# Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching

arXiv: https://arxiv.org/abs/2210.06373 · HTML: https://mlsanity.com/paper/2210.06373/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 64 references that are in the map.
- First posted on arXiv 12 Oct 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Learning from Synthetic Humans](https://mlsanity.com/paper/1701.01370/) (2017)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [4DComplete: Non-Rigid Motion Estimation Beyond the Observable Surface](https://mlsanity.com/paper/2105.01905/) (2021)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [Unsupervised Deep Learning for Structured Shape Matching](https://mlsanity.com/paper/1812.03794/) (2018)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [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)
- [Smooth Shells: Multi-Scale Shape Registration with Functional Maps](https://mlsanity.com/paper/1905.12512/) (2019)
- [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)
- [Shape registration in the time of transformers](https://mlsanity.com/paper/2106.13679/) (2021)
- [CNNs on Surfaces using Rotation-Equivariant Features](https://mlsanity.com/paper/2006.01570/) (2020)
- [Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization](https://mlsanity.com/paper/2210.02870/) (2022)
- [Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching](https://mlsanity.com/paper/2204.13453/) (2022)
- [Multi-directional Geodesic Neural Networks via Equivariant Convolution](https://mlsanity.com/paper/1810.02303/) (2018)
- [Cyclic Functional Mapping: Self-supervised correspondence between non-isometric deformable shapes](https://mlsanity.com/paper/1912.01249/) (2019)
- [SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondence](https://mlsanity.com/paper/2209.07806/) (2022)
- [Unsupervised Dense Shape Correspondence using Heat Kernels](https://mlsanity.com/paper/2010.12682/) (2020)

## Built on by (most cited first, 30 of 35)

- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [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)
- [Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching](https://mlsanity.com/paper/2312.03678/) (2023)
- [Partial-to-Partial Shape Matching with Geometric Consistency](https://mlsanity.com/paper/2404.12209/) (2024)
- [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)
- [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)
- [GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models](https://mlsanity.com/paper/2304.10523/) (2023)
- [Zero-Shot Image Feature Consensus with Deep Functional Maps](https://mlsanity.com/paper/2403.12038/) (2024)
- [DV-Matcher: Deformation-based Non-Rigid Point Cloud Matching Guided by Pre-trained Visual Features](https://mlsanity.com/paper/2408.08568/) (2024)
- [DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matching](https://mlsanity.com/paper/2507.23715/) (2025)
- [Revisiting Map Relations for Unsupervised Non-Rigid Shape Matching](https://mlsanity.com/paper/2310.11420/) (2023)
- [DiscoMatch: Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matching](https://mlsanity.com/paper/2310.08230/) (2023)
- [Synchronous Diffusion for Unsupervised Smooth Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2407.08244/) (2024)
- [Stable-SCore: A Stable Registration-based Framework for 3D Shape Correspondence](https://mlsanity.com/paper/2503.21766/) (2025)
- [AtomSurf : Surface Representation for Learning on Protein Structures](https://mlsanity.com/paper/2309.16519/) (2023)
- [Fast Globally Optimal and Geometrically Consistent 3D Shape Matching](https://mlsanity.com/paper/2504.06385/) (2025)
- [FRIDU: Functional Map Refinement with Guided Image Diffusion](https://mlsanity.com/paper/2506.14322/) (2025)
- [Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities](https://mlsanity.com/paper/2604.01274/) (2026)
- [Deformation-Guided Unsupervised Non-Rigid Shape Matching](https://mlsanity.com/paper/2311.15668/) (2023)
- [SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularization](https://mlsanity.com/paper/2603.12937/) (2026)
- [DcMatch: Unsupervised Multi-Shape Matching with Dual-Level Consistency](https://mlsanity.com/paper/2509.01204/) (2025)
- [Universal 3D Shape Matching via Coarse-to-Fine Language Guidance](https://mlsanity.com/paper/2602.19112/) (2026)
- [GLASS: Graph and Vision-Language Assisted Semantic Shape Correspondence](https://mlsanity.com/paper/2603.07652/) (2026)
- [DeepShapeMatchingKit: Accelerated Functional Map Solver and Shape Matching Pipelines Revisited](https://mlsanity.com/paper/2604.10377/) (2026)
- [Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matching](https://mlsanity.com/paper/2606.30131/) (2026)
- [Deep Frequency-Aware Functional Maps for Robust Shape Matching](https://mlsanity.com/paper/2402.03904/) (2024)

## Abstract (arXiv)

In this work, we present a novel non-rigid shape matching framework based on multi-resolution functional maps with spectral attention. Existing functional map learning methods all rely on the critical choice of the spectral resolution hyperparameter, which can severely affect the overall accuracy or lead to overfitting, if not chosen carefully. In this paper, we show that spectral resolution tuning can be alleviated by introducing spectral attention. Our framework is applicable in both supervised and unsupervised settings, and we show that it is possible to train the network so that it can adapt the spectral resolution, depending on the given shape input. More specifically, we propose to compute multi-resolution functional maps that characterize correspondence across a range of spectral resolutions, and introduce a spectral attention network that helps to combine this representation into a single coherent final correspondence. Our approach is not only accurate with near-isometric input, for which a high spectral resolution is typically preferred, but also robust and able to produce reasonable matching even in the presence of significant non-isometric distortion, which poses great challenges to existing methods. We demonstrate the superior performance of our approach through experiments on a suite of challenging near-isometric and non-isometric shape matching benchmarks.