Research map / 3D vision / Face and shape
HOPE: Shape Matching Via Aligning Different K-hop Neighbourhoods
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Proposes HOPE, a map-refinement method for shape matching that uses LMD to find poorly matched vertices and refines them with iteratively varied k-hop neighborhood consistency via GMWM.
Problem
Shape matching needs maps that are both accurate (unique vertex descriptors) and smooth (neighborhood-preserving), and existing methods typically achieve only one, or depend on isometry-specific parameters.
Approach
Refine an initial SHOT-based map only at poorly matched vertices (detected by local map distortion) by aligning k-hop neighborhood adjacency matrices for k = 1..8 across iterations, avoiding Laplacian spectral descriptors and a separate isometric/non-isometric parameter regime.
Key results
- On TOPKIDS, 2D-GEM achieves 96.7% vertices correctly matched, HOPE 94.9%, and GRAMPA 84.5%.
- On isometric shapes HOPE reaches 80.11% accuracy at geodesic error 0 on SCAPE and 92.54% on TOSCA, using a single parameter setting.
- HOPE is faster than 2D-GEM and ZoomOut on TOSCA; on a 12,500-vertex SCAPE shape it takes 52 s vs 56 s for 2D-GEM and 118 s for GRAMPA.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HOPE instead of GRAMPA | Shape matching pipeline · TOPKIDS | accuracy at geodesic error 0: 84.5% -> 94.9% | Helped |
| Use HOPE instead of 2D-GEM | Shape matching pipeline · SCAPE | accuracy at geodesic error 0: 74.8% -> 80.11% | Helped |
| Use HOPE instead of DIR-1000 | Shape matching pipeline · SCAPE | accuracy at geodesic error 0: around 69.5% -> 80.11% | Helped |
| Use HOPE instead of 2D-GEM | Shape matching pipeline · TOSCA | accuracy at geodesic error 0: 92.54% -> 92.54% | No clear effect |
| Use HOPE instead of DIR-1000 | Shape matching pipeline · TOSCA | accuracy at geodesic error 0: 59.8% -> 92.54% | Helped |
| Use HOPE instead of GRAMPA | Shape matching pipeline · SCAPE, shape with 12500 vertices | runtime per shape: 118 seconds -> 52 seconds | Helped |
| Reduce iterations from t = 60 to t = 20 (ablation) | HOPE · TOPKIDS, SCAPE, TOSCA_r | geodesic error | Mixed |
| Set the LMD threshold schedule to linespace(1, 0.2, 10) (ablation) | HOPE · TOPKIDS, SCAPE, TOSCA_r | geodesic error | Helped |
| Use fixed alternating hops k = 1 and k = 2 instead of varying hops (ablation) | HOPE · TOPKIDS, SCAPE, TOSCA_r | geodesic error | Mixed |
| Use kmax = 2 (ablation) | HOPE · TOPKIDS, SCAPE, TOSCA_r | geodesic error | Mixed |
| Vary hops from k = 1 to 8 without LMD (ablation) | HOPE · SCAPE | geodesic error | Hurt |
| Initialize with HKS instead of SHOT (ablation) | HOPE · TOPKIDS | accuracy | Hurt |
Surprising findings
- Tuning the LMD threshold (HOPE-th variant with a different epsilon range) outperforms the default HOPE setting, suggesting the default epsilon is sub-optimal.
- HOPE-varyhop and HOPE-fixhop without LMD struggle on isometric shapes, indicating k-hop descriptors alone are not unique under symmetry.
Limitations
- Relies on correlated triangulations between the shapes; performance drops on remeshed shapes with weakly correlated meshes.
- The LMD threshold schedule was chosen without tuning and is acknowledged to be sub-optimal.
- Evaluated only on shape-matching benchmarks with CPU Matlab implementation; no GPU or large-scale experiments.
Experimental setup
Datasets: TOSCA SCAPE TOPKIDS FAUST_r SCAPE_r TOSCA_r SHREC16 HOLES SHREC16 CUTS SMAL_r
Benchmarks: TOPKIDS SCAPE TOSCA FAUST_r SCAPE_r TOSCA_r SHREC16 HOLES SHREC16 CUTS SMAL_r
Metrics: geodesic error accuracy at geodesic error 0 runtime per shape
Baselines: 2D-GEM GRAMPA ZoomOut DIR-500 DIR-1000 FM SGMDS PFM Kernel-Matching Mobius
Builds on: 2D-GEM DIR ZoomOut GMWM SHOT
Closest papers by meaning
- Multi-Shape Matching with Cycle Consistency Basis via Functional Maps (AAAI 2025 · similarity 0.87)
- Locality Preserving Refinement for Shape Matching with Functional Maps (AAAI 2024 · similarity 0.87)
- Wormhole Loss for Partial Shape Matching (NeurIPS 2024 · similarity 0.86)
- Partial-to-Partial Shape Matching with Geometric Consistency (CVPR 2024 · similarity 0.86)
- SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency (CVPR 2024 · similarity 0.85)
- Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation (CVPR 2024 · similarity 0.85)
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