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A Discrete Radon Transform Based on the Area of Cube-Plane Intersection
Robert Beinert, Jonas Bresch, Michael Quellmalz
The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an a…
Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition
Matthias Beckmann, Robert Beinert, Jonas Bresch
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…
Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification
Matthias Beckmann, Robert Beinert, Jonas Bresch
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…
Max-Normalized Radon Cumulative Distribution Transform for Limited Data Classification
Matthias Beckmann, Robert Beinert, Jonas Bresch
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…
Denoising Hyperbolic-Valued Data by Relaxed Regularizations
Robert Beinert, Jonas Bresch
We introduce a novel relaxation strategy for denoising hyperbolic-valued data. The main challenge is here the non-convexity of the hyperbolic sheet. Instead of considering the deno…
Multi-marginal Approximation of the Linear Gromov-Wasserstein Distance
Florian Beier, Robert Beinert
Recently, two concepts from optimal transport theory have successfully been brought to the Gromov--Wasserstein (GW) setting. This introduces a linear version of the GW distance and…