# Joint Symmetry Detection and Shape Matching for Non-Rigid Point Cloud

arXiv: https://arxiv.org/abs/2112.02713 · HTML: https://mlsanity.com/paper/2112.02713/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 5 Dec 2021.

## Builds on (most cited first, 28 of 28)

- [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)
- [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)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [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)
- [Deep Shells: Unsupervised Shape Correspondence with Optimal Transport](https://mlsanity.com/paper/2010.15261/) (2020)
- [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)
- [ZoomOut: Spectral Upsampling for Efficient Shape Correspondence](https://mlsanity.com/paper/1904.07865/) (2019)
- [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)
- [Fast and Accurate Intrinsic Symmetry Detection](https://mlsanity.com/paper/1807.10162/) (2018)
- [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)
- [Foreground Clustering for Joint Segmentation and Localization in Videos and Images](https://mlsanity.com/paper/1811.10121/) (2018)

## Abstract (arXiv)

Despite the success of deep functional maps in non-rigid 3D shape matching, there exists no learning framework that models both self-symmetry and shape matching simultaneously. This is despite the fact that errors due to symmetry mismatch are a major challenge in non-rigid shape matching. In this paper, we propose a novel framework that simultaneously learns both self symmetry as well as a pairwise map between a pair of shapes. Our key idea is to couple a self symmetry map and a pairwise map through a regularization term that provides a joint constraint on both of them, thereby, leading to more accurate maps. We validate our method on several benchmarks where it outperforms many competitive baselines on both tasks.