Content-aware image resizing using quasi-conformal mapping

Content-aware image resizing is resizing an image such that the prominent feature of the image is intact and the homogenous content of the image is distorted as little as possible. There is a lot of research on this topic, and various approaches have been proposed so far. One problem with previous methods is the lack of a theoretical guarantee of a rigorous bijective map between an image and the target image, which may cause artifacts in the target image. In this paper, we present a new approach to solve the image resizing problem based on quasi-conformal mapping. We apply quasi-conformal mapping to set up a bijective map between an image and the target image such that the salient feature of the image is uniformly scaled, while the homogenous content of the image is distorted as little as possible. The distortion is characterized by a function defined by the Beltrami coefficient of the quasi-conformal mapping, which is minimized by solving a nonconvex optimization problem. Solving the optimization problem is reduced to solving two convex optimization problems alternatingly. We implemented our algorithm with many examples and made comparisons with previous approaches. The examples suggest that our method is comparable with previous approaches while guaranteeing that there are no foldovers. Furthermore, our method can easily preserve line features and handle large changes in the aspect ratios of images.