Image representation is critical for many visual tasks. Instead of representing images discretely with 2D arrays of pixels, a recent study, namely local implicit image function (LIIF), denotes images as a continuous function where pixel values are expansion by using the corresponding coordinates as inputs. Due to its continuous nature, LIIF can be adopted for arbitrary-scale image super-resolution tasks, resulting in a single effective and efficient model for various up-scaling factors. However, LIIF often suffers from structural distortions and ringing artifacts around edges, mostly because all pixels share the same model, thus ignoring the local properties of the image. In this paper, we propose a novel adaptive local image function (A-LIIF) to alleviate this problem. Specifically, our A-LIIF consists of two main components: an encoder and a expansion network. The former captures cross-scale image features, while the latter models the continuous up-scaling function by a weighted combination of multiple local implicit image functions. Accordingly, our A-LIIF can reconstruct the high-frequency textures and structures more accurately. Experiments on multiple benchmark datasets verify the effectiveness of our method. Our codes are available at \url{https://github.com/LeeHW-THU/A-LIIF}.

本研究提出了一种新的自适应局部图像函数（A-LIIF）模型，旨在通过采用编码器和扩展网络，建模多个局部隐式图像函数的加权组合，从而缓解局部隐式图像函数（LIIF）模型在边缘周围出现结构失真和环状伪影等问题，实现图像超分辨率的高精度重建。

自适应局部隐式图像函数用于任意比例超分辨率