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Wormhole Loss for Partial Shape Matching
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Proposes a wormhole criterion that uses extrinsic Euclidean distances between boundary points to identify more guaranteed consistent geodesic pairs, and builds an unsupervised masked geodesic loss for partial shape matching that reaches SOTA on SHREC'16 and PFAUST.
Problem
Unsupervised partial shape matching is hurt by geodesic distance preservation losses, because geodesics on the full surface may pass through regions missing from the partial surface, so many distances between corresponding points are inconsistent.
Approach
A "wormhole" criterion bounds the full-surface geodesic between two partial-surface points by the sum of their geodesic distances to boundary points plus the Euclidean distance between those boundary points, which guarantees more consistent pairs than the prior boundary-distance criterion; this is used as a soft mask in a geodesic loss.
Key results
- On PFAUST-H the wormhole method reaches 6.7 geodesic error vs 7.9 for DirectMatchNet among unsupervised methods, and 4.6 vs 5.1 on PFAUST-M.
- On SHREC'16 HOLES (trained and tested on HOLES) the wormhole loss with refinement reaches 6.6, best among compared methods, vs 8.0 for DirectMatchNet with refinement in the same setting.
- The wormhole criterion guarantees 82% of consistent pairs on PFAUST-M and 65% on PFAUST-H, roughly double the prior criterion's 48% and 30%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use wormhole criterion C_W instead of C_T to derive the binary mask (ablation) | Wormhole loss · HOLES | geodesic error ×100: 18.8 -> 15.3 | Helped |
| use wormhole criterion C_W instead of C_T to derive the non-binary mask (ablation) | Wormhole loss · HOLES | geodesic error ×100: 14.7 -> 10.9 | Helped |
| use a non-binary soft mask instead of a binary mask (ablation) | Wormhole loss with C_W · HOLES | geodesic error ×100: 15.3 -> 10.9 | Helped |
| use a non-binary mask instead of a binary mask (ablation) | Loss using C_T · HOLES | geodesic error ×100: 18.8 -> 14.7 | Helped |
| replace C_T with wormhole criterion C_W | Guaranteed-pair selection · PFAUST-M | guaranteed pairs (% of consistent pairs): 48 (± 18) -> 82 (± 14) | Helped |
| replace C_T with wormhole criterion C_W | Guaranteed-pair selection · PFAUST-H | guaranteed pairs (% of consistent pairs): 30 (± 18) -> 65 (± 18) | Helped |
| train with the wormhole loss | Unsupervised DiffusionNet shape matching · PFAUST-M | geodesic error ×100: 5.1 -> 4.6 | Helped |
| train with the wormhole loss | Unsupervised DiffusionNet shape matching · PFAUST-H | geodesic error ×100: 7.9 -> 6.7 | Helped |
| train with the wormhole loss | Unsupervised DiffusionNet shape matching · SHREC'16 HOLES (train HOLES, test HOLES) | geodesic error ×100: 11.4 -> 10.9 | Helped |
| train with the wormhole loss | Unsupervised DiffusionNet shape matching · SHREC'16 CUTS (train CUTS, test CUTS) | geodesic error ×100: 6.9 -> 6.9 | No clear effect |
Surprising findings
- The prior boundary-distance criterion guarantees only about half as many consistent pairs as the new wormhole criterion, and the soft (non-binary) mask outperforms the binary mask.
Limitations
- Does not recover all consistent pairs; less restrictive criteria may exist.
- Extension to higher dimensions and boundary detection is not straightforward.
- Only partial-to-full matching is addressed; partial-to-partial matching is left for future work.
Experimental setup
Datasets: SHREC'16 CUTS SHREC'16 HOLES PFAUST-M PFAUST-H TOSCA FAUST-Remeshed
Benchmarks: SHREC'16 CUTS SHREC'16 HOLES PFAUST-M PFAUST-H
Metrics: average geodesic error (x100) percentage of consistent pairs percentage of guaranteed pairs PCK curves
Baselines: PFM FSP GeomFMaps DPFM Unsupervised-DPFM RobustFMnet DirectMatchNet DirectMatchNet LPF
Builds on: DirectMatchNet DiffusionNet TCIE Zoom-out Unsupervised DPFM
Closest papers by meaning
- Partial-to-Partial Shape Matching with Geometric Consistency (CVPR 2024 · similarity 0.88)
- Geodesic Distance Descriptors (CVPR 2017 · similarity 0.88)
- HOPE: Shape Matching Via Aligning Different K-hop Neighbourhoods (NeurIPS 2024 · similarity 0.86)
- Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation (CVPR 2024 · similarity 0.86)
- EchoMatch: Partial-to-Partial Shape Matching via Correspondence Reflection (CVPR 2025 · similarity 0.86)
- Flow Matching on General Geometries (ICLR 2024 · similarity 0.85)
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