This volume provides an up-to-date survey on mathematical and computational methods in image registration. This is an emerging topic in applied and computational science, with profund applications for instance in medicine, and image and video processing. Especially during the last year sophisticated numerical models for registration and efficient numerical methods (in particular variational methods and partial differential equations) have been proposed. Many of them are contained in this volume. Moreover, some practical applications and novel directions with industrial relevance in data processing are indicated. The combination of practice and novel mathematical aspects makes the book very suitable for the ECMI series 'Mathematics in Industry'. The most important contributions in this volume summarize the state of the art in mathematical and computational methods in image registration, based on variational and partial differential equations. The key contributions state sophisticated mathematical modelling, as well as numerical methods. The book contains many realistic examples with real world data.