The Radon cumulative distribution transform and its application to image classification

TL;DR

This paper introduces a nonlinear, invertible image transform combining Radon and Cumulative Distribution Transform techniques, which enhances image classification by making certain problems linearly separable in the transform space.

Contribution

The paper presents a novel nonlinear invertible transform that combines Radon and Cumulative Distribution Transform for improved image classification.

Findings

Transform often renders classification problems linearly separable

The method outperforms traditional linear transforms in experiments

The transform has useful properties for feature extraction

Abstract

Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier, Wavelet, etc.) are linear transforms, and, by themselves, are unable to substantially simplify the representation of image classes for classification. Here we describe a nonlinear, invertible, low-level image processing transform based on combining the well known Radon transform for image data, and the 1D Cumulative Distribution Transform proposed earlier. We describe a few of the properties of this new transform, and with both theoretical and experimental results show that it can often render certain problems linearly separable in transform space.