  Symmetry is present in many tasks in computer vision, where the same class of
objects can appear transformed, e.g. rotated due to different camera
orientations, or scaled due to perspective. The knowledge of such symmetries in
data coupled with equivariance of neural networks can improve their
generalization to new samples. Differential invariants are equivariant
operators computed from the partial derivatives of a function. In this paper we
use differential invariants to define equivariant operators that form the
layers of an equivariant neural network. Specifically, we derive invariants of
the Special Euclidean Group SE(2), composed of rotations and translations, and
apply them to construct a SE(2)-equivariant network, called SE(2) Differential
Invariants Network (SE2DINNet). The network is subsequently tested in
classification tasks which require a degree of equivariance or invariance to
rotations. The results compare positively with the state-of-the-art, even
though the proposed SE2DINNet has far less parameters than the compared models.
