torchcdt

About

torchcdt implements the (Radon-) Cumulative Distribution Transform [1, 2] and its' inverse with different normalization approaches [3, 4] to enhance feature extraction. All transforms work with batched multi-channel data and are fully differentiable. This allows backpropagation through torchcdt transforms to train neural networks or to solve optimization problems with torch.optim (see examples).

Installation

pip install torchcdt

Basic Usage

import matplotlib.pyplot as plt
import torch
from torchskradon.functional import skradon

import torchcdt.helpers as helpers
from torchcdt.functional import ircdt, rcdt

device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

N = 128
s = torch.zeros((1, 1, N, N), device=device)
x = torch.linspace(-10, 10, N, device=device)
y = torch.linspace(-10, 10, N, device=device)
xx, yy = torch.meshgrid(x, y, indexing="ij")
x = x.unsqueeze(0)
y = y.unsqueeze(0)
xx = xx.unsqueeze(0)
yy = yy.unsqueeze(0)
s[0, 0] = torch.exp(-(xx**2 + yy**2) / 2) / (2 * torch.pi)

# This is not needed unless we want the reconstruction to have the exact same scaling
s = helpers.make_positive_density(s, dim=(-2, -1), eps=1e-6)
s_sinogram = skradon(s, circle=False)

fig, axs = plt.subplots(1, 2, figsize=(15, 5))
axs[0].imshow(s[0, 0].cpu().numpy())
axs[0].set_title("Input image")
axs[1].imshow(s_sinogram[0, 0].cpu().numpy())
axs[1].set_title("Sinogram")
plt.show()

s_hat = rcdt(s, circle=False)
s_reco = ircdt(s_hat, circle=False)

fig, ax = plt.subplots(1, 2, figsize=(15, 5))
ax[0].imshow(s_hat[0, 0].cpu().numpy())
ax[0].set_title("R-CDT")
ax[1].imshow(s_reco[0, 0].cpu().numpy())
ax[1].set_title("Reconstructed image")
plt.show()

Examples

For more detailed examples and use cases, see the examples directory:

• examples/cdt_properties.py - Basic properties of forward and inverse CDT transforms
• examples/linmnist_classifictation.ipynb - SVM classification of LinMNIST dataset

Other Packages

This package is inspired by

1. PyTransKit

2. Cumulative-Distribution-Transform

3. Radon-Cumulative-Distribution-Transform

4. NR-CDT

Acknowledgements

I would like to thank Dr. Matthias Beckmann for his supervision and guidance during a reading course on this topic.

References

1. Park SR, Kolouri S, Kundu S, Rohde GK, "The cumulative distribution transform and linear pattern classification", Applied and Computational Harmonic Analysis, 2017

2. Kolouri S, Park SR, Rohde GK, "The Radon Cumulative Distribution Transform and Its Application to Image Classification", IEEE transactions on image processing, 2016

3. Beckmann M, Beinert R, Bresch J, "Max-Normalized Radon Cumulative Distribution Transform for Limited Data Classification", International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), 2025

4. Beckmann M, Beinert R, Bresch J, "Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification", International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), 2025