  Optical flow is inherently a 2D search problem, and thus the computational
complexity grows quadratically with respect to the search window, making large
displacements matching infeasible for high-resolution images. In this paper, we
propose a new method for high-resolution optical flow estimation with
significantly less computation, which is achieved by factorizing 2D optical
flow with 1D attention and correlation. Specifically, we first perform a 1D
attention operation in the vertical direction of the target image, and then a
simple 1D correlation in the horizontal direction of the attended image can
achieve 2D correspondence modeling effect. The directions of attention and
correlation can also be exchanged, resulting in two 3D cost volumes that are
concatenated for optical flow estimation. The novel 1D formulation empowers our
method to scale to very high-resolution input images while maintaining
competitive performance. Extensive experiments on Sintel, KITTI and real-world
4K ($2160 \times 3840$) resolution images demonstrated the effectiveness and
superiority of our proposed method.
