  We present a new supervised image classification method applicable to a broad
class of image deformation models. The method makes use of the previously
described Radon Cumulative Distribution Transform (R-CDT) for image data, whose
mathematical properties are exploited to express the image data in a form that
is more suitable for machine learning. While certain operations such as
translation, scaling, and higher-order transformations are challenging to model
in native image space, we show the R-CDT can capture some of these variations
and thus render the associated image classification problems easier to solve.
The method -- utilizing a nearest-subspace algorithm in R-CDT space -- is
simple to implement, non-iterative, has no hyper-parameters to tune, is
computationally efficient, label efficient, and provides competitive accuracies
to state-of-the-art neural networks for many types of classification problems.
In addition to the test accuracy performances, we show improvements (with
respect to neural network-based methods) in terms of computational efficiency
(it can be implemented without the use of GPUs), number of training samples
needed for training, as well as out-of-distribution generalization. The Python
code for reproducing our results is available at
https://github.com/rohdelab/rcdt_ns_classifier.
