  The effectiveness of Convolutional Neural Networks stems in large part from
their ability to exploit the translation invariance that is inherent in many
learning problems. Recently, it was shown that CNNs can exploit other
invariances, such as rotation invariance, by using group convolutions instead
of planar convolutions. However, for reasons of performance and ease of
implementation, it has been necessary to limit the group convolution to
transformations that can be applied to the filters without interpolation. Thus,
for images with square pixels, only integer translations, rotations by
multiples of 90 degrees, and reflections are admissible.
  Whereas the square tiling provides a 4-fold rotational symmetry, a hexagonal
tiling of the plane has a 6-fold rotational symmetry. In this paper we show how
one can efficiently implement planar convolution and group convolution over
hexagonal lattices, by re-using existing highly optimized convolution routines.
We find that, due to the reduced anisotropy of hexagonal filters, planar
HexaConv provides better accuracy than planar convolution with square filters,
given a fixed parameter budget. Furthermore, we find that the increased degree
of symmetry of the hexagonal grid increases the effectiveness of group
convolutions, by allowing for more parameter sharing. We show that our method
significantly outperforms conventional CNNs on the AID aerial scene
classification dataset, even outperforming ImageNet pre-trained models.
