Research map / Learning theory and algorithms / Optimal transport
Bending Graphs: Hierarchical Shape Matching Using Gated Optimal Transport
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the full hierarchical graph and GOT pipeline | Bending Graph · MPI-FAUST synthetic | geodesic error: 0.0513 -> 0.0230 | Helped |
| add shape graphs to local descriptors (ablation) | Bending Graph with OT · MPI-FAUST | error: 0.58 -> 0.42 | Helped |
| add shape graphs to local descriptors (ablation) | Bending Graph with OT · MPI-FAUST | Bijectivity Rate (%): 42.1 -> 23.3 | Hurt |
| add GOT propagation to hierarchical descriptors and OT (ablation) | Bending Graph without graph regularization · MPI-FAUST | error: 0.42 -> 0.19 | Helped |
| add regularization loss to the pipeline (ablation) | Bending Graph · MPI-FAUST | error: 0.19 -> 0.13 | Helped |
| remove shape graphs (ablation) | Bending Graph · MPI-FAUST | error: 0.13 -> 0.43 | Hurt |
| remove local descriptors (ablation) | Bending Graph · MPI-FAUST | error: 0.13 -> 0.16 | Hurt |
| use one GOT operation with two GFP layers rather than no propagation (ablation) | Bending Graph · MPI-FAUST | err.: 14.11 -> 8.63 | Helped |
| increase GFP layers from 2 to 4 or 8 (ablation) | Bending Graph · MPI-FAUST | err.: 8.63 -> 10.50; 8.63 -> 10.99 | Hurt |
| increase GOT operations from 1 to 2 or 3 (ablation) | Bending Graph · MPI-FAUST | err.: 8.63 -> 9.59; 8.63 -> 11.31 | Hurt |
| use two GOT operations with two GFP layers instead of one GOT with four GFP layers (ablation) | Bending Graph · MPI-FAUST | err.: 10.50 -> 9.59 | Helped |
| apply GFP after the first Sinkhorn (ablation) | Bending Graph · FAUST | fine error: 0.0229 -> 0.0253 | Hurt |
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- SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency (CVPR 2024 · similarity 0.86)
- GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models (ICLR 2024 · similarity 0.86)
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