Research map / 3D vision / Face and shape
Optimization-based shape matching
Computes shape correspondence using spectral, combinatorial and registration-based solvers.
59 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Face and shape, keyword cluster “3d shape · shapes · object”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
16 papers in 2023–24 and 23 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 4.4% to 6.3%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · GIFT: A Real-Time and Scalable 3D Shape Search Engine (CVPR 2016 · 256 citations)
- 2017 · Can Walking and Measuring Along Chord Bunches Better Describe Leaf Shapes? (CVPR 2017 · 30 citations)
- 2019 · Deep Sketch-Shape Hashing With Segmented 3D Stochastic Viewing (CVPR 2019 · 47 citations)
- 2020 · Smooth Shells: Multi-Scale Shape Registration With Functional Maps (CVPR 2020 · 87 citations)
- 2021 · Isometric Multi-Shape Matching (CVPR 2021 · 29 citations)
- 2022 · A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching (CVPR 2022 · 27 citations)
- 2023 · Fantastic Breaks: A Dataset of Paired 3D Scans of Real-World Broken Objects and Their Complete Counterparts (CVPR 2023 · 14 citations)
- 2024 · Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation (CVPR 2024 · 17 citations)
- 2025 · EchoMatch: Partial-to-Partial Shape Matching via Correspondence Reflection (CVPR 2025 · 8 citations)
- 2026 · BridgeShape: Latent Diffusion Schrödinger Bridge for 3D Shape Completion (AAAI 2026 · 1 citation)
Earliest papers here
- GIFT: A Real-Time and Scalable 3D Shape Search Engine (CVPR 2016 · 256 citations)
- Efficient Globally Optimal 2D-To-3D Deformable Shape Matching (CVPR 2016 · 32 citations)
- Shape Analysis With Hyperbolic Wasserstein Distance (CVPR 2016 · 22 citations)
What has been tried
40 papers here report 350 measured changes (a component added, removed or swapped, compared with a baseline): helped 75%, no clear effect 6%, hurt 14%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| add spatial regularisation to spectral-only matching | SMAL · geodesic error (×100) | 3.9 -> 1.9 | Helped | Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation (CVPR 2024 · 17 citations) |
| Add the first part-graph iteration | Chair · Part Accuracy | 23.71 -> 72.81 | Helped | Category-Level Multi-Part Multi-Joint 3D Shape Assembly (CVPR 2024 · 15 citations) |
| Adapt the elastic-basis solver to non-orthogonality using the HS norm instead of the standard solver | SMAL · geodesic error (×100) | 40.2 ± 0.80 -> 5.15 ± 0.99 | Helped | Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching (CVPR 2024 · 15 citations) |
| reduce the subproblem time limit from 15min to 5min | CP2P TEST · optimization time (min) | 299.55 -> 140.13 | Helped | Partial-to-Partial Shape Matching with Geometric Consistency (CVPR 2024 · 10 citations) |
| add PES and ANS constraints | FAUST · mean geodesic error | 0.036 -> 0.034 | Helped | SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency (CVPR 2024 · 10 citations) |
| Increase correspondence-reflection neighbourhood size from 1 to 64 | BeCoS validation · mIoU (×100) | 55.04 -> 67.43 | Helped | EchoMatch: Partial-to-Partial Shape Matching via Correspondence Reflection (CVPR 2025 · 8 citations) |
| Add view-agnostic local feature alignment (VLFA) | BrokenChairs-180K test · accuracy | 67.1 -> 72.3 | Helped | Looking 3D: Anomaly Detection with 2D-3D Alignment (CVPR 2024 · 5 citations) |
| Use Neural Jacobian Field instead of per-vertex displacements | FAUST (cross-domain) · mean geodesic error ×100 | 2.88 -> 2.32 | Helped | Stable-SCore: A Stable Registration-based Framework for 3D Shape Correspondence (CVPR 2025 · 4 citations) |
| add geometric self-attention to the encoder | PartNet full shapes · Average Chamfer Distance | 0.161 -> 0.110 | Helped | KP-RED: Exploiting Semantic Keypoints for Joint 3D Shape Retrieval and Deformation (CVPR 2024 · 3 citations) |
| use the revised DLBO instead of Topology Laplacian | Shape Grading · PLCC | 0.298 -> 0.567 | Helped | Spectrum AUC Difference (SAUCD): Human-aligned 3D Shape Evaluation (CVPR 2024 · 2 citations) |
| add landmark-point functional maps | Ablation study · relative geodesic error | 0.0115 -> 0.0095 | Helped | Multi-Shape Matching with Cycle Consistency Basis via Functional Maps (AAAI 2025 · 1 citation) |
| Add pose optimization to FMA | AlignDockBench cross-docking · mean RMSD (Å) | 1.97 ± 1.36 -> 1.86 ± 1.42 | Helped | Template-Guided 3D Molecular Pose Generation via Flow Matching and Differentiable Optimization (NeurIPS 2025 · 1 citation) |
What reviewers will expect
Datasets and baselines named in the 7 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- FAUST · 2 of 7 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 39 papers; from OpenAlex and the papers' affiliations).
- University of Bonn · 5 papers
- Technical University of Munich · 4 papers
- University of Siegen · 2 papers
- Massachusetts Institute of Technology · 2 papers
- University of Texas, Austin · 2 papers
- University of Texas at Austin · 2 papers
Use it
Download BibTeX of 37 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Primitive-based shape abstraction (99 papers)
- Single-view 3D reconstruction (96 papers)
- Articulated and non-rigid shape learning (75 papers)
- 3D shape generative modeling (74 papers)
Elsewhere in the topic
- Neural implicit surface reconstruction (131 papers)
- Gaussian and implicit head avatars (115 papers)
- Textured mesh generation (111 papers)
- Face reflectance and relightable rendering (85 papers)
- 3D morphable face model regression (80 papers)
- Full-body avatar reconstruction (78 papers)
- Learned mesh and geometric representations (73 papers)
- Clothed human modeling (60 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).