# Unsupervised Deep Learning for Structured Shape Matching

arXiv: https://arxiv.org/abs/1812.03794 · HTML: https://mlsanity.com/paper/1812.03794/

## Key facts

- Cited by 81 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2018.

## Built on by (most cited first, 30 of 81)

- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [DPFM: Deep Partial Functional Maps](https://mlsanity.com/paper/2110.09994/) (2021)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Features](https://mlsanity.com/paper/2311.17024/) (2023)
- [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022)
- [Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching](https://mlsanity.com/paper/2204.13453/) (2022)
- [Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching](https://mlsanity.com/paper/2210.06373/) (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)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transport](https://mlsanity.com/paper/2202.01537/) (2022)
- [Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2303.10971/) (2023)
- [A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifold](https://mlsanity.com/paper/2302.08210/) (2023)
- [Understanding and Improving Features Learned in Deep Functional Maps](https://mlsanity.com/paper/2303.16527/) (2023)
- [A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching](https://mlsanity.com/paper/2204.12805/) (2022)
- [NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matching](https://mlsanity.com/paper/2301.05839/) (2023)
- [Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching](https://mlsanity.com/paper/2312.03678/) (2023)
- [Memory-Scalable and Simplified Functional Map Learning](https://mlsanity.com/paper/2404.00330/) (2024)
- [Denoising Functional Maps: Diffusion Models for Shape Correspondence](https://mlsanity.com/paper/2503.01845/) (2025)
- [Hierarchical Neural Semantic Representation for 3D Semantic Correspondence](https://mlsanity.com/paper/2509.17431/) (2025)
- [Implicit field supervision for robust non-rigid shape matching](https://mlsanity.com/paper/2203.07694/) (2022)
- [SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondence](https://mlsanity.com/paper/2209.07806/) (2022)
- [Non-Rigid Shape Registration via Deep Functional Maps Prior](https://mlsanity.com/paper/2311.04494/) (2023)
- [Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learning](https://mlsanity.com/paper/2403.01781/) (2024)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [Wormhole Loss for Partial Shape Matching](https://mlsanity.com/paper/2410.22899/) (2024)
- [S3M: Scalable Statistical Shape Modeling through Unsupervised Correspondences](https://mlsanity.com/paper/2304.07515/) (2023)
- [GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models](https://mlsanity.com/paper/2304.10523/) (2023)

## Abstract (arXiv)

We present a novel method for computing correspondences across 3D shapes using unsupervised learning. Our method computes a non-linear transformation of given descriptor functions, while optimizing for global structural properties of the resulting maps, such as their bijectivity or approximate isometry. To this end, we use the functional maps framework, and build upon the recent FMNet architecture for descriptor learning. Unlike that approach, however, we show that learning can be done in a purely unsupervised setting, without having access to any ground truth correspondences. This results in a very general shape matching method that we call SURFMNet for Spectral Unsupervised FMNet, and which can be used to establish correspondences within 3D shape collections without any prior information. We demonstrate on a wide range of challenging benchmarks, that our approach leads to state-of-the-art results compared to the existing unsupervised methods and achieves results that are comparable even to the supervised learning techniques. Moreover, our framework is an order of magnitude faster, and does not rely on geodesic distance computation or expensive post-processing.