# Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition

arXiv: https://arxiv.org/abs/2512.08099 · HTML: https://mlsanity.com/paper/2512.08099/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 64 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 26 of 26)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Unsupervised Alignment of Embeddings with Wasserstein Procrustes](https://mlsanity.com/paper/1805.11222/) (2018)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [Sliced Gromov-Wasserstein](https://mlsanity.com/paper/1905.10124/) (2019)
- [The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation](https://mlsanity.com/paper/2009.04266/) (2020)
- [Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations](https://mlsanity.com/paper/2008.09165/) (2020)
- [The Radon cumulative distribution transform and its application to image classification](https://mlsanity.com/paper/1511.03206/) (2015)
- [The Cumulative Distribution Transform and Linear Pattern Classification](https://mlsanity.com/paper/1507.05936/) (2015)
- [On a linear Gromov-Wasserstein distance](https://mlsanity.com/paper/2112.11964/) (2021)
- [Radon cumulative distribution transform subspace modeling for image classification](https://mlsanity.com/paper/2004.03669/) (2020)
- [Parallelly Sliced Optimal Transport on Spheres and on the Rotation Group](https://mlsanity.com/paper/2401.16896/) (2024)
- [The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification](https://mlsanity.com/paper/2106.02146/) (2021)
- [A Novel Sliced Fused Gromov-Wasserstein Distance](https://mlsanity.com/paper/2508.02364/) (2025)
- [On Assignment Problems Related to Gromov-Wasserstein Distances on the Real Line](https://mlsanity.com/paper/2205.09006/) (2022)
- [Intrinsic Sliced Wasserstein Distances for Comparing Collections of Probability Distributions on Manifolds and Graphs](https://mlsanity.com/paper/2010.15285/) (2020)
- [Invariance encoding in sliced-Wasserstein space for image classification with limited training data](https://mlsanity.com/paper/2201.02980/) (2022)
- [Slicing the Gaussian Mixture Wasserstein Distance](https://mlsanity.com/paper/2504.08544/) (2025)
- [Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Space](https://mlsanity.com/paper/2310.11256/) (2023)
- [Fast rigid alignment of heterogeneous images in sliced Wasserstein distance](https://mlsanity.com/paper/2503.13756/) (2025)
- [Interpolating between Optimal Transport and KL regularized Optimal Transport using R'enyi Divergences](https://mlsanity.com/paper/2404.18834/) (2024)
- [Data representation with optimal transport](https://mlsanity.com/paper/2406.15503/) (2024)
- [Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification](https://mlsanity.com/paper/2506.08761/) (2025)
- [An in depth look at the Procrustes-Wasserstein distance: properties and barycenters](https://mlsanity.com/paper/2507.00894/) (2025)
- [Unsupervised Ground Metric Learning](https://mlsanity.com/paper/2507.13094/) (2025)

## Abstract (arXiv)

The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely related to the sliced Wasserstein distance and facilitates classification tasks, especially in the small data regime, like the recognition of watermarks in filigranology. Here, a typical issue is that the given data may be subject to affine transformations caused by the measuring process. To make the R-CDT invariant under arbitrary affine transformations, a two-step normalization of the R-CDT has been proposed in our earlier works. The aim of this paper is twofold. First, we propose a family of generalized normalizations to enhance flexibility for applications. Second, we study multi-dimensional and non-Euclidean settings by making use of generalized Radon transforms. We prove that our novel feature representations are invariant under certain transformations and allow for linear separation in feature space. Our theoretical results are supported by numerical experiments based on 2d images, 3d shapes and 3d rotation matrices, showing near perfect classification accuracies and clustering results.