Research map / 3D vision / Face and shape
Learning 3D Equivariant Implicit Function with Patch-Level Pose-Invariant Representation
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes PEIF, an SE(3)-equivariant neural vector field for surface reconstruction that uses PCA-based patch-level pose normalization and multi-head memory banks to learn intrinsic patch geometry, outperforming prior UDF/occupancy methods on ShapeNet, ABC, Synthetic Rooms and MGN.
Problem
Implicit neural surface reconstruction methods depend on fixed coordinate frames and entangle pose with local geometry, which hurts cross-domain generalization and robustness to arbitrary SE(3)/SO(3) rotations.
Approach
Normalize each query/patch pair by a PCA-based pose normalization (with a unique sign convention) so the displacement predictor is SE(3)-invariant, then equivariantly map back to predict displacement vectors; a shared multi-head learnable memory bank captures recurring intrinsic patch geometry.
Key results
- On ShapeNet novel classes, PEIF reaches CD 0.209 and F-Score 0.997, versus 0.219 and 0.997 for GeoUDF (best baseline).
- On Synthetic Rooms, PEIF achieves CD 0.314 versus 0.383 for GeoUDF, and cross-domain MGN CD 0.241 versus 0.249 for GeoUDF.
- Under arbitrary SO(3) rotations on ABC, PEIF keeps CD 0.241 (vs 0.245 unrotated), while NVF degrades from 0.245 to 0.261.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add patch-level pose normalization (ablation) | PEIF · ABC | NC: 0.933 -> 0.969 | Helped |
| add the multi-head memory bank (NM=4) rather than remove it (ablation) | PEIF · ABC | CD: 0.275 -> 0.241 | Helped |
| increase memory bank size from NM=1 to NM=4 (ablation) | PEIF · ABC | CD: 0.244 -> 0.241 | Helped |
| increase memory bank size from NM=4 to NM=5 (ablation) | PEIF · ABC | CD: 0.241 -> 0.244 | Hurt |
| vary KNN patch size to K = 54 or K = 20 instead of full-model K = 32 (ablation) | PEIF · ABC | CD: 0.241 -> 0.245; 0.241 -> 0.249 | Mixed |
| add keypoint-boosted patch feature f̄Ps (ablation) | PEIF · ABC | CD: 0.247 -> 0.241 | Helped |
| set loss coefficient β to 0.0 or 0.01 instead of 0.1 (ablation) | PEIF · ABC | CD: 0.241 -> 0.244; 0.241 -> 0.245 | Hurt |
| set loss coefficient β to 0.5 instead of 0.1 (ablation) | PEIF · ABC | CD: 0.241 -> 0.248 | Hurt |
| apply arbitrary SO(3) rotations to test inputs | PEIF · ABC with rotations vs without rotations | CD: 0.241 -> 0.241 | No clear effect |
| apply arbitrary SO(3) rotations to test inputs | NVF · ABC with rotations vs without rotations | CD: 0.245 -> 0.261 | Hurt |
| apply arbitrary SO(3) rotations to test inputs | GeoUDF · ABC with rotations vs without rotations | CD: 0.245 -> 0.253 | Hurt |
| apply arbitrary SO(3) rotations to test inputs | E-GraphONet · ABC with rotations vs without rotations | CD: 0.432 -> 0.433 | Hurt |
Surprising findings
- Removing pose normalization mainly hurts normal consistency (NC drops from 0.969 to 0.933 on ABC).
- Table 3's PEIF row (CD 0.241, EMD 2.672, NC 0.969) duplicates the ABC/Synthetic Rooms numbers, and the MGN comparison appears inconsistent in EMD scale.
Limitations
- Relies on point-wise displacement estimation over many query points, so scaling to large scenes is costly.
- Inference time is higher than several baselines (GridFormer, E-GraphONet).
Experimental setup
Datasets: ShapeNet ABC Synthetic Rooms MGN
Benchmarks: ShapeNet ABC Synthetic Rooms MGN
Metrics: Chamfer-L1 distance Earth Mover Distance Normal Consistency F-Score
Baselines: POCO GIFS ALTO NVF GeoUDF GridFormer GraphONet E-GraphONet
Builds on: Neural Vector Fields (NVF) E-GraphONet MeshUDF Vector Neurons
Closest papers by meaning
- Neural Vector Fields: Implicit Representation by Explicit Learning (CVPR 2023 · similarity 0.88)
- NeuSurf: On-Surface Priors for Neural Surface Reconstruction from Sparse Input Views (AAAI 2024 · similarity 0.87)
- LISR: Learning Linear 3D Implicit Surface Representation Using Compactly Supported Radial Basis Functions (AAAI 2024 · similarity 0.86)
- A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions (CVPR 2025 · similarity 0.86)
- Neural Isometries: Taming Transformations for Equivariant ML (NeurIPS 2024 · similarity 0.86)
- NeuralIndicator: Implicit Surface Reconstruction from Neural Indicator Priors (ICML 2024 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.