# Learning Canonical Embedding for Non-rigid Shape Matching

arXiv: https://arxiv.org/abs/2110.02994 · HTML: https://mlsanity.com/paper/2110.02994/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 25 of 25)

- [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)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [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-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)
- [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)
- [Continuous Surface Embeddings](https://mlsanity.com/paper/2011.12438/) (2020)
- [Continuous and Orientation-preserving Correspondences via Functional Maps](https://mlsanity.com/paper/1806.04455/) (2018)
- [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)
- [VConv-DAE: Deep Volumetric Shape Learning Without Object Labels](https://mlsanity.com/paper/1604.03755/) (2016)
- [Correspondence Learning via Linearly-invariant Embedding](https://mlsanity.com/paper/2010.13136/) (2020)
- [Cyclic Functional Mapping: Self-supervised correspondence between non-isometric deformable shapes](https://mlsanity.com/paper/1912.01249/) (2019)
- [Dense Human Body Correspondences Using Convolutional Networks](https://mlsanity.com/paper/1511.05904/) (2015)
- [Unsupervised Learning of Category-Specific Symmetric 3D Keypoints from Point Sets](https://mlsanity.com/paper/2003.07619/) (2020)
- [A Functional Representation for Graph Matching](https://mlsanity.com/paper/1901.05179/) (2019)
- [MapTree: Recovering Multiple Solutions in the Space of Maps](https://mlsanity.com/paper/2006.02532/) (2020)
- [Wavelet-based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis](https://mlsanity.com/paper/2007.11632/) (2020)
- [Weakly Supervised Deep Functional Map for Shape Matching](https://mlsanity.com/paper/2009.13339/) (2020)
- [SymmetryNet: Learning to Predict Reflectional and Rotational Symmetries of 3D Shapes from Single-View RGB-D Images](https://mlsanity.com/paper/2008.00485/) (2020)
- [Matrix Decomposition on Graphs: A Functional View](https://mlsanity.com/paper/2102.03233/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformations](https://mlsanity.com/paper/2209.02152/) (2022)

## Abstract (arXiv)

This paper provides a novel framework that learns canonical embeddings for non-rigid shape matching. In contrast to prior work in this direction, our framework is trained end-to-end and thus avoids instabilities and constraints associated with the commonly-used Laplace-Beltrami basis or sequential optimization schemes. On multiple datasets, we demonstrate that learning self symmetry maps with a deep functional map projects 3D shapes into a low dimensional canonical embedding that facilitates non-rigid shape correspondence via a simple nearest neighbor search. Our framework outperforms multiple recent learning based methods on FAUST and SHREC benchmarks while being computationally cheaper, data-efficient, and robust.