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.
β¦ Table of Contents
Front Matter....Pages i-x
Front Matter....Pages 1-1
Basic Concepts and Definitions....Pages 3-13
Shape Inference and the Offset-Normal Distribution....Pages 15-31
Dynamic Shape Analysis Through the Offset-Normal Distribution....Pages 33-56
Front Matter....Pages 57-57
Parametric and Non-parametric Testing of Mean Shapes....Pages 59-72
Applications of NPC Methodology....Pages 73-103
Back Matter....Pages 105-115
β¦ Subjects
Statistical Theory and Methods; Probability and Statistics in Computer Science; Computational Mathematics and Numerical Analysis