance by 17% on KITTI; decreasing Chamfer-ℓ₁ distance by 14% on OmniObject3D; and outperforming competing methods even under stricter evaluation protocols than those used in prior work.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

3D shape completion methods typically assume scans are pre-aligned to a canonical frame. This leaks pose and scale cues that networks may exploit to memorize absolute positions rather than inferring intrinsic geometry. When such alignment is absent in real data, performance collapses. We argue that robust generalization demands architectural equivariance to the similarity group, SIM(3), so the model remains agnostic to pose and scale. Following this principle, we introduce the first SIM(3)-equivariant shape completion network, whose modular layers successively canonicalize features, reason over similarity-invariant geometry, and restore the original frame. Under a de-biased evaluation protocol that removes the hidden cues, our model outperforms both equivariant and augmentation baselines on the PCN benchmark. It also sets new cross-domain records on real driving and indoor scans, lowering minimal matching distance on KITTI by 17% and Chamfer distance $ell1$ on OmniObject3D by 14%. Perhaps surprisingly, ours under the stricter protocol still outperforms competitors under their biased settings. These results establish full SIM(3) equivariance as an effective route to truly generalizable shape completion. Project page: https://sime-completion.github.io.

Problem

• Addresses 3D shape completion without relying on pre-aligned canonical frames
• Achieves robust generalization through SIM(3)-equivariant architecture design
• Improves cross-domain performance on real-world driving and indoor scans

Innovation

• SIM(3)-equivariant network for shape completion
• Modular layers canonicalize and restore features
• Achieves generalization under de-biased evaluation protocol