  Guided depth super-resolution is a practical task where a low-resolution and
noisy input depth map is restored to a high-resolution version, with the help
of a high-resolution RGB guide image. Existing methods usually view this task
as a generalized guided filtering problem that relies on designing explicit
filters and objective functions, or a dense regression problem that directly
predicts the target image via deep neural networks. These methods suffer from
either model capability or interpretability. Inspired by the recent progress in
implicit neural representation, we propose to formulate the guided
super-resolution as a neural implicit image interpolation problem, where we
take the form of a general image interpolation but use a novel Joint Implicit
Image Function (JIIF) representation to learn both the interpolation weights
and values. JIIF represents the target image domain with spatially distributed
local latent codes extracted from the input image and the guide image, and uses
a graph attention mechanism to learn the interpolation weights at the same time
in one unified deep implicit function. We demonstrate the effectiveness of our
JIIF representation on guided depth super-resolution task, significantly
outperforming state-of-the-art methods on three public benchmarks. Code can be
found at \url{https://git.io/JC2sU}.
