| The currently most accepted strategies for comparing shapes, such as Procrustes Analysis, use some kind of superimposition of the objects under study, scaling and rotating the shapes to minimize a certain loss function. When describing dynamic shapes such as the face, these features of the superimposition process are not desirable. In this thesis, several aspects that come into play when performing cross-analysis on dynamic shapes are considered. First, the alignment process is examined. Images of dynamic shapes should not be compared at different stages of the shape change. A method to ensure alignment while keeping most of the individuality in tact is proposed. Next, an algorithm is described that enables us to average dynamic shapes such as facial animations, by means of distance matrix representation. To avoid difficulties due to differences in size, the use of the relative distance matrix is introduced. This relative distance matrix is used again when we measure variation between dynamic shapes using functional principal component analysis. An approximation method for large data sets is also introduced. Next, it is shown how these ideas can be utilized to handle problems involving inference, using principal component scores as a simple numerical representation of the shape change functions. |
