# Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matching

arXiv: https://arxiv.org/abs/2211.14604 · HTML: https://mlsanity.com/paper/2211.14604/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 102 references that are in the map.
- First posted on arXiv 26 Nov 2022.

## Builds on (most cited first, 30 of 39)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [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)
- [Panoptic Studio: A Massively Multiview System for Social Interaction Capture](https://mlsanity.com/paper/1612.03153/) (2016)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [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)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [Neural Cages for Detail-Preserving 3D Deformations](https://mlsanity.com/paper/1912.06395/) (2019)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [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)
- [VolumeDeform: Real-time Volumetric Non-rigid Reconstruction](https://mlsanity.com/paper/1603.08161/) (2016)
- [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)
- [3DN: 3D Deformation Network](https://mlsanity.com/paper/1903.03322/) (2019)
- [LIMP: Learning Latent Shape Representations with Metric Preservation Priors](https://mlsanity.com/paper/2003.12283/) (2020)
- [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)
- [CorrNet3D: Unsupervised End-to-end Learning of Dense Correspondence for 3D Point Clouds](https://mlsanity.com/paper/2012.15638/) (2020)
- [Joint Learning of 3D Shape Retrieval and Deformation](https://mlsanity.com/paper/2101.07889/) (2021)
- [ZoomOut: Spectral Upsampling for Efficient Shape Correspondence](https://mlsanity.com/paper/1904.07865/) (2019)

## Built on by (most cited first, 8 of 8)

- [Template Free Reconstruction of Human-object Interaction with Procedural Interaction Generation](https://mlsanity.com/paper/2312.07063/) (2023)
- [NICP: Neural ICP for 3D Human Registration at Scale](https://mlsanity.com/paper/2312.14024/) (2023)
- [Advancing Bayesian Optimization via Learning Correlated Latent Space](https://mlsanity.com/paper/2310.20258/) (2023)
- [textttNePhi: Neural Deformation Fields for Approximately Diffeomorphic Medical Image Registration](https://mlsanity.com/paper/2309.07322/) (2023)
- [Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities](https://mlsanity.com/paper/2604.01274/) (2026)
- [SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registration](https://mlsanity.com/paper/2405.20188/) (2024)
- [MeshLoom: Feed-Forward Non-Rigid Registration of Mesh Sequences](https://mlsanity.com/paper/2606.17027/) (2026)
- [Ordered Diffusion for 3D Human Registration](https://mlsanity.com/paper/2608.05804/) (2026)

## Abstract (arXiv)

In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a general-purpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness. With this reduction in degrees of freedom, we show significant improvement in terms of data-efficiency thus enabling limited supervision. Furthermore, our approximation provides direct access to first-order derivatives of deformation fields, which facilitates enforcing desirable regularization effectively. Our resulting model has high expressive power and is able to capture complex deformations. We illustrate its effectiveness through state-of-the-art results across multiple deformable shape matching benchmarks. Our code and data are publicly available at: https://github.com/Sentient07/DeformationBasis.