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Shape in Picture

Mathematical Description of Shape in Grey-level Images

  • Conference proceedings
  • © 1994

Overview

Editors:
  1. Ying-Lie O

    1. Centre for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands

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  2. Alexander Toet

    1. Institute for Human Factors (TNO-IZF), Netherlands Organization for Applied Scientific Research, Soesterberg, The Netherlands

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  3. David Foster

    1. Department of Communication and Neuroscience, University of Keele, Keele, Staffordshire, UK

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  4. Henk J. A. M. Heijmans

    1. Centre for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands

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  5. Peter Meer

    1. Department of Electrical and Computer Engineering, Rutgers University, Piscataway, USA

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Part of the book series: NATO ASI Subseries F: (NATO ASI F, volume 126)

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Table of contents (49 papers)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Introduction

    1. Introduction

      • Ying-Lie O, Alexander Toet, David Foster, Henk J. A. M. Heijmans, Peter Meer
      Pages 1-2

  3. Mathematical Background

    1. Topology and Geometry

      1. The Khalimsky Line as a Foundation for Digital Topology
        • Ralph Kopperman
        Pages 3-20
      2. Topological Foundations of Shape Analysis
        • Vladimir A. Kovalevsky
        Pages 21-36
      3. A New Concept for Digital Geometry
        • Vladimir A. Kovalevsky
        Pages 37-51
      4. Theoretical Approaches to <i>N</i>-Dimensional Digital Objects
        • Klaus Voss
        Pages 53-70
      5. On Boundaries and Boundary Crack-Codes of Multidimensional Digital Images
        • T. Yung Kong
        Pages 71-80
      6. Studying Shape Through Size Functions
        • Claudio Uras, Alessandro Verri
        Pages 81-90

  4. Local Extraction

    1. Mathematical Morphology

      1. Mathematical Morphology as a Tool for Shape Description
        • Henk J. A. M. Heijmans
        Pages 147-176
      2. On Information Contained in the Erosion Curve
        • Juliette Mattioli, Michel Schmitt
        Pages 177-195
      3. Morphological Area Openings and Closings for Grey-scale Images
        • Luc Vincent
        Pages 197-208
      4. Manifold Shape: from Differential Geometry to Mathematical Morphology
        • Jos B. T. M. Roerdink
        Pages 209-223
      5. On Negative Shape
        • Pijush K. Ghosh
        Pages 225-247

    2. Wavelets

      1. An Overview of the Theory and Applications of Wavelets
        • Björn Jawerth, Wim Sweldens
        Pages 249-274
      2. Fractal Surfaces, Multiresolution Analyses and Wavelet Transforms
        • Jeffrey S. Geronimo, Douglas P. Hardin, Peter R. Massopust
        Pages 275-290
      3. Interpolation in Multiscale Representations
        • Charles H. Anderson, Subrata Rakshit
        Pages 291-300

  5. Theory of Shape

    1. Keynote Address

      1. Discrete Stochastic Growth Models for Two-Dimensional Shapes
        • Scott Thompson, Azriel Rosenfeld
        Pages 301-318
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Keywords

About this book

The fields of image analysis, computer vision, and artificial intelligence all make use of descriptions of shape in grey-level images. Most existing algorithms for the automatic recognition and classification of particular shapes have been devel­ oped for specific purposes, with the result that these methods are often restricted in their application. The use of advanced and theoretically well-founded math­ ematical methods should lead to the construction of robust shape descriptors having more general application. Shape description can be regarded as a meeting point of vision research, mathematics, computing science, and the application fields of image analy­ sis, computer vision, and artificial intelligence. The NATO Advanced Research Workshop "Shape in Picture" was organised with a twofold objective: first, it should provide all participants with an overview of relevant developments in these different disciplines; second, it should stimulate researchers to exchange original results and ideas across the boundaries of these disciplines. This book comprises a widely drawn selection of papers presented at the workshop, and many contributions have been revised to reflect further progress in the field. The focus of this collection is on mathematical approaches to the construction of shape descriptions from grey-level images. The book is divided into five parts, each devoted to a different discipline. Each part contains papers that have tutorial sections; these are intended to assist the reader in becoming acquainted with the variety of approaches to the problem.

Editors and Affiliations

  • Centre for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands

    Ying-Lie O, Henk J. A. M. Heijmans

  • Institute for Human Factors (TNO-IZF), Netherlands Organization for Applied Scientific Research, Soesterberg, The Netherlands

    Alexander Toet

  • Department of Communication and Neuroscience, University of Keele, Keele, Staffordshire, UK

    David Foster

  • Department of Electrical and Computer Engineering, Rutgers University, Piscataway, USA

    Peter Meer

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