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The Radon cumulative distribution transform and its application to image classification

arXiv 1511.03206 ↗First posted 10 Nov 2015cs.CVcited by 28

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Abstract (arXiv)

Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier, Wavelet, etc.) are linear transforms, and, by themselves, are unable to substantially simplify the representation of image classes for classification. Here we describe a nonlinear, invertible, low-level image processing transform based on combining the well known Radon transform for image data, and the 1D Cumulative Distribution Transform proposed earlier. We describe a few of the properties of this new transform, and with both theoretical and experimental results show that it can often render certain problems linearly separable in transform space.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). First posted on arXiv 10 Nov 2015.

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Citing papers per year: 2021: 3; 2022: 7; 2023: 8; 2024: 2; 2025: 8.

28 papers.

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  1. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  2. 2022Sliced Optimal Partial Transportcited by 20
  3. 2022Generalized One-shot Domain Adaptation of Generative Adversarial Networkscited by 19
  4. 2022Wassmap: Wasserstein Isometric Mapping for Image Manifold Learningcited by 15
  5. 2022Supervised learning of sheared distributions using linearized optimal transportcited by 14
  6. 2023Set Features for Fine-grained Anomaly Detectioncited by 13
  7. 2021The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classificationcited by 9
  8. 2021SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddingscited by 9
  9. 2025A Novel Sliced Fused Gromov-Wasserstein Distancecited by 9
  10. 2025Fourier Sliced-Wasserstein Embedding for Multisets and Measurescited by 8
  11. 2022Invariance encoding in sliced-Wasserstein space for image classification with limited training datacited by 7
  12. 2025Slicing the Gaussian Mixture Wasserstein Distancecited by 7
16 more
  1. 2023Applications of No-Collision Transportation Maps in Manifold Learningcited by 6
  2. 2021Identifying Women with Mammographically-Occult Breast Cancer Leveraging GAN-Simulated Mammogramscited by 5
  3. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  4. 2022Local Sliced-Wasserstein Feature Sets for Illumination-invariant Face Recognitioncited by 4
  5. 2025Fast rigid alignment of heterogeneous images in sliced Wasserstein distancecited by 4
  6. 2023Set Features for Anomaly Detectioncited by 3
  7. 2025Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classificationcited by 3
  8. 2023PTLp: Partial Transport Lp Distancescited by 2
  9. 2023Partial Transport for Point-Cloud Registrationcited by 2
  10. 2025Constrained Sliced Wasserstein Embeddingcited by 2
  11. 2022Time Series Anomaly Detection by Cumulative Radon Featurescited by 1
  12. 2023The Radon Signed Cumulative Distribution Transform and its applications in classification of Signed Imagescited by 1
  13. 2024Max-sliced Wasserstein concentration and uniform ratio bounds of empirical measures on RKHScited by 1
  14. 2023A sliced-Wasserstein distance-based approach for out-of-class-distribution detectioncited by 0
  15. 2024Fourier Sliced-Wasserstein Embedding for Multisets and Measurescited by 0
  16. 2025Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognitioncited by 0