Chapter 2 - Spatial Normalization

Abstract

This chapter addresses the problem of spatial normalization, namely, how to map a single subject's brain image into a standard space. The solution of this problem, assuming that the standard space adopted has a known relationship to other standard spaces, allows for a wide range of voxel-based analyses and facilitates the comparison of different subjects and databases. There are a variety of approaches to these types of spatial normalization. These include the use of spatial basis functions, viscous fluid models, elastic models, and multiresolution approaches. The mathematical foundations and ideas that are applied in a number of contexts include Gauss–Newton-like optimization algorithms and a Bayesian framework used to find maximum a posteriori (MAP) estimates of the deformation fields. The chapter describes methods for performing rapid and automatic nonlabel based nonlinear spatial normalizations. The method which is considered in detail in this chapter minimizes the residual squared difference between the image and a template image of the same modality. The first step of the registration is to correct for differences in position, orientation, and size by optimizing the parameters of an affine transformation. Knowledge of the variability in head size is incorporated into this optimization to obtain a more stable solution and rapid convergence.