This book considers specific inferential issues arising from the
analysis of dynamic shapes with the attempt to solve the problems at
hand using probability models and nonparametric tests. The models are
simple to understand and interpret and provide a useful tool to describe
the global dynamics of the landmark configurations. However, because of
the non-Euclidean nature of shape spaces, distributions in shape spaces
are not straightforward to obtain.
The book explores the use of the Gaussian distribution in the
configuration space, with similarity transformations integrated out.
Specifically, it works with the offset-normal shape distribution as a
probability model for statistical inference on a sample of a temporal
sequence of landmark configurations. This enables inference for Gaussian
processes from configurations onto the shape space.
The book is divided in two parts, with the first three chapters covering
material on the offset-normal shape distribution, and the remaining
chapters covering the theory of NonParametric Combination (NPC) tests.
The chapters offer a collection of applications which are bound together
by the theme of this book.
They refer to the analysis of data from the FG-NET (Face and Gesture
Recognition Research Network) database with facial expressions. For
these data, it may be desirable to provide a description of the dynamics
of the expressions, or testing whether there is a difference between the
dynamics of two facial expressions or testing which of the landmarks are
more informative in explaining the pattern of an expression.
