  How to represent an image? While the visual world is presented in a
continuous manner, machines store and see the images in a discrete way with 2D
arrays of pixels. In this paper, we seek to learn a continuous representation
for images. Inspired by the recent progress in 3D reconstruction with implicit
neural representation, we propose Local Implicit Image Function (LIIF), which
takes an image coordinate and the 2D deep features around the coordinate as
inputs, predicts the RGB value at a given coordinate as an output. Since the
coordinates are continuous, LIIF can be presented in arbitrary resolution. To
generate the continuous representation for images, we train an encoder with
LIIF representation via a self-supervised task with super-resolution. The
learned continuous representation can be presented in arbitrary resolution even
extrapolate to x30 higher resolution, where the training tasks are not
provided. We further show that LIIF representation builds a bridge between
discrete and continuous representation in 2D, it naturally supports the
learning tasks with size-varied image ground-truths and significantly
outperforms the method with resizing the ground-truths.
