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Multi-Shape Matching with Cycle Consistency Basis via Functional Maps
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Proposes CyCoMatch, a two-stage multi-shape matching method in the functional maps framework that refines pairwise maps using landmarks identified by local mapping distortion, then enforces cycle consistency via a cycle consistency basis optimized with ADMM.
Problem
Multi-shape matching on non-rigid 3D shapes requires both accurate pairwise correspondences and cycle-consistent correspondences across a collection, which prior methods struggle to balance at scale.
Approach
Model the shape collection as a directed graph; use local mapping distortion to pick landmarks for accurate pairwise functional maps (with spectral wavelet upsampling and data-driven functional dimension), then impose a sampled cycle consistency basis as constraints solved via ADMM.
Key results
- Achieves average relative geodesic error of 0.0030 on FAUST, 0.0075 on SCAPE and 0.0251 on TOSCA, the lowest among compared methods in Table 1.
- Cycle error of 0.0014 on FAUST, 0.0034 on SCAPE and 0.0066 on TOSCA, improving on Consistent Zoomout's cycle errors in most settings.
- Ablation shows removing spectral domain upsampling raises error from 0.0095 to 0.0255 on the reported ablation setting.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the proposed multi-shape matching method instead of LOPR | FAUST matching · FAUST | relative geodesic error: 0.0030 -> 0.0030 | No clear effect |
| use the proposed multi-shape matching method instead of LOPR | FAUST matching · FAUST | cycle error: 0.0015 -> 0.0014 | Helped |
| use the proposed multi-shape matching method instead of LOPR | SCAPE matching · SCAPE | relative geodesic error: 0.0089 -> 0.0075 | Helped |
| use the proposed multi-shape matching method instead of Consistent Zoomout | SCAPE matching · SCAPE | cycle error: 0.0027 -> 0.0034 | Hurt |
| use the proposed multi-shape matching method instead of LOPR | TOSCA matching · TOSCA | relative geodesic error: 0.0266 -> 0.0251 | Helped |
| use the proposed multi-shape matching method instead of Consistent Zoomout | TOSCA matching · TOSCA | cycle error: 0.0031 -> 0.0066 | Hurt |
| add landmark-point functional maps (ablation) | proposed multi-shape matching method · Ablation study | relative geodesic error: 0.0115 -> 0.0095 | Helped |
| add landmark-point functional maps (ablation) | proposed multi-shape matching method · Ablation study | cycle error: 0.0073 -> 0.0060 | Helped |
| add spectral-domain upsampling to reconstruct functional maps (ablation) | proposed multi-shape matching method · Ablation study | relative geodesic error: 0.0255 -> 0.0095 | Helped |
| add spectral-domain upsampling to reconstruct functional maps (ablation) | proposed multi-shape matching method · Ablation study | cycle error: 0.0174 -> 0.0060 | Helped |
| add cycle consistency refinement (ablation) | proposed multi-shape matching method · Ablation study | relative geodesic error: 0.0106 -> 0.0095 | Helped |
| add cycle consistency refinement (ablation) | proposed multi-shape matching method · Ablation study | cycle error: 0.0070 -> 0.0060 | Helped |
Surprising findings
- Runtime is substantially higher than most baselines (e.g., 23.8s on FAUST vs. 4.9s for LOPR and 13.2s for Zoomout), while CCuantuMM is far slower.
Limitations
- Runtime is higher than several pairwise baselines due to geodesic distance matrix computation.
- Relies on initial SHOT-based correspondences and LMD thresholds chosen empirically.
Experimental setup
Datasets: FAUST SCAPE TOSCA
Benchmarks: FAUST SCAPE TOSCA
Metrics: relative geodesic error cycle error CQC curve runtime
Baselines: Zoomout Sinkhorn MWP PC-GAU URSSM LOPR CSM Limit Shapes Consistent Zoomout CCuantuMM
Builds on: functional maps Consistent Zoomout cycle consistency basis (Guibas et al. 2019) spectral manifold wavelets (Hu et al. 2021) LOPR
Closest papers by meaning
- Partial-to-Partial Shape Matching with Geometric Consistency (CVPR 2024 · similarity 0.89)
- Higher-Order Ratio Cycles for Fast and Globally Optimal Shape Matching (CVPR 2025 · similarity 0.88)
- Locality Preserving Refinement for Shape Matching with Functional Maps (AAAI 2024 · similarity 0.87)
- Stable-SCore: A Stable Registration-based Framework for 3D Shape Correspondence (CVPR 2025 · similarity 0.87)
- HOPE: Shape Matching Via Aligning Different K-hop Neighbourhoods (NeurIPS 2024 · similarity 0.87)
- SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency (CVPR 2024 · similarity 0.87)
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