Level Set Methods and Dynamic Implicit Surfaces

ISBN-13: 9780387954820 / Angielski / Twarda / 2002 / 273 str.

Stanley Osher; Ronald Fedkiw; Ronald Fedkiw

Opis

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.

Recenzje

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. ... A student 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)

Spis treści

Preface * Part I Implicit Surfaces * Implicit Functions * Signed Distance Functions * Part II Level Set Methods * Motion in an Externally Generated Velocity Field * Motion Involving Mean Curvature * Hamilton-Jacobi Equations * Motion in the Normal Direction * Constructing Signed Distance Functions * Extrapolation in the Normal Direction * Particle Level Set Method * Codimension Two Objects * Part III Image Processing and Computer Vision * Image Restoration * Snakes, Active Contours and Segmentation * Reconstruction of Surfaces from Unorganized Data Points * Part IV Computational Physics * Hyperbolic Conservation Laws and Compressible Flow * Two Phase Compressible Flow * Shocks, Detonations and Deflagrations * Solid Fluid Coupling * Incompressible Flow * Free Surfaces * Liquid Gas Interactions * Two Phase Incompressible Flow * Low Speed Flames * Heat Flow

Blurb

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.