# Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities

arXiv: https://arxiv.org/abs/2604.01274 · HTML: https://mlsanity.com/paper/2604.01274/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 125 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Builds on (most cited first, 30 of 54)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [3D Morphable Face Models -- Past, Present and Future](https://mlsanity.com/paper/1909.01815/) (2019)
- [Embodied Hands: Modeling and Capturing Hands and Bodies Together](https://mlsanity.com/paper/2201.02610/) (2022)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [State of the Art on Diffusion Models for Visual Computing](https://mlsanity.com/paper/2310.07204/) (2023)
- [LoopReg: Self-supervised Learning of Implicit Surface Correspondences, Pose and Shape for 3D Human Mesh Registration](https://mlsanity.com/paper/2010.12447/) (2020)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [Continuous and Orientation-preserving Correspondences via Functional Maps](https://mlsanity.com/paper/1806.04455/) (2018)
- [Deep Shells: Unsupervised Shape Correspondence with Optimal Transport](https://mlsanity.com/paper/2010.15261/) (2020)
- [Partial Functional Correspondence](https://mlsanity.com/paper/1506.05274/) (2015)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Shape registration in the time of transformers](https://mlsanity.com/paper/2106.13679/) (2021)
- [Correspondence Learning via Linearly-invariant Embedding](https://mlsanity.com/paper/2010.13136/) (2020)
- [DiffCAD: Weakly-Supervised Probabilistic CAD Model Retrieval and Alignment from an RGB Image](https://mlsanity.com/paper/2311.18610/) (2023)
- [Non-rigid Point Cloud Registration with Neural Deformation Pyramid](https://mlsanity.com/paper/2205.12796/) (2022)
- [Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching](https://mlsanity.com/paper/2210.06373/) (2022)
- [Zero-Shot 3D Shape Correspondence](https://mlsanity.com/paper/2306.03253/) (2023)
- [MedShapeNet -- A Large-Scale Dataset of 3D Medical Shapes for Computer Vision](https://mlsanity.com/paper/2308.16139/) (2023)
- [ZoomOut: Spectral Upsampling for Efficient Shape Correspondence](https://mlsanity.com/paper/1904.07865/) (2019)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes](https://mlsanity.com/paper/2205.02904/) (2022)
- [From Skin to Skeleton: Towards Biomechanically Accurate 3D Digital Humans](https://mlsanity.com/paper/2509.06607/) (2025)
- [FARM: Functional Automatic Registration Method for 3D Human Bodies](https://mlsanity.com/paper/1807.10517/) (2018)
- [Reversible Harmonic Maps between Discrete Surfaces](https://mlsanity.com/paper/1801.02453/) (2018)
- [NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matching](https://mlsanity.com/paper/2301.05839/) (2023)
- [Complex Functional Maps : a Conformal Link Between Tangent Bundles](https://mlsanity.com/paper/2112.09546/) (2021)
- [Synchronisation of Partial Multi-Matchings via Non-negative Factorisations](https://mlsanity.com/paper/1803.06320/) (2018)

## Built on by (most cited first, 4 of 4)

- [DeepShapeMatchingKit: Accelerated Functional Map Solver and Shape Matching Pipelines Revisited](https://mlsanity.com/paper/2604.10377/) (2026)
- [Ordered Diffusion for 3D Human Registration](https://mlsanity.com/paper/2608.05804/) (2026)
- [Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments](https://mlsanity.com/paper/2605.29004/) (2026)
- [TokenMatch: 3D Mesh Correspondence Transformer with Curvature-Guided Tokenisation](https://mlsanity.com/paper/2609.04202/) (2026)

## Abstract (arXiv)

Estimating correspondences between deformed shape instances is a long-standing problem in computer graphics; numerous applications, from texture transfer to statistical modelling, rely on recovering an accurate correspondence map. Many methods have thus been proposed to tackle this challenging problem from varying perspectives, depending on the downstream application. This state-of-the-art report is geared towards researchers, practitioners, and students seeking to understand recent trends and advances in the field. We categorise developments into three paradigms: spectral methods based on functional maps, combinatorial formulations that impose discrete constraints, and deformation-based methods that directly recover a global alignment. Each school of thought offers different advantages and disadvantages, which we discuss throughout the report. Meanwhile, we highlight the latest developments in each area and suggest new potential research directions. Finally, we provide an overview of emerging challenges and opportunities in this growing field, including the recent use of vision foundation models for zero-shot correspondence and the particularly challenging task of matching partial shapes.