Chapter 3 – Multiscale/Multiresolution Representations

This chapter presents a comprehensive overview of the current state in multiscale–multiresolution image representation with a special emphasis on the medical image application. It discusses the notion of scale in the framework of image registration, and reviews some selected multiscale methods on brain image registration, most notably on brain warping. Today, multiscale–multiresolution approaches form an important part of many medical image segmentation and registration techniques. Processing data is more efficient if it can be done in some hierarchical fashion rather than done randomly. This is especially true when the amount of data is large as it is in medical imaging. Fundamentally, discrete hierarchical structures—namely tree structures—are mathematical constructs representing concepts from gross with respect to shape and size, global with respect to spatial context, complex with respect to number of components, general with respect to categories to more detailed, local, simple, or special features of the concept. On the other hand, there is a scale at the continuous signal and measurement level that signifies the sampling resolution in space, time, and spectrum, which in turn reveals not only the matter being measured but also the apparatus that measures it. The result is the resolution of observables.