Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications

Authors: Brombin, C., Salmaso, L., Fontanella, L., Ippoliti, L., Fusilli, C.
Explores specific inferential issues arising from the analysis of dynamic shapes with the attempt to solve the problems at hand using probability models and nonparametric testsUses the Expectation Maximization (EM) algorithm to give essential results for a likelihood-based approach to statistical inference in shape analysisCovers the theory of NonParametric Combination (NPC) tests as well as the applications of the methodology to the Face and Gesture Recognition Research Network (FG-NET) data

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.

Number of Illustrations and Tables
21 b/w illustrations, 27 illustrations in colour
Topics
Statistical Theory and Methods
Probability and Statistics in Computer Science
Computational Mathematics and Numerical Analysis

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