Advanced Series on Statistical Science and Applied Probability - Vol. 5
LOCAL STEREOLOGY
by Eva B Vedel Jensen (University of Aarhus, Denmark)
This book provides a unified exposition of local-stereological methods developed within the last 15 years. The object of local stereology is to draw inference about quantitative parameters of spatial structures which can be regarded as neighbourhoods of points, called reference points. The model example is a biological cell which can be regarded as a neighbourhood of its nucleus. In local stereology, information from sections through the reference point is used. Only very weak assumptions are needed for the structure under study. For instance, specific cell shape assumptions are not necessary.
In order to reach a broader audience, the book has been written not only for specialists in stereology, integral geometry and geometric measure theory. In particular, Chapter 1 is an elementary introduction to stereology and the book contains about 75 illustrations. The theory of local steroelogy involves, however, advanced mathematical tools, which constitute an important part of the book.
Local-stereological methods are now in world-wide use in the microscopical study of biological tissue, and this invaluable book also contains a description of how the local methods are used in practice.
Contents:
- Introduction to Stereology
- The Coarea Formula
- Rotation Invariant
Measures on Lnp
- The Classical Blaschke–Petkantschin Formula
- The Generalized Blaschke–Petkantschin Formula
- Local Slice Formulae
- Design and Implementation of Local-Stereological Experiments
- The Model-Based Approach
- Perspectives and Future Trends
Readership: Researchers, teachers and graduate students in mathematical
statistics and probability.
"This book adds weighty theoretical support to the increasingly important field of spatial sampling."
"The whole book is very carefully written from both the mathematical and didactical points of view. This excellent style is supported by a series of suggestive figures and of exercises. It is written for researchers working in theory or in applications, for teachers and for graduate students."
"The book is self-contained, and well-readable with a number of explanatory figures. All chapters are followed by useful exercises and bibliographical notes. Overall, this book is going to become a standard graduate text on design-based local stereology."
| 264pp |
Pub. date: Mar 1998 |
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