The Radon Signed Cumulative Distribution Transform and its applications in classification of Signed Images

TL;DR

This paper introduces a novel image representation technique combining Radon transform and Signed Cumulative Distribution Transform, enhancing classification accuracy for signed images over existing methods and deep learning approaches.

Contribution

The paper presents a new transport-based image representation method that generalizes previous techniques to arbitrary images, improving classification performance.

Findings

More accurate representation of signed images.

Higher classification accuracy compared to existing methods.

Implementation available in PyTransKit on Github.

Abstract

Here we describe a new image representation technique based on the mathematics of transport and optimal transport. The method relies on the combination of the well-known Radon transform for images and a recent signal representation method called the Signed Cumulative Distribution Transform. The newly proposed method generalizes previous transport-related image representation methods to arbitrary functions (images), and thus can be used in more applications. We describe the new transform, and some of its mathematical properties and demonstrate its ability to partition image classes with real and simulated data. In comparison to existing transport transform methods, as well as deep learning-based classification methods, the new transform more accurately represents the information content of signed images, and thus can be used to obtain higher classification accuracies. The implementation of the proposed method in Python language is integrated as a part of the software package PyTransKit, available on Github.