mlsanityData to 7 Oct 2026

Fast Globally Optimal and Geometrically Consistent 3D Shape Matching

arXiv 2504.06385 ↗First posted 8 Apr 2025cs.GR cs.CVcited by 4

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Abstract (arXiv)

Geometric consistency, i.e. the preservation of neighbourhoods, is a natural and strong prior in 3D shape matching. Geometrically consistent matchings are crucial for many downstream applications, such as texture transfer or statistical shape modelling. Yet, in practice, geometric consistency is often overlooked, or only achieved under severely limiting assumptions (e.g. a good initialisation). In this work, we propose a novel formalism for computing globally optimal and geometrically consistent matchings between 3D shapes which is scalable in practice. Our key idea is to represent the surface of the source shape as a collection of cyclic paths, which are then consistently matched to the target shape. Mathematically, we construct a hyper product graph (between source and target shape), and then cast 3D shape matching as a minimum-cost circulation flow problem in this hyper graph, which yields global geometrically consistent matchings between both shapes. We empirically show that our formalism is efficiently solvable and that it leads to high-quality results.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 35 of its 102 references that are in the map. First posted on arXiv 8 Apr 2025.

Builds on

35 of 102 references.

References · 35

  1. 2020End-to-End Object Detection with Transformerscited by 7,384
  2. 2024Grounding Image Matching in 3D with MASt3Rcited by 960
  3. 20163D Menagerie: Modeling the 3D shape and pose of animalscited by 310
  4. 20193D Morphable Face Models -- Past, Present and Futurecited by 269
  5. 2020DiffusionNet: Discretization Agnostic Learning on Surfacescited by 163
  6. 20183D-CODED : 3D Correspondences by Deep Deformationcited by 160
  7. 2017Deep Functional Maps: Structured Prediction for Dense Shape Correspondencecited by 134
  8. 2020Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondencecited by 125
  9. 20214DComplete: Non-Rigid Motion Estimation Beyond the Observable Surfacecited by 123
  10. 2018Continuous and Orientation-preserving Correspondences via Functional Mapscited by 77
  11. 2019Smooth Shells: Multi-Scale Shape Registration with Functional Mapscited by 72
  12. 2022A Survey of Non-Rigid 3D Registrationcited by 59
23 more
  1. 2023Unsupervised Learning of Robust Spectral Shape Matchingcited by 57
  2. 2023Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Featurescited by 55
  3. 2021Shape registration in the time of transformerscited by 51
  4. 2020CNNs on Surfaces using Rotation-Equivariant Featurescited by 42
  5. 2022Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimizationcited by 37
  6. 2022Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matchingcited by 36
  7. 2022Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matchingcited by 35
  8. 2017Product Manifold Filter: Non-Rigid Shape Correspondence via Kernel Density Estimation in the Product Spacecited by 30
  9. 2021Q-Match: Iterative Shape Matching via Quantum Annealingcited by 27
  10. 2020MINA: Convex Mixed-Integer Programming for Non-Rigid Shape Alignmentcited by 20
  11. 2023Understanding and Improving Features Learned in Deep Functional Mapscited by 20
  12. 2022A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matchingcited by 19
  13. 2023Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matchingcited by 18
  14. 2024Partial-to-Partial Shape Matching with Geometric Consistencycited by 16
  15. 2022A Comparative Study of Graph Matching Algorithms in Computer Visioncited by 14
  16. 2023Geometrically Consistent Partial Shape Matchingcited by 13
  17. 2024Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Surface Matching Algorithmscited by 11
  18. 2017Sinkhorn Algorithm for Lifted Assignment Problemscited by 9
  19. 2023DiscoMatch: Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matchingcited by 7
  20. 2022Conjugate Product Graphs for Globally Optimal 2D-3D Shape Matchingcited by 6
  21. 2023ReMatching: Low-Resolution Representations for Scalable Shape Correspondencecited by 5
  22. 2023SIGMA: Scale-Invariant Global Sparse Shape Matchingcited by 4
  23. 2014Solving Totally Unimodular LPs with the Shadow Vertex Algorithmcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Symmetry Informative and Agnostic Feature Disentanglement for 3D Shapescited by 2
  2. 2026An Integer Linear Programming Approach to Geometrically Consistent Partial-Partial Shape Matchingcited by 1
  3. 2026Ordered Diffusion for 3D Human Registrationcited by 1
  4. 2026NHO: A Neural Hamiltonian Operator for Anchor-based Region Localization and Dense Correspondencecited by 0