In the recent years, there have been significant advances in the development and manufacturing of 3D scanners capable of capturing detailed (external) images of whole human bodies. Such hardware offers the opportunity to collect information that could be used to describe, interpret and analyse the shape of the human body for a variety of applications where shape information plays a vital role (e.g. apparel sizing and customisation; medical research in fields such as nutrition, obesity/anorexia and perceptive psychology; ergonomics for vehicle and furniture design). However, the representations delivered by such hardware typically consist of unstructured or partially structured point clouds, whereas it would be desirable to have models that allow shape-related information to be more immediately accessible. This thesis describes a method of extracting the differential geometry properties of the body surface from unorganized point cloud datasets. In effect, this is a way of constructing curvature maps that allows the detection on the surface of features that are deformable (such as ridges) rather than reformable under certain transformations. Such features could subsequently be used to interpret the topology of a human body and to enable classification according to its shape, rather than its size (as is currently the standard practice for many of the applications concemed). The background, motivation and significance of this research are presented in chapter one. Chapter two is a literature review describing the previous and current attempts to model 3D objects in general and human bodies in particular, as well as the mathematical and technical issues associated with the modelling. Chapter three presents an overview of: the methodology employed throughout the research; the assumptions regarding the data to be processed; and the strategy for evaluating the results for each stage of the methodology. Chapter four describes an algorithm (and some variations) for approximating the local surface geometry around a given point of the input data set by means of a least-squares minimization. The output of such an algorithm is a surface patch described in an analytic (implicit) form. This is necessary for the next step described below. The case is made for using implicit surfaces rather than more popular 3D surface representations such as parametric forms or height functions. Chapter five describes the processing needed for calculating curvature-related characteristics for each point of the input surface. This utilises the implicit surface patches generated by the algorithm described in the previous chapter, and enables the construction of a "curvature map" of the original surface, which incorporates rich information such as the principal curvatures, shape indices and curvature directions. Chapter six describes a family of algorithms for calculating features such as ridges and umbilic points on the surface from the curvature map, in a manner that bypasses the problem of separating a vector field (i.e. the principal curvature directions) across the entire surface of an object. An alternative approach, using the focal surface information, is also considered briefly in comparison. The concluding chapter summarises the results from all steps of the processing and evaluates them in relation to the requirements set in chapter one. Directions for further research are also proposed
