# Partial Wasserstein Adversarial Network for Non-rigid Point Set Registration

arXiv: https://arxiv.org/abs/2203.02227 · HTML: https://mlsanity.com/paper/2203.02227/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 55 references that are in the map.
- First posted on arXiv 4 Mar 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2001.06937/) (2020)
- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Learning with minibatch Wasserstein : asymptotic and gradient properties](https://mlsanity.com/paper/1910.04091/) (2019)
- [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://mlsanity.com/paper/1610.06519/) (2016)
- [Sliced Wasserstein Kernels for Probability Distributions](https://mlsanity.com/paper/1511.03198/) (2015)
- [PCRNet: Point Cloud Registration Network using PointNet Encoding](https://mlsanity.com/paper/1908.07906/) (2019)
- [Sinkhorn Divergences for Unbalanced Optimal Transport](https://mlsanity.com/paper/1910.12958/) (2019)
- [SurfelWarp: Efficient Non-Volumetric Single View Dynamic Reconstruction](https://mlsanity.com/paper/1904.13073/) (2019)
- [Imaging with Kantorovich-Rubinstein discrepancy](https://mlsanity.com/paper/1407.0221/) (2014)
- [A Framework for Wasserstein-1-Type Metrics](https://mlsanity.com/paper/1701.01945/) (2017)
- [Adversarial Partial Multi-Label Learning](https://mlsanity.com/paper/1909.06717/) (2019)
- [From 2D to 3D Geodesic-based Garment Matching](https://mlsanity.com/paper/1809.08064/) (2018)

## Built on by (most cited first, 5 of 5)

- [Partial Transport for Point-Cloud Registration](https://mlsanity.com/paper/2309.15787/) (2023)
- [Partial Distribution Matching via Partial Wasserstein Adversarial Networks](https://mlsanity.com/paper/2409.10499/) (2024)
- [Theoretical Performance Guarantees for Partial Domain Adaptation via Partial Optimal Transport](https://mlsanity.com/paper/2506.02712/) (2025)
- [Tracking Temporal Dynamics of Vector Sets with Gaussian Process](https://mlsanity.com/paper/2512.15538/) (2025)
- [Accelerated Sinkhorn Algorithms for Partial Optimal Transport](https://mlsanity.com/paper/2601.17196/) (2026)

## Abstract (arXiv)

Given two point sets, the problem of registration is to recover a transformation that matches one set to the other. This task is challenging due to the presence of the large number of outliers, the unknown non-rigid deformations and the large sizes of point sets. To obtain strong robustness against outliers, we formulate the registration problem as a partial distribution matching (PDM) problem, where the goal is to partially match the distributions represented by point sets in a metric space. To handle large point sets, we propose a scalable PDM algorithm by utilizing the efficient partial Wasserstein-1 (PW) discrepancy. Specifically, we derive the Kantorovich-Rubinstein duality for the PW discrepancy, and show its gradient can be explicitly computed. Based on these results, we propose a partial Wasserstein adversarial network (PWAN), which is able to approximate the PW discrepancy by a neural network, and minimize it by gradient descent. In addition, it also incorporates an efficient coherence regularizer for non-rigid transformations to avoid unrealistic deformations. We evaluate PWAN on practical point set registration tasks, and show that the proposed PWAN is robust, scalable and performs more favorably than the state-of-the-art methods.