XdRadonTransform

This repository contains the code and experiments for the papers:

1. Robert Beinert, Jonas Bresch, Michael Quellmalz 'A Discrete Radon Transform Based on the Area of Cube-Plane Intersection', arxiv:xxxx.xxxxx, 2026.

Please cite the papers if you use the code.

Usage

To initialize the environment for the experiments, start a Julia REPL in the main directory and use the following commands:

import Pkg
Pkg.activate(".")
Pkg.instantiate()

Examples

The basic usage of the code is shown in the following Pluto notebooks:

• Pluto/iterface.jl: Simple example for setting the Radon transform. Example usage on a simple object.

To run Pluto notebooks, open a Julia REPL in the main directory and start Pluto via

using Pluto; Pluto.run()

Experiments

The simulations in [1] can be reproduced using the following Pluto notebooks:

• IEEE/Tab2_3_shape_matching_nonaff.jl: Nearest neighbour classification for ModelNet10 dataset using the closed formula of the Radon transform for shape matching via trace-transform (Daras et al.). This experiment corresponds to Table 2 and 3 and Figure 6.
• IEEE/Tab3_4_shape_recognition_nonaff.jl: Nearest neighbour classification for for ModelNet10 dataset using the closed formula of the Radon transform for object recognition vi mNR-CDT (Beckmann et al.). This experiment corresponds to Table 4 and 5 and Figure 7.
• IEEE/SecIII.E_shape_matching_aff.jl: Setting as in (a) on affine transformed object classes.
• IEEE/SecIII.E_shape_recognition_aff.jl: Setting as in (b) on affine transformed object classes.
• IEEE/Fig8_9_clustering_2d_sliced_wasserstein.jl: Best fitting histograms for 2D. This experiment corresponds to Figure 8 and 9 (top).
• IEEE/Fig8_9_clustering_3d_sliced_wasserstein.jl: Best fitting histograms for 3D. This experiment corresponds to Figure 9 (bottom).
• IEEE/Fig10_11_sliced_Wasserstein_barycenter.jl: Sliced Wasserstein barycenter calculation. This experiment corresponds to Figure 10 and 11.
• IEEE/Fig12_Monte_Carlo_4d.jl: Monte Carlo integration - a comparison for approximating the Radon transform in 4D. This experiment corresponds to Figure 12.

License

This code is licensed under a MIT License.