We focus on modelling application-specific prior knowledge in image processing. Precisely formulating such prior knowledge in the form of an energy function makes it possible to systematically develop image processing methods that are more accurate and require less data. The resulting problems are often non-differentiable and high- or infinite-dimensional, which requires the development of new numerical optimization methods. we focus in particular on problems with combinatorial aspects, where a number of discrete decisions has to be made, such as the image segmentation problem. Application areas include processing and analysis of images, videos, as well as general two- and higher-dimensional data, such as directional, tensor-, or height data in medicine, biology, and earth sciences.