Mathematics Meets Medicine, an Optimal Alignment

Image registration is the process of aligning two or moreimages of the same scene taken at different times, fromdifferent viewpoints and/or by different sensors. Imageregistration is a crucial step in imaging problems wherethe valuable information is contained in more than oneimage. Here, spatial alignment is required to properly in-tegrate useful information from the separate images. Itis the goal of this note to give an overview on moderntechniques in this area. It turns out that the registrationproblem is an inverse problem which requires regulariza-tion and the use of modern optimization methods. Weaddress these issues and supplement it by real-life exam-ples.