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Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications

  • Chiara Brombin
  • Luigi Salmaso
  • Lara Fontanella
  • Luigi Ippoliti
  • Caterina Fusilli

Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Table of contents

  1. Front Matter
    Pages i-x
  2. Offset Normal Distribution for Dynamic Shapes

    1. Front Matter
      Pages 1-1
    2. Chiara Brombin, Luigi Salmaso, Lara Fontanella, Luigi Ippoliti, Caterina Fusilli
      Pages 3-13
    3. Chiara Brombin, Luigi Salmaso, Lara Fontanella, Luigi Ippoliti, Caterina Fusilli
      Pages 15-31
    4. Chiara Brombin, Luigi Salmaso, Lara Fontanella, Luigi Ippoliti, Caterina Fusilli
      Pages 33-56
  3. Combination-Based Permutation Tests for Shape Analysis

    1. Front Matter
      Pages 57-57
    2. Chiara Brombin, Luigi Salmaso, Lara Fontanella, Luigi Ippoliti, Caterina Fusilli
      Pages 59-72
    3. Chiara Brombin, Luigi Salmaso, Lara Fontanella, Luigi Ippoliti, Caterina Fusilli
      Pages 73-103
  4. Back Matter
    Pages 105-115

About this book

Introduction

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.                                                                                                                      

Keywords

Shape Analysis Dynamic Shapes NonParametric Combination (NPC) Parametric Methodology Nonparametric Methodology Statistical Shape Analysis Shape Inference Expectation Maximization Algorithm Offset-normal Shape Distribution

Authors and affiliations

  • Chiara Brombin
    • 1
  • Luigi Salmaso
    • 2
  • Lara Fontanella
    • 3
  • Luigi Ippoliti
    • 4
  • Caterina Fusilli
    • 5
  1. 1.Department of PsychologyVita-Salute San Raffaele UniversityMILANOItaly
  2. 2.Department of Management and EngineeringUniversity of PadovaPadovaItaly
  3. 3.Department of Legal and Social SciencesUniversity of Chieti-PescaraChietiItaly
  4. 4.Department of EconomicsUniversity of Chieti-PescaraPescaraItaly
  5. 5.Bioinformatics UnitCasa Sollievo della Sofferenza-MendelRomeItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-26311-3
  • Copyright Information The Authors 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-26310-6
  • Online ISBN 978-3-319-26311-3
  • Series Print ISSN 2191-544X
  • Series Online ISSN 2191-5458
  • Buy this book on publisher's site
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