  Image inpainting aims to fill the missing hole of the input. It is hard to
solve this task efficiently when facing high-resolution images due to two
reasons: (1) Large reception field needs to be handled for high-resolution
image inpainting. (2) The general encoder and decoder network synthesizes many
background pixels synchronously due to the form of the image matrix. In this
paper, we try to break the above limitations for the first time thanks to the
recent development of continuous implicit representation. In detail, we
down-sample and encode the degraded image to produce the spatial-adaptive
parameters for each spatial patch via an attentional Fast Fourier
Convolution(FFC)-based parameter generation network. Then, we take these
parameters as the weights and biases of a series of multi-layer
perceptron(MLP), where the input is the encoded continuous coordinates and the
output is the synthesized color value. Thanks to the proposed structure, we
only encode the high-resolution image in a relatively low resolution for larger
reception field capturing. Then, the continuous position encoding will be
helpful to synthesize the photo-realistic high-frequency textures by
re-sampling the coordinate in a higher resolution. Also, our framework enables
us to query the coordinates of missing pixels only in parallel, yielding a more
efficient solution than the previous methods. Experiments show that the
proposed method achieves real-time performance on the 2048$\times$2048 images
using a single GTX 2080 Ti GPU and can handle 4096$\times$4096 images, with
much better performance than existing state-of-the-art methods visually and
numerically. The code is available at:
https://github.com/NiFangBaAGe/CoordFill.
