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Here we describe a new image representation technique based on themathematics of transport and optimal transport. The method relies on thecombination of the well-known Radon transform for images and a recent signalrepresentation method called the Signed Cumulative Distribution Transform. Thenewly proposed method generalizes previous transport-related imagerepresentation methods to arbitrary functions (images), and thus can be used inmore applications. We describe the new transform, and some of its mathematicalproperties and demonstrate its ability to partition image classes with real andsimulated data. In comparison to existing transport transform methods, as wellas deep learning-based classification methods, the new transform moreaccurately represents the information content of signed images, and thus can beused to obtain higher classification accuracies. The implementation of theproposed method in Python language is integrated as a part of the softwarepackage PyTransKit, available on Github.

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