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Local Features in Natural Images via Singularity Theory

  • James Damon
  • Peter Giblin
  • Gareth Haslinger
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2165)

Table of contents

  1. Front Matter
    Pages i-x
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. James Damon, Peter Giblin, Gareth Haslinger
      Pages 3-10
    3. James Damon, Peter Giblin, Gareth Haslinger
      Pages 11-20
  3. Mathematical Basis for Analysis of Feature-Shade/Shadow-Contours

    1. Front Matter
      Pages 21-21
    2. James Damon, Peter Giblin, Gareth Haslinger
      Pages 23-33
    3. James Damon, Peter Giblin, Gareth Haslinger
      Pages 35-39
    4. James Damon, Peter Giblin, Gareth Haslinger
      Pages 41-71
    5. James Damon, Peter Giblin, Gareth Haslinger
      Pages 73-99
    6. James Damon, Peter Giblin, Gareth Haslinger
      Pages 101-114
  4. The Classification of Interactions Involving Feature-Shade/Shadow-Contours

    1. Front Matter
      Pages 115-115
    2. James Damon, Peter Giblin, Gareth Haslinger
      Pages 117-134
    3. James Damon, Peter Giblin, Gareth Haslinger
      Pages 135-155
    4. James Damon, Peter Giblin, Gareth Haslinger
      Pages 157-177
  5. Classifications of Interactions of Pairs of Feature-Shade/Shadow-Contours

    1. Front Matter
      Pages 179-179
    2. James Damon, Peter Giblin, Gareth Haslinger
      Pages 193-212
  6. Classifications of Multiple Interactions

    1. Front Matter
      Pages 213-213
    2. James Damon, Peter Giblin, Gareth Haslinger
      Pages 215-241
    3. James Damon, Peter Giblin, Gareth Haslinger
      Pages 243-252
  7. Back Matter
    Pages 253-257

About this book

Introduction

This monograph considers a basic problem in the computer analysis of natural images, which are images of scenes involving multiple objects that are obtained by a camera lens or a viewer’s eye. The goal is to detect geometric features of objects in the image and to separate regions of the objects with distinct visual properties. When the scene is illuminated by a single principal light source, we further include the visual clues resulting from the interaction of the geometric features of objects, the shade/shadow regions on the objects, and the “apparent contours”.  We do so by a mathematical analysis using a repertoire of methods in singularity theory. This is applied for generic light directions of both the “stable configurations” for these interactions, whose features remain unchanged under small viewer movement, and the generic changes which occur under changes of view directions. These may then be used to differentiate between objects and determine their shapes and positions.

Keywords

Natural Images Local Features Singularity Theory on Stratified Spaces Stable Views Generic Changes under Viewer Movement

Authors and affiliations

  • James Damon
    • 1
  • Peter Giblin
    • 2
  • Gareth Haslinger
    • 3
  1. 1.Department of MathematicsUniversity of North Carolina Chapel HillUSA
  2. 2.Dept. of Mathematical SciencesUniversity of Liverpool Dept. of Mathematical SciencesLiverpoolUnited Kingdom
  3. 3.AinsdaleUnited Kingdom

Bibliographic information