# Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformations

arXiv: https://arxiv.org/abs/2209.02152 · HTML: https://mlsanity.com/paper/2209.02152/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 100 references that are in the map.
- First posted on arXiv 5 Sep 2022.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (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)
- [BEHAVE: Dataset and Method for Tracking Human Object Interactions](https://mlsanity.com/paper/2204.06950/) (2022)
- [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)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [LoopReg: Self-supervised Learning of Implicit Surface Correspondences, Pose and Shape for 3D Human Mesh Registration](https://mlsanity.com/paper/2010.12447/) (2020)
- [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)
- [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)
- [Smooth Shells: Multi-Scale Shape Registration with Functional Maps](https://mlsanity.com/paper/1905.12512/) (2019)
- [3DStyleNet: Creating 3D Shapes with Geometric and Texture Style Variations](https://mlsanity.com/paper/2108.12958/) (2021)
- [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)
- [Learned Vertex Descent: A New Direction for 3D Human Model Fitting](https://mlsanity.com/paper/2205.06254/) (2022)
- [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)
- [Cyclic Functional Mapping: Self-supervised correspondence between non-isometric deformable shapes](https://mlsanity.com/paper/1912.01249/) (2019)
- [Locally Linear Embedding and its Variants: Tutorial and Survey](https://mlsanity.com/paper/2011.10925/) (2020)
- [MADMM: a generic algorithm for non-smooth optimization on manifolds](https://mlsanity.com/paper/1505.07676/) (2015)
- [Self-Supervised Robust Scene Flow Estimation via the Alignment of Probability Density Functions](https://mlsanity.com/paper/2203.12193/) (2022)
- [Functional correspondence by matrix completion](https://mlsanity.com/paper/1412.8070/) (2014)

## Built on by (most cited first, 2 of 2)

- [Point2SSM++: Self-Supervised Learning of Anatomical Shape Models from Point Clouds](https://mlsanity.com/paper/2405.09707/) (2024)
- [LP2DH: A Locality-Preserving Pixel-Difference Hashing Framework for Dynamic Texture Recognition](https://mlsanity.com/paper/2604.15707/) (2026)

## Abstract (arXiv)

We present a new approach to unsupervised shape correspondence learning between pairs of point clouds. We make the first attempt to adapt the classical locally linear embedding algorithm (LLE) -- originally designed for nonlinear dimensionality reduction -- for shape correspondence. The key idea is to find dense correspondences between shapes by first obtaining high-dimensional neighborhood-preserving embeddings of low-dimensional point clouds and subsequently aligning the source and target embeddings using locally linear transformations. We demonstrate that learning the embedding using a new LLE-inspired point cloud reconstruction objective results in accurate shape correspondences. More specifically, the approach comprises an end-to-end learnable framework of extracting high-dimensional neighborhood-preserving embeddings, estimating locally linear transformations in the embedding space, and reconstructing shapes via divergence measure-based alignment of probabilistic density functions built over reconstructed and target shapes. Our approach enforces embeddings of shapes in correspondence to lie in the same universal/canonical embedding space, which eventually helps regularize the learning process and leads to a simple nearest neighbors approach between shape embeddings for finding reliable correspondences. Comprehensive experiments show that the new method makes noticeable improvements over state-of-the-art approaches on standard shape correspondence benchmark datasets covering both human and nonhuman shapes.