# Mapping in a cycle: Sinkhorn regularized unsupervised learning for point cloud shapes

arXiv: https://arxiv.org/abs/2007.09594 · HTML: https://mlsanity.com/paper/2007.09594/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2020.

## Built on by (most cited first, 11 of 11)

- [Spatially and Spectrally Consistent Deep Functional Maps](https://mlsanity.com/paper/2308.08871/) (2023)
- [A Unified Framework for Implicit Sinkhorn Differentiation](https://mlsanity.com/paper/2205.06688/) (2022)
- [Sampling Network Guided Cross-Entropy Method for Unsupervised Point Cloud Registration](https://mlsanity.com/paper/2109.06619/) (2021)
- [Reliable Inlier Evaluation for Unsupervised Point Cloud Registration](https://mlsanity.com/paper/2202.11292/) (2022)
- [Discovering Relationships between Object Categories via Universal Canonical Maps](https://mlsanity.com/paper/2106.09758/) (2021)
- [Unseen Object 6D Pose Estimation: A Benchmark and Baselines](https://mlsanity.com/paper/2206.11808/) (2022)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [Planning with Learned Dynamic Model for Unsupervised Point Cloud Registration](https://mlsanity.com/paper/2108.02613/) (2021)
- [Learning ABCs: Approximate Bijective Correspondence for isolating factors of variation with weak supervision](https://mlsanity.com/paper/2103.03240/) (2021)
- [Point Cloud Registration-Driven Robust Feature Matching for 3D Siamese Object Tracking](https://mlsanity.com/paper/2209.06395/) (2022)
- [Overlap Bias Matching is Necessary for Point Cloud Registration](https://mlsanity.com/paper/2308.09364/) (2023)

## Abstract (arXiv)

We propose an unsupervised learning framework with the pretext task of finding dense correspondences between point cloud shapes from the same category based on the cycle-consistency formulation. In order to learn discriminative pointwise features from point cloud data, we incorporate in the formulation a regularization term based on Sinkhorn normalization to enhance the learned pointwise mappings to be as bijective as possible. Besides, a random rigid transform of the source shape is introduced to form a triplet cycle to improve the model's robustness against perturbations. Comprehensive experiments demonstrate that the learned pointwise features through our framework benefits various point cloud analysis tasks, e.g. partial shape registration and keypoint transfer. We also show that the learned pointwise features can be leveraged by supervised methods to improve the part segmentation performance with either the full training dataset or just a small portion of it.