Level Set Methods and Dynamic Implicit Surfaces

  • Stanley Osher
  • Ronald Fedkiw

Part of the Applied Mathematical Sciences book series (AMS, volume 153)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Implicit Surfaces

    1. Front Matter
      Pages 1-1
    2. Stanley Osher, Ronald Fedkiw
      Pages 3-16
    3. Stanley Osher, Ronald Fedkiw
      Pages 17-22
  3. Level Set Methods

    1. Front Matter
      Pages 23-23
    2. Stanley Osher, Ronald Fedkiw
      Pages 25-39
    3. Stanley Osher, Ronald Fedkiw
      Pages 41-46
    4. Stanley Osher, Ronald Fedkiw
      Pages 47-54
    5. Stanley Osher, Ronald Fedkiw
      Pages 55-61
    6. Stanley Osher, Ronald Fedkiw
      Pages 63-74
    7. Stanley Osher, Ronald Fedkiw
      Pages 75-77
    8. Stanley Osher, Ronald Fedkiw
      Pages 79-86
    9. Stanley Osher, Ronald Fedkiw
      Pages 87-93
  4. Image Processing and Computer Vision

    1. Front Matter
      Pages 95-95
    2. Stanley Osher, Ronald Fedkiw
      Pages 97-118
    3. Stanley Osher, Ronald Fedkiw
      Pages 119-138
    4. Stanley Osher, Ronald Fedkiw
      Pages 139-146
  5. Computational Physics

    1. Front Matter
      Pages 147-148
    2. Stanley Osher, Ronald Fedkiw
      Pages 149-166
    3. Stanley Osher, Ronald Fedkiw
      Pages 167-188

About this book

Introduction

This book is an introduction to level set methods and dynamic implicit surfaces. These are powerful techniques for analyzing and computing moving fronts in a variety of different settings. While the book gives many examples of the usefulness of the methods for a diverse set of applications, it also gives complete numerical analysis and recipes, which will enable users to quickly apply the techniques to real problems.

The book begins with the description of implicit surfaces and their basic properties, and then devises the level set geometry and calculus toolbox, including the construction of signed distance functions. Part II adds dynamics to this static calculus. Topics include the level set equation itself, Hamilton-Jacobi equations, motion of a surface normal to itself, reinitialization to a signed distance function, extrapolation in the normal direction, the particle level set method, and the motion of codimension two (and higher) objects. Part III is concerned with topics taken from the field of image processing and computer vision. These include the restoration of images degraded by noise and blur, image segmentation with active contours (snakes), and reconstruction of surfaces from unorganized data points. Part IV is dedicated to computational physics. It begins with one-phase compressible fluid dynamics, then two-phase compressible flow involving possibly different equations of state, detonation and deflagration waves, and solid/fluid structure interaction. Next it discusses incompressible fluid dynamics, including a computer graphics simulation of smoke; free surface flows, including a computer graphics simulation of water; and fully two-phase incompressible flow. Additional related topics include incompressible flames with applications to computer graphics and coupling a compressible and incompressible fluid. Finally, heat flow and Stefan problems are discussed.

A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change it's topology or develop singularities, will find this book interesting and useful.

Keywords

computer graphics computer vision fluid dynamics image processing image restoration numerical analysis simulation topology

Authors and affiliations

  • Stanley Osher
    • 1
  • Ronald Fedkiw
    • 2
  1. 1.Department of MathematicsUniversity of California at Los AngelesLos AngelesUSA
  2. 2.Department of Computer ScienceStanford UniversityStanfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b98879
  • Copyright Information Springer-Verlag New York, Inc. 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-9251-4
  • Online ISBN 978-0-387-22746-7
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • About this book