The Statistical Theory of Shape (Springer Series in Statistics) - Hardcover

Small, Christopher G.

Hardcover

ISBN 10: 0387947299 ISBN 13: 9780387947297

Publisher: Springer, 1996

Synopsis

In general terms, the shape of an object, data set, or image can be de­ fined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measure­ ment error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statis­ tical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathe­ matical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature.

About this title

About the Author

Christopher G. Small is Professor of Statistics at the University of Waterloo.

From the Back Cover

This book provides a comprehensive coverage of the statistical theory of shape. The shape of a data set can be defined as the total of all information invariant under translations, rotations, and scale changes to the data. Over the last decade, shape analysis has emerged as a promising new field of statistics with applications to morphometrics, pattern recognition, archeology, and other disciplines.

Edition details

• Publisher: Springer
• Publication date: 1996
• Language: English
• ISBN 10: 0387947299
• ISBN 13: 9780387947297
• Binding: Hardcover
• Number of pages: 240