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.

基于运输和最优运输的数学，我们描述了一种新的图像表示技术。该方法基于图像的 Radon 变换和最近的信号表示方法 Signed Cumulative Distribution Transform 的组合，将以前与运输相关的图像表示方法推广到任意函数（图像）。与现有的运输变换方法以及基于深度学习的分类方法相比，该新变换更准确地表示有符号图像的信息内容，因此可以获得更高的分类准确性。