Stereophotogrammetric imaging systems produce representations of surfaces (two-dimensional manifolds in three-dimensional space) through triangulations of a large number of estimated surface points. Traditional forms of analysis of these surfaces are based on point locations (manually marked anatomical landmarks) as described in Chapter 1. An advanced application of these types of landmarks will be thoroughly examined in Chapter 2 through the concept of Ghost Imaging. The results of this chapter necessitated a reliability study of stereophotogrammetric imaging systems which is discussed in Chapter 3. Given the results of the reliability study, an investigation info new definitions of landmarks and facial shape description is undertaken in Chapter 4. A much richer representation is expressed by the curves which track the ridges and valleys of the dense surface and by the relatively smooth surface patches which lie between these curves. New automatic methods for identifying anatomical curves and the resulting full surface representation, based on shape index, curvature, smoothing techniques, warping, and bending energy, are described. Chapter 5 discussed new and extended tools of analysis that are necessary for this richer representation of facial shape. These methods will be applied in Chapter 6 to different shape objects, including the human face, mussel shells, and computational imaging comparisons. Issues of sexual dimorphism (differences in shapes between males and females), change in shape with age, as well as pre- and post-facial surgical intervention will be explored. These comparisons will be made using new methodological tools developed specifically for the new curve and surface identification method. In particular, the assessment of facial asymmetry and the questions involved in comparing facial shapes in general, at both the individual and the group level, will also be considered. In Chapter 7, Bayesian methods are explored to determine further ways in which to understand and compare human facial features. In summary, this thesis shows a novel method of curve and full facial mesh identification that is used, successfully, in pilot case studies of multiple types of surfaces. It then shows a novel proof of principle for using Bayesian methods to create a fully automatic process in facial shape characterisation. In order to view this thesis in full, please view in Adobe Reader.