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

• URL: http://arxiv.org/abs/2512.08099v1
• Date: Mon, 08 Dec 2025 23:16:19 GMT
• Title: Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition
• Authors: Matthias Beckmann, Robert Beinert, Jonas Bresch,
• Abstract summary: The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images.<n>We show that our novel feature representations are invariant under certain transformations and allow for linear separation in feature space.
• Score: 1.4018975578160688
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensions [0.9940728137241214]
  gradient flows of the Kullback--Leibler divergence evolve a distribution toward a target density known only up to a normalizing constant.<n>We introduce new gradient flows of the KL divergence with a remarkable combination of properties.<n>They admit accurate interacting-particle approximations in high dimensions, and the per-step cost scales linearly in both the number of particles and the dimension.
  arXiv  Detail & Related papers  (2026-02-05T02:38:56Z)
• Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification [1.3654846342364308]
  The Radon cumulative distribution transform (R-CDT) is an easy-to-compute feature extractor that facilitates image classification tasks.<n>We introduce the so-called max-normalized R-CDT that only requires elementary operations and guaranties the separability under arbitrary affine transformations.<n>Our sensitivity analysis shows that its separability properties are stable provided the Wasserstein-infinity distance between the samples can be controlled.
  arXiv  Detail & Related papers  (2025-06-10T13:03:20Z)
• Variable-size Symmetry-based Graph Fourier Transforms for image compression [65.7352685872625]
  We propose a new family of Symmetry-based Graph Fourier Transforms of variable sizes into a coding framework. Our proposed algorithm generates symmetric graphs on the grid by adding specific symmetrical connections between nodes. Experiments show that SBGFTs outperform the primary transforms integrated in the explicit Multiple Transform Selection.
  arXiv  Detail & Related papers  (2024-11-24T13:00:44Z)
• RLE: A Unified Perspective of Data Augmentation for Cross-Spectral Re-identification [59.5042031913258]
  Non-linear modality discrepancy mainly comes from diverse linear transformations acting on the surface of different materials. We propose a Random Linear Enhancement (RLE) strategy which includes Moderate Random Linear Enhancement (MRLE) and Radical Random Linear Enhancement (RRLE) The experimental results not only demonstrate the superiority and effectiveness of RLE but also confirm its great potential as a general-purpose data augmentation for cross-spectral re-identification.
  arXiv  Detail & Related papers  (2024-11-02T12:13:37Z)
• Bayesian Circular Regression with von Mises Quasi-Processes [57.88921637944379]
  In this work we explore a family of expressive and interpretable distributions over circle-valued random functions.<n>For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling.<n>We present experiments applying this model to the prediction of wind directions and the percentage of the running gait cycle as a function of joint angles.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Cross-domain and Cross-dimension Learning for Image-to-Graph Transformers [48.74331852418905]
  Direct image-to-graph transformation is a challenging task that involves solving object detection and relationship prediction in a single model.<n>Due to this task's complexity, large training datasets are rare in many domains, making the training of deep-learning methods challenging.<n>We introduce a set of methods enabling cross-domain and cross-dimension learning for image-to-graph transformers.
  arXiv  Detail & Related papers  (2024-03-11T10:48:56Z)
• MGAug: Multimodal Geometric Augmentation in Latent Spaces of Image Deformations [2.2954246824369218]
  We propose a novel model that generates augmenting transformations in a multimodal latent space of geometric deformations.<n> Experimental results show that our proposed approach outperforms all baselines by significantly improved prediction accuracy.
  arXiv  Detail & Related papers  (2023-12-20T21:30:55Z)
• Adaptive Multi-step Refinement Network for Robust Point Cloud Registration [82.64560249066734]
  Point Cloud Registration estimates the relative rigid transformation between two point clouds of the same scene.<n>We propose an adaptive multi-step refinement network that refines the registration quality at each step by leveraging the information from the preceding step.<n>Our method achieves state-of-the-art performance on both the 3DMatch/3DLoMatch and KITTI benchmarks.
  arXiv  Detail & Related papers  (2023-12-05T18:59:41Z)
• Orthonormal Convolutions for the Rotation Based Iterative Gaussianization [64.44661342486434]
  This paper elaborates an extension of rotation-based iterative Gaussianization, RBIG, which makes image Gaussianization possible. In images its application has been restricted to small image patches or isolated pixels, because rotation in RBIG is based on principal or independent component analysis. We present the emphConvolutional RBIG: an extension that alleviates this issue by imposing that the rotation in RBIG is a convolution.
  arXiv  Detail & Related papers  (2022-06-08T12:56:34Z)
• Invariant Deep Compressible Covariance Pooling for Aerial Scene Categorization [80.55951673479237]
  We propose a novel invariant deep compressible covariance pooling (IDCCP) to solve nuisance variations in aerial scene categorization. We conduct extensive experiments on the publicly released aerial scene image data sets and demonstrate the superiority of this method compared with state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-11-11T11:13:07Z)
• Region adaptive graph fourier transform for 3d point clouds [51.193111325231165]
  We introduce the Region Adaptive Graph Fourier Transform (RA-GFT) for compression of 3D point cloud attributes. The RA-GFT achieves better complexity-performance trade-offs than previous approaches.
  arXiv  Detail & Related papers  (2020-03-04T02:47:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.