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The purpose of the objective function is to quantify the goal of NRR algorithms by introducing measurable attributes. This typically involves quantification of image dissimilarity, either by a direct pixel-by-pixel or voxel-by-voxel comparison, or by using less direct image histogram methods. Most of the methods below are area based, which means that the NRR algorithm analyses structures in the images via correlation metrics and other means of performing a structural analysis, e.g. Fourier properties. Feature-based registration methods are discussed as well, although the results presented later in this thesis do not make use of such methods and need not consider Euclidean distance measures within images, only between separate images in hyperspace.
I describe several variants of these two sorts of approaches in what follows. In essence, all are methods for establishing a measure of distance between images (by direct comparison or minimising distances), so only the means vary.
