# Shape Non-rigid Kinematics (SNK): A Zero-Shot Method for Non-Rigid Shape Matching via Unsupervised Functional Map Regularized Reconstruction

arXiv: https://arxiv.org/abs/2403.06804 · HTML: https://mlsanity.com/paper/2403.06804/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 86 references that are in the map.
- First posted on arXiv 11 Mar 2024.

## Builds on (most cited first, 30 of 40)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [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)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [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)
- [PointDAN: A Multi-Scale 3D Domain Adaption Network for Point Cloud Representation](https://mlsanity.com/paper/1911.02744/) (2019)
- [3D Point Capsule Networks](https://mlsanity.com/paper/1812.10775/) (2018)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (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)
- [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)
- [Partial Functional Correspondence](https://mlsanity.com/paper/1506.05274/) (2015)
- [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)
- [Shape registration in the time of transformers](https://mlsanity.com/paper/2106.13679/) (2021)
- [Deformable Shape Completion with Graph Convolutional Autoencoders](https://mlsanity.com/paper/1712.00268/) (2017)
- [Correspondence Learning via Linearly-invariant Embedding](https://mlsanity.com/paper/2010.13136/) (2020)
- [Building Statistical Shape Spaces for 3D Human Modeling](https://mlsanity.com/paper/1503.05860/) (2015)
- [Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching](https://mlsanity.com/paper/2204.13453/) (2022)

## Built on by (most cited first, 7 of 7)

- [DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matching](https://mlsanity.com/paper/2507.23715/) (2025)
- [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)
- [RINO: Rotation-Invariant Non-Rigid Correspondences](https://mlsanity.com/paper/2603.27773/) (2026)
- [ScanMove: Motion Prediction and Transfer for Unregistered Body Meshes](https://mlsanity.com/paper/2508.21095/) (2025)
- [SemMorph3D: Unsupervised Semantic-Aware 3D Morphing via Mesh-Guided Gaussians](https://mlsanity.com/paper/2510.02034/) (2025)
- [SGSoft: Learning Fused Semantic-Geometric Features for 3D Shape Correspondence via Template-Guided Soft Signals](https://mlsanity.com/paper/2605.18039/) (2026)

## Abstract (arXiv)

We present Shape Non-rigid Kinematics (SNK), a novel zero-shot method for non-rigid shape matching that eliminates the need for extensive training or ground truth data. SNK operates on a single pair of shapes, and employs a reconstruction-based strategy using an encoder-decoder architecture, which deforms the source shape to closely match the target shape. During the process, an unsupervised functional map is predicted and converted into a point-to-point map, serving as a supervisory mechanism for the reconstruction. To aid in training, we have designed a new decoder architecture that generates smooth, realistic deformations. SNK demonstrates competitive results on traditional benchmarks, simplifying the shape-matching process without compromising accuracy. Our code can be found online: https://github.com/pvnieo/SNK