Kendall / Barden / Carne Shape and Shape Theory

1. Auflage 2009
ISBN: 978-0-470-31784-6
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 318 Seiten, E-Book

Reihe: Wiley Series in Probability and Statistics

Shape and Shape Theory D. G. Kendall Churchill College, Universityof Cambridge, UK D. Barden Girton College, University of Cambridge,UK T. K. Carne King's College, University of Cambridge, UK H. LeUniversity of Nottingham, UK The statistical theory of shape is arelatively new topic and is generating a great deal of interest andcomment by statisticians, engineers and computer scientists.Mathematically, 'shape' is the geometrical information required todescribe an object when location, scale and rotational effects areremoved. The theory was pioneered by Professor David Kendall tosolve practical problems concerning shape. This text presents anelegant account of the theory of shape that has evolved fromKendall's work. Features include:
* A comprehensive account of Kendall's shape spaces
* A variety of topological and geometric invariants of thesespaces
* Emphasis on the mathematical aspects of shape analysis
* Coverage of the mathematical issues for a wide range ofapplications
The early chapters provide all the necessary backgroundinformation, including the history and applications of shapetheory. The authors then go on to analyse the topic, in brilliantdetail, in a variety of different shape spaces. Kendall's ownprocedures for visualising distributions of shapes and shapeprocesses are covered at length. Implications from other branchesof mathematics are explored, along with more advanced applications,incorporating statistics and stochastic analysis. Appliedstatisticians, applied mathematicians, engineers and computerscientists working and researching in the fields of archaeology,astronomy, biology, geography and physical chemistry will find thisbook of great benefit. The theories presented are used today in awide range of subjects from archaeology through to physics, andwill provide fascinating reading to anyone engaged in suchresearch. Visit our web page! http://www.wiley.com/

Autoren/Hrsg.

Kendall, D. G.

Barden, D.

Carne, T. K.

Le, H.

Inhaltsverzeichnis

Shapes and Shape Spaces.
The Global Structure of Shape Spaces.
Computing the Homology of Cell Complexes.
A Chain Complex for Shape Spaces.
The Homology Groups of Shape Spaces.
Geodesics in Shape Spaces.
The Riemannian Structure of Shape Spaces.
Induced Shape-Measures.
Mean Shapes and the Shape of the Means.
Visualising the Higher Dimensional Shape Spaces.
General Shape Spaces.
Appendix.
Bibliography.
Index.