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  • © 2003

Level Set Methods and Dynamic Implicit Surfaces

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

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-xiii
  2. Implicit Surfaces

    1. Front Matter

      Pages 1-1
    2. Implicit Functions

      • Stanley Osher, Ronald Fedkiw
      Pages 3-16
    3. Signed Distance Functions

      • Stanley Osher, Ronald Fedkiw
      Pages 17-22
  3. Level Set Methods

    1. Front Matter

      Pages 23-23
    2. Motion in an Externally Generated Velocity Field

      • Stanley Osher, Ronald Fedkiw
      Pages 25-39
    3. Motion Involving Mean Curvature

      • Stanley Osher, Ronald Fedkiw
      Pages 41-46
    4. Hamilton-Jacobi Equations

      • Stanley Osher, Ronald Fedkiw
      Pages 47-54
    5. Motion in the Normal Direction

      • Stanley Osher, Ronald Fedkiw
      Pages 55-61
    6. Constructing Signed Distance Functions

      • Stanley Osher, Ronald Fedkiw
      Pages 63-74
    7. Extrapolation in the Normal Direction

      • Stanley Osher, Ronald Fedkiw
      Pages 75-77
    8. Particle Level Set Method

      • Stanley Osher, Ronald Fedkiw
      Pages 79-86
    9. Codimension-Two Objects

      • Stanley Osher, Ronald Fedkiw
      Pages 87-93
  4. Image Processing and Computer Vision

    1. Front Matter

      Pages 95-95
    2. Image Restoration

      • Stanley Osher, Ronald Fedkiw
      Pages 97-118
    3. Snakes, Active Contours, and Segmentation

      • Stanley Osher, Ronald Fedkiw
      Pages 119-138
    4. Reconstruction of Surfaces from Unorganized Data Points

      • Stanley Osher, Ronald Fedkiw
      Pages 139-146
  5. Computational Physics

    1. Front Matter

      Pages 147-148
    2. Hyperbolic Conservation Laws and Compressible Flow

      • Stanley Osher, Ronald Fedkiw
      Pages 149-166
    3. Two-Phase Compressible Flow

      • Stanley Osher, Ronald Fedkiw
      Pages 167-188

About this book

Scope, Aims, and Audiences This book, Level Set Methods and Dynamic Implicit Surfaces is designed to serve two purposes: Parts I and II introduce the reader to implicit surfaces and level set methods. We have used these chapters to teach introductory courses on the material to students with little more than a fundamental math background. No prior knowledge of partial di?erential equations or numerical analysis is required. These ?rst eight chapters include enough detailed information to allow students to create working level set codes from scratch. Parts III and IV of this book are based on a series of papers published by us and our colleagues. For the sake of brevity, a few details have been occasionally omitted. These chapters do include thorough explanations and enough of the signi?cant details along with the appropriate references to allow the reader to get a ?rm grasp on the material. This book is an introduction to the subject. We have given examples of the utility of the method to a diverse (but by no means complete) collection of application areas. We have also tried to give complete numerical recipes and a self-contained course in the appropriate numerical analysis. We - lieve that this book will enable users to apply the techniques presented here to real problems.

Reviews

From the reviews:

S.J. Osher and R. Fedkiw

Level Set Methods and Dynamic Implicit Surfaces

"This book is an introduction to level set methods and dynamic implicit surfaces. While it gives many examples of the utility of the methods to 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. A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful."—ZENTRALBLATT MATH

"Over the past few decades, level set methods have found applications in astounding range of areas. The authors, having contributed so profoundly, are in an excellent position to write an authoritative text. … Without overly much cumbersome apparatus, the text introduces into an active area of scientific computing in a very informative way." (H. Muthsam, Monatshefte für Mathematik, Vol. 145 (3), 2005)

"Level set methods have successfully been used for a wide range of applications since the pioneering paper of Osher and Sethian. This book is an excellent introduction to the field, allowing newcomers to quickly grasp the key ideas. It also covers, in sufficient detail, the level set approach to several problems arising in image processing and computational physics. … This book is suitable for researchers interested in modeling interface motion, and would be an excellent book for a graduate level course in mathematics/engineering/science." (Tariq Aslam, Mathematics of Computation, Vol. 73 (247), 2004)

"This book is an introduction to level set methods and dynamic implicit surfaces. … Together with many examples, the book also gives a complete description of numerical aspects which will enable users to quickly apply these techniques to real problems. … Astudent or researcher working in mathematics, computer graphics, science or engineering and interested in dynamically moving fronts which might change their topology or develop singularities, will find this book interesting and useful." (V. M. Soundalgekar, Zentralblatt MATH, Vol. 1026, 2004)

"The book contains many pictures, several of them in color, which give a good sample of the results achieved. This is a stimulating book for those interested in modeling dynamic interfaces with numerical methods that can handle topology changes and singularities. Level set methods are such methods and have been successful in several applications." (Luiz Henrique de Figueiredo, Mathematical Reviews, 2003 j)

Authors and Affiliations

  • Department of Mathematics, University of California at Los Angeles, Los Angeles, USA

    Stanley Osher

  • Department of Computer Science, Stanford University, Stanford, USA

    Ronald Fedkiw

Bibliographic Information

Buy it now

Buying options

eBook USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access