Synopses & Reviews
The chapters in this volume are based on a scientific workshop on the "Applications and Theory of Random Sets". They address theoretical and applied aspects of this field in diverse areas of applications such as Image Modeling and Analysis, Information/Data Fusion, and Theoretical Statistics and Expert Systems. Emphasis is given to potential applications in engineering problems of practical interest. This volume is of interest to mathematicians, engineers and scientists who are interested in the potential application of random set theory to practical problems in imaging, information fusion, and expert systems.
Synopsis
This IMA Volume in Mathematics and its Applications RANDOM SETS: THEORY AND APPLICATIONS is based on the proceedings of a very successful 1996 three-day Summer Program on "Application and Theory of Random Sets." We would like to thank the scientific organizers: John Goutsias (Johns Hopkins University), Ronald P.S. Mahler (Lockheed Martin), and Hung T. Nguyen (New Mexico State University) for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the Army Research Office (ARO), the Office ofNaval Research (0NR), and the Eagan, MinnesotaEngineering Center ofLockheed Martin Tactical Defense Systems, whose financial support made the summer program possible. Avner Friedman Robert Gulliver v PREFACE "Later generations will regard set theory as a disease from which one has recovered. " - Henri Poincare Random set theory was independently conceived by D.G. Kendall and G. Matheron in connection with stochastic geometry. It was however G.
Table of Contents
Contents.- Foreword.- Preface.- Part I. Image Modeling and Analysis.- Morphological analysis of random sets.- An introduction.- Statistical problems for random sets.- On estimating granulometric discrete size distributions of random sets.- Logical granulometric filtering in the signal-union-clutter.- On optimal filtering of morphologically smooth discrete random sets and related open problems.- Part II. Information/Data Fusion and Expert Systems.- On the maximum of conditonal entropy for upper/lower probabilities generated by random sets.- Random sets in information fusion.- An overview Cramer-Rao type bounds for random set problems.- Random sets in data fusion.- Multi-object state-estimation and much more