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Partial-to-Partial Shape Matching with Geometric Consistency
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Proposes a geometrically consistent partial-to-partial 3D shape matching method using a non-linear integer program over triangle product spaces, solved via a pruned sequence of ILPs, and introduces the PARTIALSMAL inter-class dataset.
Problem
Finding correspondences between partially observed 3D shapes where neither shape is complete, so only overlapping regions should be matched, while avoiding the trivial empty matching and without requiring 3D labels or hole closing.
Approach
Formulate partial-to-partial matching as a fractional integer program over product triangles that enforces at-most-once matching, at least one non-boundary triangle match, and neighborhood (orientation) consistency; solve it globally via a sequence of ILPs with a Lipschitz-style pruning rule over the number of matched triangles, using deep features from a SOTA extractor for costs.
Key results
- On CP2P TEST, mean IoU of 69.29 vs 57.86 for Sm-comb and 54.93 for DPFM.
- On PARTIALSMAL, mean IoU of 64.34 vs 54.76 (Sm-comb) and 48.31 (DPFM).
- Time-limit heuristic reduces mIoU-evaluation time from 299.55 to 50.68 min with similar mIoU (68.89 to 69.47).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the proposed geometrically consistent matching method instead of Sm-comb | partial-to-partial shape matching · CP2P TEST | mean IoU (x100): 57.86 -> 69.29 | Helped |
| use the proposed geometrically consistent matching method instead of Sm-comb | partial-to-partial shape matching · PARTIALSMAL | mean IoU (x100): 54.76 -> 64.34 | Helped |
| reduce the subproblem time limit from 15min to 5min (ablation) | Ours · CP2P TEST | optimization time (min): 299.55 -> 140.13 | Helped |
| reduce the subproblem time limit from 15min to 5min (ablation) | Ours · CP2P TEST | mIoU: 69.29 -> 69.15 | No clear effect |
| reduce the subproblem time limit from 15min to 1min (ablation) | Ours · CP2P TEST | optimization time (min): 299.55 -> 57.31 | Helped |
| reduce the subproblem time limit from 15min to 1min (ablation) | Ours · CP2P TEST | mIoU: 69.29 -> 69.47 | No clear effect |
| reduce the subproblem time limit from 15min to 10s (ablation) | Ours · CP2P TEST | optimization time (min): 299.55 -> 50.68 | Helped |
| reduce the subproblem time limit from 15min to 10s (ablation) | Ours · CP2P TEST | mIoU: 69.29 -> 68.89 | No clear effect |
| reduce the subproblem time limit from 15min to 10s (ablation) | Ours · CP2P TEST | GlobOpt: 22% -> 4% | Hurt |
Surprising findings
- Pruned search with a time-limit heuristic keeps mean IoU nearly unchanged while cutting runtime substantially, but global optimality is reached in fewer cases.
Limitations
- ILP subproblems still have high runtime and exponential worst-case complexity.
- Neighboring constraint applies only to inner triangles, so boundary matches are not constrained; geometric consistency guaranteed only at coarse level.
- Relies on explicit mesh representations, not implicit ones.
Experimental setup
Datasets: CP2P (SHREC16 CUTS partial shapes) SMAL DT4D FAUST SCAPE
Benchmarks: CP2P TEST PARTIALSMAL
Metrics: IoU mean IoU geodesic error AUC
Baselines: Sm-comb DPFM
Builds on: Windheuser et al. elastic geometrically consistent matching Roetzer et al. Sm-comb DPFM Cao et al. deep partial functional maps (Sm-comb)
Closest papers by meaning
- EchoMatch: Partial-to-Partial Shape Matching via Correspondence Reflection (CVPR 2025 · similarity 0.92)
- Multi-Shape Matching with Cycle Consistency Basis via Functional Maps (AAAI 2025 · similarity 0.89)
- Wormhole Loss for Partial Shape Matching (NeurIPS 2024 · similarity 0.88)
- SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency (CVPR 2024 · similarity 0.88)
- 3D Geometric Shape Assembly via Efficient Point Cloud Matching (ICML 2024 · similarity 0.88)
- Higher-Order Ratio Cycles for Fast and Globally Optimal Shape Matching (CVPR 2025 · similarity 0.86)
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