The Radon Signed Cumulative Distribution Transform and its applications in classification of Signed Images
This work addresses the challenge of classifying signed images, which is important for applications in fields like medical imaging or computer vision, but it appears incremental as it generalizes prior transport methods to arbitrary functions.
The authors tackled the problem of representing signed images for classification by introducing the Radon Signed Cumulative Distribution Transform, a new image representation technique based on transport theory, which achieved higher classification accuracies compared to existing transport and deep learning methods.
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.