Numerical Methods for Image Registration

Abstract

This text provides an introduction to the theoretical, practical, and numerical aspects of image registration, with special emphasis on medical imaging. Given a so-called reference and template image, the goal of image registration is to find a reasonable transformation such that the transformed template is similar to the reference image. Image registration is utilized whenever information obtained from different viewpoints times and sensors needs to be combined or compared, and unwanted distortion needs to be eliminated. The book provides a systematic introduction to image registration and discusses the basic mathematical principles, including aspects from approximations theory, image processing, numerics, optimization, partial differential equations, and statistics, with a strong focus on numerical methods. A unified variational approach is introduced and enables a separation into data-related issues like image feature or image intensity-based similarity measures, and problem inherent regularization like elastic or diffusion registration. This general framework is further used for the explanation and classification of established methods as well as the design of new schemes and building blocks including landmark-, thin-plate-spline, mutual information, elastic, fluid, demon, diffusion, and curvature registration.