  Equivariance of neural networks to transformations helps to improve their
performance and reduce generalization error in computer vision tasks, as they
apply to datasets presenting symmetries (e.g. scalings, rotations,
translations). The method of moving frames is classical for deriving operators
invariant to the action of a Lie group in a manifold.Recently, a rotation and
translation equivariant neural network for image data was proposed based on the
moving frames approach. In this paper we significantly improve that approach by
reducing the computation of moving frames to only one, at the input stage,
instead of repeated computations at each layer. The equivariance of the
resulting architecture is proved theoretically and we build a rotation and
translation equivariant neural network to process volumes, i.e. signals on the
3D space. Our trained model overperforms the benchmarks in the medical volume
classification of most of the tested datasets from MedMNIST3D.
