mlsanityData to 7 Oct 2026

DiscoMatch: Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matching

arXiv 2310.08230 ↗First posted 12 Oct 2023cs.CVcited by 7

Not on the map. Why?

Abstract (arXiv)

In this work we propose to combine the advantages of learningbased and combinatorial formalisms for 3D shape matching. While learningbased methods lead to state-of-the-art matching performance, they do not ensure geometric consistency, so that obtained matchings are locally non-smooth. On the contrary, axiomatic, optimisation-based methods allow to take geometric consistency into account by explicitly constraining the space of valid matchings. However, existing axiomatic formalisms do not scale to practically relevant problem sizes, and require user input for the initialisation of non-convex optimisation problems. We work towards closing this gap by proposing a novel combinatorial solver that combines a unique set of favourable properties: our approach (i) is initialisation free, (ii) is massively parallelisable and powered by a quasi-Newton method, (iii) provides optimality gaps, and (iv) delivers improved matching quality with decreased runtime and globally optimal results for many instances.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 27 of its 74 references that are in the map. First posted on arXiv 12 Oct 2023.

Builds on

27 of 74 references.

References · 27

  1. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  2. 2019KPConv: Flexible and Deformable Convolution for Point Cloudscited by 1,202
  3. 20163D Menagerie: Modeling the 3D shape and pose of animalscited by 310
  4. 20183D-CODED : 3D Correspondences by Deep Deformationcited by 160
  5. 2020Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondencecited by 125
  6. 20214DComplete: Non-Rigid Motion Estimation Beyond the Observable Surfacecited by 123
  7. 2018Unsupervised Deep Learning for Structured Shape Matchingcited by 81
  8. 2018Continuous and Orientation-preserving Correspondences via Functional Mapscited by 77
  9. 2021DPFM: Deep Partial Functional Mapscited by 58
  10. 2023Unsupervised Learning of Robust Spectral Shape Matchingcited by 57
  11. 2021Shape registration in the time of transformerscited by 51
  12. 2020Correspondence Learning via Linearly-invariant Embeddingcited by 48
15 more
  1. 2020CNNs on Surfaces using Rotation-Equivariant Featurescited by 42
  2. 2022Unsupervised Deep Multi-Shape Matchingcited by 39
  3. 2022Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimizationcited by 37
  4. 2022Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matchingcited by 36
  5. 2022Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matchingcited by 35
  6. 2017Product Manifold Filter: Non-Rigid Shape Correspondence via Kernel Density Estimation in the Product Spacecited by 30
  7. 2017Efficient Deformable Shape Correspondence via Kernel Matchingcited by 25
  8. 2023Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matchingcited by 23
  9. 2020MINA: Convex Mixed-Integer Programming for Non-Rigid Shape Alignmentcited by 20
  10. 2023Understanding and Improving Features Learned in Deep Functional Mapscited by 20
  11. 2022A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matchingcited by 19
  12. 2023Neural Intrinsic Embedding for Non-rigid Point Cloud Matchingcited by 9
  13. 2020Efficient Message Passing for 0-1 ILPs with Binary Decision Diagramscited by 8
  14. 2021FastDOG: Fast Discrete Optimization on GPUcited by 8
  15. 2022Conjugate Product Graphs for Globally Optimal 2D-3D Shape Matchingcited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 4; 2026: 1.

7 papers.

  1. 2024Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolationcited by 26
  2. 2024Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Surface Matching Algorithmscited by 11
  3. 2025DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matchingcited by 10
  4. 20254Deform: Neural Surface Deformation for Robust Shape Interpolationcited by 7
  5. 2025Stable-SCore: A Stable Registration-based Framework for 3D Shape Correspondencecited by 7
  6. 2025Fast Globally Optimal and Geometrically Consistent 3D Shape Matchingcited by 4
  7. 2026An Integer Linear Programming Approach to Geometrically Consistent Partial-Partial Shape Matchingcited by 1