Image completion is an important photo-editing task which involves synthetically filling a hole in the image such that the image still appears natural. State-of-the-art image completion methods work by searching for patches in the image that fit well in the hole region. Our key insight is that image patches remain natural under a variety of transformations (such as scale, rotation and brightness change), and it is important to exploit this. We propose and investigate the use of different optimisation methods to search for the best patches and their respective transformations for producing consistent, improved completions. Experiments on a number of challenging problem instances demonstrate that our methods outperform state-of-the-art techni...