الفهرس 
Shape dataOnly 14 pages are availabe for public view
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Abstract
In this thesis, approaches are proposed for analyzing longitudinal three-dimensional data where is presented in a novel application within the area of shape analysis, illustrated by comparing facial skeletal and soft-tissue shape between patients with dental malocclusion before and after orthodontic treatment. Both are anatomical landmarks of facial skeletal and soft-tissue shape. Chapter 1, an introduction to the linear model considered is presented and it contains a general introduction expressing the definitions and the main information used in the remaining chapters. Moreover, it also highlights some theories and results that are related to the main items of this thesis, Chapter 2 presents the statistical shape definition of a shape and introduces the area of statistical shape analysis in detail, specifically presenting the technicalities of shape space and distances. In some addition methods in the literature in the area of shape analysis are presented. In Chapter 3, the procruste alignments of a set of shapes to remove unwanted effects are discussed. The concept of tangent coordinates is introduced as a projection of shape data into a Euclidean space, to enable the use of multivariate methods. An outline is given of thin-plate splines and deformations for the analysis of surfaces. It gives a broad overview of some standard shape analysis techniques, including Procrustes methods for alignment of objects, and gives further details of methods based on curvature. Functional data analysis techniques which are of use throughout the thesis are also discussed.