# Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification

arXiv: https://arxiv.org/abs/2506.08761 · HTML: https://mlsanity.com/paper/2506.08761/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [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)
- [Partitioning signal classes using transport transforms for data analysis and machine learning](https://mlsanity.com/paper/2008.03452/) (2020)
- [Radon cumulative distribution transform subspace modeling for image classification](https://mlsanity.com/paper/2004.03669/) (2020)
- [Linearized Wasserstein dimensionality reduction with approximation guarantees](https://mlsanity.com/paper/2302.07373/) (2023)
- [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)
- [On Assignment Problems Related to Gromov-Wasserstein Distances on the Real Line](https://mlsanity.com/paper/2205.09006/) (2022)
- [Invariance encoding in sliced-Wasserstein space for image classification with limited training data](https://mlsanity.com/paper/2201.02980/) (2022)
- [Local Sliced-Wasserstein Feature Sets for Illumination-invariant Face Recognition](https://mlsanity.com/paper/2202.10642/) (2022)

## Built on by (most cited first, 3 of 3)

- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Unsupervised Ground Metric Learning](https://mlsanity.com/paper/2507.13094/) (2025)
- [Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition](https://mlsanity.com/paper/2512.08099/) (2025)

## Abstract (arXiv)

The Radon cumulative distribution transform (R-CDT), is an easy-to-compute feature extractor that facilitates image classification tasks especially in the small data regime. It is closely related to the sliced Wasserstein distance and provably guaranties the linear separability of image classes that emerge from translations or scalings. In many real-world applications, like the recognition of watermarks in filigranology, however, the data is subject to general affine transformations originating from the measurement process. To overcome this issue, we recently introduced the so-called max-normalized R-CDT that only requires elementary operations and guaranties the separability under arbitrary affine transformations. The aim of this paper is to continue our study of the max-normalized R-CDT especially with respect to its robustness against non-affine image deformations. Our sensitivity analysis shows that its separability properties are stable provided the Wasserstein-infinity distance between the samples can be controlled. Since the Wasserstein-infinity distance only allows small local image deformations, we moreover introduce a mean-normalized version of the R-CDT. In this case, robustness relates to the Wasserstein-2 distance and also covers image deformations caused by impulsive noise for instance. Our theoretical results are supported by numerical experiments showing the effectiveness of our novel feature extractors as well as their robustness against local non-affine deformations and impulsive noise.