# Isometric Multi-Shape Matching

arXiv: https://arxiv.org/abs/2012.02689 · HTML: https://mlsanity.com/paper/2012.02689/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2020.

## Built on by (most cited first, 30 of 33)

- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [Spatially and Spectrally Consistent Deep Functional Maps](https://mlsanity.com/paper/2308.08871/) (2023)
- [Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2303.10971/) (2023)
- [A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching](https://mlsanity.com/paper/2204.12805/) (2022)
- [Geometrically Consistent Partial Shape Matching](https://mlsanity.com/paper/2309.05013/) (2023)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes](https://mlsanity.com/paper/2303.16202/) (2023)
- [GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models](https://mlsanity.com/paper/2304.10523/) (2023)
- [DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matching](https://mlsanity.com/paper/2507.23715/) (2025)
- [Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization](https://mlsanity.com/paper/2203.12633/) (2022)
- [G-MSM: Unsupervised Multi-Shape Matching with Graph-based Affinity Priors](https://mlsanity.com/paper/2212.02910/) (2022)
- [Revisiting Map Relations for Unsupervised Non-Rigid Shape Matching](https://mlsanity.com/paper/2310.11420/) (2023)
- [Synchronous Diffusion for Unsupervised Smooth Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2407.08244/) (2024)
- [Sparse Quadratic Optimisation over the Stiefel Manifold with Application to Permutation Synchronisation](https://mlsanity.com/paper/2110.00053/) (2021)
- [Kissing to Find a Match: Efficient Low-Rank Permutation Representation](https://mlsanity.com/paper/2308.13252/) (2023)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Universe Points Representation Learning for Partial Multi-Graph Matching](https://mlsanity.com/paper/2212.00780/) (2022)
- [Symmetry Understanding of 3D Shapes via Chirality Disentanglement](https://mlsanity.com/paper/2508.05505/) (2025)
- [Optimizing Incomplete, Large-Scale and Sparse Multi-Graph Matching in Bioimaging](https://mlsanity.com/paper/2406.18215/) (2024)
- [SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularization](https://mlsanity.com/paper/2603.12937/) (2026)
- [RINO: Rotation-Invariant Non-Rigid Correspondences](https://mlsanity.com/paper/2603.27773/) (2026)
- [Riemannian Functional Map Synchronization for Probabilistic Partial Correspondence in Shape Networks](https://mlsanity.com/paper/2111.14762/) (2021)
- [A Novel and Optimal Spectral Method for Permutation Synchronization](https://mlsanity.com/paper/2303.12051/) (2023)
- [Non-Negative Spherical Relaxations for Universe-Free Multi-Matching and Clustering](https://mlsanity.com/paper/2310.13311/) (2023)
- [ARC-Flow : Articulated, Resolution-Agnostic, Correspondence-Free Matching and Interpolation of 3D Shapes Under Flow Fields](https://mlsanity.com/paper/2503.02606/) (2025)
- [DcMatch: Unsupervised Multi-Shape Matching with Dual-Level Consistency](https://mlsanity.com/paper/2509.01204/) (2025)
- [Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matching](https://mlsanity.com/paper/2606.30131/) (2026)
- [Temporally-Consistent Surface Reconstruction using Metrically-Consistent Atlases](https://mlsanity.com/paper/2111.06838/) (2021)

## Abstract (arXiv)

Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence methods aim to find a solution between pairs of shapes, even if multiple instances of the same class are available. While isometries are often studied in shape correspondence problems, they have not been considered explicitly in the multi-matching setting. This paper closes this gap by proposing a novel optimisation formulation for isometric multi-shape matching. We present a suitable optimisation algorithm for solving our formulation and provide a convergence and complexity analysis. Our algorithm obtains multi-matchings that are by construction provably cycle-consistent. We demonstrate the superior performance of our method on various datasets and set the new state-of-the-art in isometric multi-shape matching.