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.

翻译：本文描述了一种基于输运和最优输运数学理论的新型图像表示技术。该方法将广为人知的图像Radon变换与近期提出的信号表示方法——符号累积分布变换相结合。本文提出的新方法将先前与输运相关的图像表示方法推广至任意函数（图像），从而可应用于更广泛的场景。我们阐述了该新变换及其部分数学性质，并通过真实与模拟数据验证了其对图像类别的划分能力。与现有输运变换方法及基于深度学习的分类方法相比，该新变换能更精确地表示符号图像的信息内容，因此可用于获得更高的分类准确率。所提方法的Python实现已集成至软件包PyTransKit中，该软件包可在GitHub上获取。