  Convolutional Neural Networks (CNNs) have exhibited their great power in a
variety of vision tasks. However, the lack of transform-invariant property
limits their further applications in complicated real-world scenarios. In this
work, we proposed a novel generalized one dimension convolutional operator
(OneDConv), which dynamically transforms the convolution kernels based on the
input features in a computationally and parametrically efficient manner. The
proposed operator can extract the transform-invariant features naturally. It
improves the robustness and generalization of convolution without sacrificing
the performance on common images. The proposed OneDConv operator can substitute
the vanilla convolution, thus it can be incorporated into current popular
convolutional architectures and trained end-to-end readily. On several popular
benchmarks, OneDConv outperforms the original convolution operation and other
proposed models both in canonical and distorted images.
