The inherent challenge of detecting symmetries stems from arbitrary
orientations of symmetry patterns; a reflection symmetry mirrors itself against
an axis with a specific orientation while a rotation symmetry matches its
rotated copy with a specific orientation. Discovering such symmetry patterns
from an image thus benefits from an equivariant feature representation, which
varies consistently with reflection and rotation of the image. In this work, we
introduce a group-equivariant convolutional network for symmetry detection,
dubbed EquiSym, which leverages equivariant feature maps with respect to a
dihedral group of reflection and rotation. The proposed network is built
end-to-end with dihedrally-equivariant layers and trained to output a spatial
map for reflection axes or rotation centers. We also present a new dataset,
DENse and DIverse symmetry (DENDI), which mitigates limitations of existing
benchmarks for reflection and rotation symmetry detection. Experiments show
that our method achieves the state of the arts in symmetry detection on LDRS
and DENDI datasets.

该研究提出了一种基于等变特征表示的群等变卷积神经网络 (EquiSym)，用于检测具有反射和旋转对称性的图像中的对称性模式，并在新的 DENDI 数据集上取得了最佳表现。