  It has been shown that equivariant convolution is very helpful for many types
of computer vision tasks. Recently, the 2D filter parametrization technique
plays an important role when designing equivariant convolutions. However, the
current filter parametrization method still has its evident drawbacks, where
the most critical one lies in the accuracy problem of filter representation.
Against this issue, in this paper we modify the classical Fourier series
expansion for 2D filters, and propose a new set of atomic basis functions for
filter parametrization. The proposed filter parametrization method not only
finely represents 2D filters with zero error when the filter is not rotated,
but also substantially alleviates the fence-effect-caused quality degradation
when the filter is rotated. Accordingly, we construct a new equivariant
convolution method based on the proposed filter parametrization method, named
F-Conv. We prove that the equivariance of the proposed F-Conv is exact in the
continuous domain, which becomes approximate only after discretization.
Extensive experiments show the superiority of the proposed method.
Particularly, we adopt rotation equivariant convolution methods to image
super-resolution task, and F-Conv evidently outperforms previous filter
parametrization based method in this task, reflecting its intrinsic capability
of faithfully preserving rotation symmetries in local image features.
