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Random Sets

Theory and Applications

  • Book
  • © 1997

Overview

Editors:
  1. John Goutsias

    1. Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, USA

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  2. Ronald P. S. Mahler

    1. Tactical Defense Systems, Lockheed Martin Corporation, Eagan, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Hung T. Nguyen

    1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 97)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Image Modeling and Analysis

    1. Front Matter

      Pages 1-1
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    2. Morphological Analysis of Random Sets an Introduction

      • John Goutsias
      Pages 3-26

    3. Statistical Problems for Random Sets

      • Ilya Molchanov
      Pages 27-45

    4. On Estimating Granulometric Discrete Size Distributions of Random Sets

      • Krishnamoorthy Sivakumar, John Goutsias
      Pages 47-71

    5. Logical Granulometric Filtering in the Signal—Union—Clutter Model

      • Edward R. Dougherty, Yidong Chen
      Pages 73-95

    6. On Optimal Filtering of Morphologically Smooth Discrete Random Sets and Related Open Problems

      • Nikolaos D. Sidiropoulos
      Pages 97-104

  4. Theoretical Statistics and Expert Systems

    1. Front Matter

      Pages 257-257
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    2. Uncertainty Measures, Realizations and Entropies*

      • Ulrich Hőhle, Siegfried Weber
      Pages 259-295

    3. Random Sets in Decision—Making

      • Hung T. Nguyen, Nhu T. Nguyen
      Pages 297-320

    4. Random Sets Unify, Explain, and Aid Known Uncertainty Methods in Expert Systems

      • Vladik Kreinovich
      Pages 321-345

    5. Laws of Large Numbers for Random Sets

      • Robert L. Taylor, Hiroshi Inoue
      Pages 347-360

    6. Geometric Structure of Lower Probabilities

      • Paul K. Black
      Pages 361-383
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About this book

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.

Editors and Affiliations

  • Department of Electrical and Computer Engineering, The Johns Hopkins University, Baltimore, USA

    John Goutsias

  • Tactical Defense Systems, Lockheed Martin Corporation, Eagan, USA

    Ronald P. S. Mahler

  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

    Hung T. Nguyen

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