# Deformation-Guided Unsupervised Non-Rigid Shape Matching

arXiv: https://arxiv.org/abs/2311.15668 · HTML: https://mlsanity.com/paper/2311.15668/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 27 Nov 2023.

## Builds on (most cited first, 20 of 20)

- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [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)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [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)
- [Deep Shells: Unsupervised Shape Correspondence with Optimal Transport](https://mlsanity.com/paper/2010.15261/) (2020)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [CorrNet3D: Unsupervised End-to-end Learning of Dense Correspondence for 3D Point Clouds](https://mlsanity.com/paper/2012.15638/) (2020)
- [Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching](https://mlsanity.com/paper/2204.13453/) (2022)
- [Dual Geometric Graph Network (DG2N) -- Iterative network for deformable shape alignment](https://mlsanity.com/paper/2011.14723/) (2020)
- [Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching](https://mlsanity.com/paper/2210.06373/) (2022)
- [Cyclic Functional Mapping: Self-supervised correspondence between non-isometric deformable shapes](https://mlsanity.com/paper/1912.01249/) (2019)
- [Unsupervised cycle-consistent deformation for shape matching](https://mlsanity.com/paper/1907.03165/) (2019)
- [4DHumanOutfit: a multi-subject 4D dataset of human motion sequences in varying outfits exhibiting large displacements](https://mlsanity.com/paper/2306.07399/) (2023)
- [A structured latent space for human body motion generation](https://mlsanity.com/paper/2106.04387/) (2021)
- [Neural Human Deformation Transfer](https://mlsanity.com/paper/2109.01588/) (2021)

## Built on by (most cited first, 3 of 3)

- [DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matching](https://mlsanity.com/paper/2507.23715/) (2025)
- [NF3DM: Combining Neural Fields and Deformation Models for 3D Non-Rigid Motion Reconstruction](https://mlsanity.com/paper/2412.08511/) (2024)
- [Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach](https://mlsanity.com/paper/2509.06862/) (2025)

## Abstract (arXiv)

We present an unsupervised data-driven approach for non-rigid shape matching. Shape matching identifies correspondences between two shapes and is a fundamental step in many computer vision and graphics applications. Our approach is designed to be particularly robust when matching shapes digitized using 3D scanners that contain fine geometric detail and suffer from different types of noise including topological noise caused by the coalescence of spatially close surface regions. We build on two strategies. First, using a hierarchical patch based shape representation we match shapes consistently in a coarse to fine manner, allowing for robustness to noise. This multi-scale representation drastically reduces the dimensionality of the problem when matching at the coarsest scale, rendering unsupervised learning feasible. Second, we constrain this hierarchical matching to be reflected in 3D by fitting a patch-wise near-rigid deformation model. Using this constraint, we leverage spatial continuity at different scales to capture global shape properties, resulting in matchings that generalize well to data with different deformations and noise characteristics. Experiments demonstrate that our approach obtains significantly better results on raw 3D scans than state-of-the-art methods, while performing on-par on standard test scenarios.