  With the growth of data from new radio telescope facilities, machine-learning
approaches to the morphological classification of radio galaxies are
increasingly being utilised. However, while widely employed deep-learning
models using convolutional neural networks (CNNs) are equivariant to
translations within images, neither CNNs nor most other machine-learning
approaches are equivariant to additional isometries of the Euclidean plane,
such as rotations and reflections. Recent work has attempted to address this by
using G-steerable CNNs, designed to be equivariant to a specified subset of
2-dimensional Euclidean, E(2), transformations. Although this approach improved
model performance, the computational costs were a recognised drawback. Here we
consider the use of directly extracted E(2)-equivariant features for the
classification of radio galaxies. Specifically, we investigate the use of
Minkowski functionals (MFs), Haralick features (HFs) and elliptical Fourier
descriptors (EFDs). We show that, while these features do not perform
equivalently well to CNNs in terms of accuracy, they are able to inform the
classification of radio galaxies, requiring ~50 times less computational
runtime. We demonstrate that MFs are the most informative, EFDs the least
informative, and show that combinations of all three result in only
incrementally improved performance, which we suggest is due to information
overlap between feature sets.
