# DPFM: Deep Partial Functional Maps

arXiv: https://arxiv.org/abs/2110.09994 · HTML: https://mlsanity.com/paper/2110.09994/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 67 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [PointContrast: Unsupervised Pre-training for 3D Point Cloud Understanding](https://mlsanity.com/paper/2007.10985/) (2020)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [PRNet: Self-Supervised Learning for Partial-to-Partial Registration](https://mlsanity.com/paper/1910.12240/) (2019)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Activation Functions: Comparison of trends in Practice and Research for Deep Learning](https://mlsanity.com/paper/1811.03378/) (2018)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [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)
- [Partial Functional Correspondence](https://mlsanity.com/paper/1506.05274/) (2015)
- [Building Statistical Shape Spaces for 3D Human Modeling](https://mlsanity.com/paper/1503.05860/) (2015)
- [CNNs on Surfaces using Rotation-Equivariant Features](https://mlsanity.com/paper/2006.01570/) (2020)
- [Multi-directional Geodesic Neural Networks via Equivariant Convolution](https://mlsanity.com/paper/1810.02303/) (2018)

## Built on by (most cited first, 30 of 58)

- [Lepard: Learning partial point cloud matching in rigid and deformable scenes](https://mlsanity.com/paper/2111.12591/) (2021)
- [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)
- [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022)
- [Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching](https://mlsanity.com/paper/2210.06373/) (2022)
- [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)
- [Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2303.10971/) (2023)
- [NICP: Neural ICP for 3D Human Registration at Scale](https://mlsanity.com/paper/2312.14024/) (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)
- [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)
- [Geometric Retargeting: A Principled, Ultrafast Neural Hand Retargeting Algorithm](https://mlsanity.com/paper/2503.07541/) (2025)
- [SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondence](https://mlsanity.com/paper/2209.07806/) (2022)
- [Geometrically Consistent Partial Shape Matching](https://mlsanity.com/paper/2309.05013/) (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)
- [On Unsupervised Partial Shape Correspondence](https://mlsanity.com/paper/2310.14692/) (2023)
- [Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Surface Matching Algorithms](https://mlsanity.com/paper/2411.03511/) (2024)
- [Zero-Shot Image Feature Consensus with Deep Functional Maps](https://mlsanity.com/paper/2403.12038/) (2024)
- [Finsler-Laplace-Beltrami Operators with Application to Shape Analysis](https://mlsanity.com/paper/2404.03999/) (2024)
- [DV-Matcher: Deformation-based Non-Rigid Point Cloud Matching Guided by Pre-trained Visual Features](https://mlsanity.com/paper/2408.08568/) (2024)
- [G-MSM: Unsupervised Multi-Shape Matching with Graph-based Affinity Priors](https://mlsanity.com/paper/2212.02910/) (2022)
- [Learning Harmonic Molecular Representations on Riemannian Manifold](https://mlsanity.com/paper/2303.15520/) (2023)
- [Revisiting Map Relations for Unsupervised Non-Rigid Shape Matching](https://mlsanity.com/paper/2310.11420/) (2023)

## Abstract (arXiv)

We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given hand-crafted shape descriptors. In this paper, we propose the first learning method aimed directly at partial non-rigid shape correspondence. Our approach uses the functional map framework, can be trained in a supervised or unsupervised manner, and learns descriptors directly from the data, thus both improving robustness and accuracy in challenging cases. Furthermore, unlike existing techniques, our method is also applicable to partial-to-partial non-rigid matching, in which the common regions on both shapes are unknown a priori. We demonstrate that the resulting method is data-efficient, and achieves state-of-the-art results on several benchmark datasets. Our code and data can be found online: https://github.com/pvnieo/DPFM