# Deep Functional Maps: Structured Prediction for Dense Shape Correspondence

arXiv: https://arxiv.org/abs/1704.08686 · HTML: https://mlsanity.com/paper/1704.08686/

## Key facts

- Cited by 134 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2017.

## Built on by (most cited first, 30 of 134)

- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Operator Learning: Algorithms and Analysis](https://mlsanity.com/paper/2402.15715/) (2024)
- [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)
- [Shape registration in the time of transformers](https://mlsanity.com/paper/2106.13679/) (2021)
- [Deformable 3D Gaussian Splatting for Animatable Human Avatars](https://mlsanity.com/paper/2312.15059/) (2023)
- [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022)
- [Accurate Point Cloud Registration with Robust Optimal Transport](https://mlsanity.com/paper/2111.00648/) (2021)
- [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)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [Zero-Shot 3D Shape Correspondence](https://mlsanity.com/paper/2306.03253/) (2023)
- [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)
- [Q-Match: Iterative Shape Matching via Quantum Annealing](https://mlsanity.com/paper/2105.02878/) (2021)
- [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)
- [ACID: Action-Conditional Implicit Visual Dynamics for Deformable Object Manipulation](https://mlsanity.com/paper/2203.06856/) (2022)
- [Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2303.10971/) (2023)
- [InterTrack: Tracking Human Object Interaction without Object Templates](https://mlsanity.com/paper/2408.13953/) (2024)
- [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)
- [Complex Functional Maps : a Conformal Link Between Tangent Bundles](https://mlsanity.com/paper/2112.09546/) (2021)
- [Partial-to-Partial Shape Matching with Geometric Consistency](https://mlsanity.com/paper/2404.12209/) (2024)

## Abstract (arXiv)

We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a deep residual network which takes dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and partiality.