  Image retargeting aims to resize an image to one with a prescribed aspect
ratio. Simple scaling inevitably introduces unnatural geometric distortions on
the important content of the image. In this paper, we propose a simple and yet
effective method to resize an image, which preserves the geometry of the
important content, using the Beltrami representation. Our algorithm allows
users to interactively label content regions as well as line structures. Image
resizing can then be achieved by warping the image by an orientation-preserving
bijective warping map with controlled distortion. The warping map is
represented by its Beltrami representation, which captures the local geometric
distortion of the map. By carefully prescribing the values of the Beltrami
representation, images with different complexity can be effectively resized.
Our method does not require solving any optimization problems and tuning
parameters throughout the process. This results in a simple and efficient
algorithm to solve the image retargeting problem. Extensive experiments have
been carried out, which demonstrate the efficacy of our proposed method.
