Ulf Grenander

This systematic approach covers semi-groups, groups, linear vector spaces, and algebra. It states and studies fundamental probabilistic problems for these spaces, focusing on concrete results. 1963 edition.

Probabilities on Algebraic Structures

Murray Rosenblatt

Written in the terminology of the theoretical statistician, this book presents an approach to time series analysis. It presents a unified treatment of methods that are being used in the physical sciences and technology.

Statistical Analysis of Stationary Time Series

Y. Chow

Daniel M. Keenan

In this book a global shape model is developed and applied to the analysis of real pictures acquired with a visible light camera under varying conditions of optical degradation. Computational feasibility of the algorithms derived from this model is achieved by analytical means. The aim is to develop methods for image understanding based on structured restoration, for example automatic detection of abnormalities. We also want to find the limits of applicability of the algorithms. This is done by making the optical degradations more and more severe until the algorithms no longer succeed in their task. This computer experiment in pattern theory is one of several. The others, LEAVES, X-RAYS, and RANGE are described elsewhere. This book is suitable for an advanced undergraduate or graduate seminar in pattern theory, or as an accompanying book for applied probability, computer vision, or pattern recognition.

A Pattern Theoretic Study of Biological Shapes

Hands

Walter Freiberger

This book arose out of a number of different contexts, and numerous persons have contributed to its conception and development. It had its origin in a project initiated jointly with the IBM Cambridge Scien tific Center, particularly with Dr. Rhett Tsao, then of that Center. We are grateful to Mr. Norman Rasmussen, Manager of the IBM Scientific Center Complex, for his initial support. The work is being carried on at Brown University with generous support from the Office of Computing Activities of the National Science Foundation (grants GJ-174 and GJ-7l0); we are grateful to Dr. John Lehmann of this Office for his interest and encouragement. Professors Donald McClure and Richard Vitale of the Division of Applied Mathematics at Brown University contributed greatly to the project and taught courses in its spirit. We are indebted to them and to Dr. Tore Dalenius of the University of Stockholm for helpful criticisms of the manuscript. The final stimulus to the book's completion came from an invLtation to teach a course at the IBM European Systems Research Institute at Geneva. We are grateful to Dr. J.F. Blackburn, Director of the Institute, for his invitation, and to him and his wife Beverley for their hospitality. We are greatly indebted to Mrs. Katrina Avery for her splendid secretarial and editorial work on the manuscript.

A Course in Computational Probability and Statistics

Emeritus Professor Division of Applied Mathematics Ulf Grenander

The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyse the mathematical properties of the resulting regular structures, and to apply them to practically occuring patterns in nature and the man-made world. Starting from an algebraic formulation of such representations they are studied in terms of their topological, dynamical and probabilistic aspects. Patterns are expressed through their typical behaviour as well as through their variability around their typical form. Employing the representations (regular structures) algorithms are derived for the understanding, recognition, and restoration of observed patterns. The algorithms are investigated through computer experiments.

Ulf Grenander

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