Shape and Shape Theory
Wiley Series in Probability and Statistics
1. Edition August 1999
XII, 306 Pages, Hardcover
Wiley & Sons Ltd
Short Description
Pioneered by David Kendall, the statistical theory of shape is an emerging area generating considerable interest for statisticians, engineers, and computer scientists. Co-written by Dr. Kendall, this volume presents a coherent theory of shape developed from Kendall's own approach known as static and kinematic theory. Illustrated with a variety of practical examples, the book shows how the theories presented are useful in solving practical problems in shape for a range of fields from archaeology to astronomy. This work is destined to become the cornerstone reference on shape theory, written by its leading theorist.
Shape and Shape Theory D. G. Kendall Churchill College, University of Cambridge, UK D. Barden Girton College, University of Cambridge, UK T. K. Carne King's College, University of Cambridge, UK H. Le University of Nottingham, UK The statistical theory of shape is a relatively new topic and is generating a great deal of interest and comment by statisticians, engineers and computer scientists. Mathematically, 'shape' is the geometrical information required to describe an object when location, scale and rotational effects are removed. The theory was pioneered by Professor David Kendall to solve practical problems concerning shape. This text presents an elegant account of the theory of shape that has evolved from Kendall's work. Features include:
* A comprehensive account of Kendall's shape spaces
* A variety of topological and geometric invariants of these spaces
* Emphasis on the mathematical aspects of shape analysis
* Coverage of the mathematical issues for a wide range of applications
The early chapters provide all the necessary background information, including the history and applications of shape theory. The authors then go on to analyse the topic, in brilliant detail, in a variety of different shape spaces. Kendall's own procedures for visualising distributions of shapes and shape processes are covered at length. Implications from other branches of mathematics are explored, along with more advanced applications, incorporating statistics and stochastic analysis. Applied statisticians, applied mathematicians, engineers and computer scientists working and researching in the fields of archaeology, astronomy, biology, geography and physical chemistry will find this book of great benefit. The theories presented are used today in a wide range of subjects from archaeology through to physics, and will provide fascinating reading to anyone engaged in such research. Visit our web page! http://www.wiley.com/
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.
