# HOT-POT: Optimal Transport for Sparse Stereo Matching

arXiv: https://arxiv.org/abs/2601.12423 · HTML: https://mlsanity.com/paper/2601.12423/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 78 references that are in the map.
- First posted on arXiv 18 Jan 2026.

## Builds on (most cited first, 30 of 36)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [How far are we from solving the 2D & 3D Face Alignment problem? (and a dataset of 230,000 3D facial landmarks)](https://mlsanity.com/paper/1703.07332/) (2017)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [The MegaFace Benchmark: 1 Million Faces for Recognition at Scale](https://mlsanity.com/paper/1512.00596/) (2015)
- [Fake It Till You Make It: Face analysis in the wild using synthetic data alone](https://mlsanity.com/paper/2109.15102/) (2021)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [FLOT: Scene Flow on Point Clouds Guided by Optimal Transport](https://mlsanity.com/paper/2007.11142/) (2020)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [Facial Landmark Detection: a Literature Survey](https://mlsanity.com/paper/1805.05563/) (2018)
- [Hierarchical Optimal Transport for Document Representation](https://mlsanity.com/paper/1906.10827/) (2019)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Multi-marginal optimal transport: theory and applications](https://mlsanity.com/paper/1406.0026/) (2014)
- [Self-Point-Flow: Self-Supervised Scene Flow Estimation from Point Clouds with Optimal Transport and Random Walk](https://mlsanity.com/paper/2105.08248/) (2021)
- [Accurate Point Cloud Registration with Robust Optimal Transport](https://mlsanity.com/paper/2111.00648/) (2021)
- [On the Complexity of Approximating Multimarginal Optimal Transport](https://mlsanity.com/paper/1910.00152/) (2019)
- [Sliced Optimal Partial Transport](https://mlsanity.com/paper/2212.08049/) (2022)
- [Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2402.04613/) (2024)
- [FAB: A Robust Facial Landmark Detection Framework for Motion-Blurred Videos](https://mlsanity.com/paper/1910.12100/) (2019)
- [H-Net: Unsupervised Attention-based Stereo Depth Estimation Leveraging Epipolar Geometry](https://mlsanity.com/paper/2104.11288/) (2021)
- [Unbalanced Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2103.10854/) (2021)
- [Flowing Datasets with Wasserstein over Wasserstein Gradient Flows](https://mlsanity.com/paper/2506.07534/) (2025)
- [DASC: Robust Dense Descriptor for Multi-modal and Multi-spectral Correspondence Estimation](https://mlsanity.com/paper/1604.07944/) (2016)
- [Parallelly Sliced Optimal Transport on Spheres and on the Rotation Group](https://mlsanity.com/paper/2401.16896/) (2024)
- [Lightspeed Geometric Dataset Distance via Sliced Optimal Transport](https://mlsanity.com/paper/2501.18901/) (2025)
- [Lagrangian Motion Magnification with Double Sparse Optical Flow Decomposition](https://mlsanity.com/paper/2204.07636/) (2022)
- [On Partial Optimal Transport: Revising the Infeasibility of Sinkhorn and Efficient Gradient Methods](https://mlsanity.com/paper/2312.13970/) (2023)
- [T-FAKE: Synthesizing Thermal Images for Facial Landmarking](https://mlsanity.com/paper/2408.15127/) (2024)
- [Slicing the Gaussian Mixture Wasserstein Distance](https://mlsanity.com/paper/2504.08544/) (2025)

## Abstract (arXiv)

Stereo vision between images faces a range of challenges, including occlusions, motion, and camera distortions, across applications in autonomous driving, robotics, and face analysis. Due to parameter sensitivity, further complications arise for stereo matching with sparse features, such as facial landmarks. To overcome this ill-posedness and enable unsupervised sparse matching, we consider line constraints of the camera geometry from an optimal transport (OT) viewpoint. Formulating camera-projected points as (half)lines, we propose the use of the classical epipolar distance as well as a 3D ray distance to quantify matching quality. Employing these distances as a cost function of a (partial) OT problem, we arrive at efficiently solvable assignment problems. Moreover, we extend our approach to unsupervised object matching by formulating it as a hierarchical OT problem. The resulting algorithms allow for efficient feature and object matching, as demonstrated in our numerical experiments. Here, we focus on applications in facial analysis, where we aim to match distinct landmarking conventions.