Learning Local Implicit Fourier Representation for Image Warping

Abstract: Image warping aims to reshape images defined on rectangular grids into arbitrary shapes. Recently, implicit neural functions have shown remarkable performances in representing images in a continuous manner. However, a standalone multi-layer perceptron suffers from learning high-frequency Fourier coefficients. In this paper, we propose a local texture estimator for image warping (LTEW) followed by an implicit neural representation to deform images into continuous shapes. Local textures estimated from a deep super-resolution (SR) backbone are multiplied by locally-varying Jacobian matrices of a coordinate transformation to predict Fourier responses of a warped image. Our LTEW-based neural function outperforms existing warping methods for asymmetric-scale SR and homography transform. Furthermore, our algorithm well generalizes arbitrary coordinate transformations, such as homography transform with a large magnification factor and equirectangular projection (ERP) perspective transform, which are not provided in training.