# Radon cumulative distribution transform subspace modeling for image classification

arXiv: https://arxiv.org/abs/2004.03669 · HTML: https://mlsanity.com/paper/2004.03669/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2020.

## Built on by (most cited first, 14 of 14)

- [The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification](https://mlsanity.com/paper/2106.02146/) (2021)
- [SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddings](https://mlsanity.com/paper/2112.05872/) (2021)
- [Invariance encoding in sliced-Wasserstein space for image classification with limited training data](https://mlsanity.com/paper/2201.02980/) (2022)
- [End-to-End Signal Classification in Signed Cumulative Distribution Transform Space](https://mlsanity.com/paper/2205.00348/) (2022)
- [Local Sliced-Wasserstein Feature Sets for Illumination-invariant Face Recognition](https://mlsanity.com/paper/2202.10642/) (2022)
- [Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification](https://mlsanity.com/paper/2506.08761/) (2025)
- [PTLp: Partial Transport Lp Distances](https://mlsanity.com/paper/2307.13571/) (2023)
- [Constrained Sliced Wasserstein Embedding](https://mlsanity.com/paper/2506.02203/) (2025)
- [The Radon Signed Cumulative Distribution Transform and its applications in classification of Signed Images](https://mlsanity.com/paper/2307.15339/) (2023)
- [Linear optimal transport subspaces for point set classification](https://mlsanity.com/paper/2403.10015/) (2024)
- [Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysis](https://mlsanity.com/paper/2206.01984/) (2022)
- [A sliced-Wasserstein distance-based approach for out-of-class-distribution detection](https://mlsanity.com/paper/2302.01459/) (2023)
- [Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition](https://mlsanity.com/paper/2512.08099/) (2025)
- [3D Transport-based Morphometry (3D-TBM) for medical image analysis](https://mlsanity.com/paper/2602.07260/) (2026)

## Abstract (arXiv)

We present a new supervised image classification method applicable to a broad class of image deformation models. The method makes use of the previously described Radon Cumulative Distribution Transform (R-CDT) for image data, whose mathematical properties are exploited to express the image data in a form that is more suitable for machine learning. While certain operations such as translation, scaling, and higher-order transformations are challenging to model in native image space, we show the R-CDT can capture some of these variations and thus render the associated image classification problems easier to solve. The method -- utilizing a nearest-subspace algorithm in R-CDT space -- is simple to implement, non-iterative, has no hyper-parameters to tune, is computationally efficient, label efficient, and provides competitive accuracies to state-of-the-art neural networks for many types of classification problems. In addition to the test accuracy performances, we show improvements (with respect to neural network-based methods) in terms of computational efficiency (it can be implemented without the use of GPUs), number of training samples needed for training, as well as out-of-distribution generalization. The Python code for reproducing our results is available at https://github.com/rohdelab/rcdt_ns_classifier.