# Unsupervised Point Cloud Completion through Unbalanced Optimal Transport

arXiv: https://arxiv.org/abs/2410.02671 · HTML: https://mlsanity.com/paper/2410.02671/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 43 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Builds on (most cited first, 27 of 27)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [Stabilizing Training of Generative Adversarial Networks through Regularization](https://mlsanity.com/paper/1705.09367/) (2017)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation](https://mlsanity.com/paper/2010.05862/) (2020)
- [Generative Modeling with Optimal Transport Maps](https://mlsanity.com/paper/2110.02999/) (2021)
- [Unsupervised 3D Shape Completion through GAN Inversion](https://mlsanity.com/paper/2104.13366/) (2021)
- [Unpaired Point Cloud Completion on Real Scans using Adversarial Training](https://mlsanity.com/paper/1904.00069/) (2019)
- [Multimodal Shape Completion via Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2003.07717/) (2020)
- [Cycle4Completion: Unpaired Point Cloud Completion using Cycle Transformation with Missing Region Coding](https://mlsanity.com/paper/2103.07838/) (2021)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transport](https://mlsanity.com/paper/2305.14777/) (2023)
- [Neural Monge Map estimation and its applications](https://mlsanity.com/paper/2106.03812/) (2021)
- [Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translation](https://mlsanity.com/paper/2311.15100/) (2023)
- [ASFM-Net: Asymmetrical Siamese Feature Matching Network for Point Completion](https://mlsanity.com/paper/2104.09587/) (2021)
- [Learning Local Displacements for Point Cloud Completion](https://mlsanity.com/paper/2203.16600/) (2022)
- [Analyzing and Improving Optimal-Transport-based Adversarial Networks](https://mlsanity.com/paper/2310.02611/) (2023)

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

- [Overcoming Spurious Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plan](https://mlsanity.com/paper/2502.04583/) (2025)

## Abstract (arXiv)

Unpaired point cloud completion is crucial for real-world applications, where ground-truth data for complete point clouds are often unavailable. By learning a completion map from unpaired incomplete and complete point cloud data, this task avoids the reliance on paired datasets. In this paper, we propose the textitUnbalanced Optimal Transport Map for Unpaired Point Cloud Completion (UOT-UPC) model, which formulates the unpaired completion task as the (Unbalanced) Optimal Transport (OT) problem. Our method employs a Neural OT model learning the UOT map using neural networks. Our model is the first attempt to leverage UOT for unpaired point cloud completion, achieving competitive or superior performance on both single-category and multi-category benchmarks. In particular, our approach is especially robust under the class imbalance problem, which is frequently encountered in real-world unpaired point cloud completion scenarios. The code is available at https://github.com/LEETK99/UOT-UPC.