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Level Set Methods and Dynamic Implicit Surfaces

by: Stanley J. Osher, Ronald P. Fedkiw
en

9780387227467  9780387954820  0387954821 

Level Set Methods and Dynamic Implicit Surfaces
By Stanley J. Osher, Ronald P. Fedkiw




Product Description:

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 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. The book begins with a description of implicit surfaces and their basic properties, 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, re-initialization to a signed distance function, extrapolation in the normal direction, the particle level set method and the motion of co-dimension two (and higher) objects. Part III is concerned with topics taken from the fields 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 comible fluid dynamics, then two-phase comible flow involving possibly different equations of state, detonation and deflagration waves, and solid/fluid structure interaction. Next it discusses incomible fluid dynamics, including a computer graphics simulation of smoke, free surface flows, including a computer graphics simulation of water, and fully two-phase incomible flow. Additional related topics include incomible flames with applications to computer graphics and coupling a comible and incomible 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 its topology or develop singularities, will find this book interesting and useful.




Summary: A solid introduction to level sets
Rating: 5

I read this book and Sethian's book and found this one to be much easier to read. The presentation follows a logical sequence and looks much less like someone's thesis than Sethian's text. Level sets and many of their various applications are covered in relative detail for a book of this size.

However, this is more of a survey book, as others have mentioned, and in my opinion that is a benefit. In addition to covering the fundamentals of level sets, the text covers many modern methods for solving hyperbolic conservations laws. I learned as much, or more, about high-order interpolation, flux-splitting, etc. from this book as from books by Laney and Leveque. For more detail on any of these topics, some of the best references are pred.

An excellent text at a good price.



Summary: Solid introduction intended for numerical PDE people
Rating: 4

This book pres a good introduction (and extensive references) to the level set method. The major implementation details are given (with the finite difference formulas). The book is intended for people who already know something about numerical PDE's and CFD (computational fluid dynamics). Not all of the details are given (such as smoothing of the level set when computing curvature), but this will probably be addressed in a future volume. Overall, this book will get you started with actual computations. But do not be afraid to consult the more recent literature on the subject.



Summary: A Bad Way To Learn Level Set Methods
Rating: 2

If you're new to level set methods and are hoping to learn to implement them computationally, this is the WRONG book for you. This book reads like a 250 page review paper. Most of the material it covers is explained in much better detail in the references it pres.
I'm not sure what audience this book is intended for. The only use I can see for this book is to help theorists learn level set methods. It certainly is of no help to those interested in implementing them. This book contains no code or psuedocode examples which would be helpful to a novice, nor does it contain any cutting edge techniques which would be useful to experts.
I would give this a 1 star rating, but I must admit that it is clearly written. Also to its credit are the colored figures, which inspire one to want to use level set methods, even if this book is of no help in implementing them.



Summary: from zero to hero in a few weeks
Rating: 5

This book is good. It covers level set methods from the very basics through some rather advanced material. Sure it takes some material from published papers (the subject matter is way to recent to be done any other way).

You can pick this book up with some knowledge of how to write a simple computer program and with in a few weeks be up to speed on numerical methods for solving interesting problems in image processing and other interface tracking problems.

It doesn't have all the numerical proofs you might want, but if you're willing to believe they exist then you can get off to a fast start with this text and with a little creativity you should be able to start submitting your own papers using the tools presented here.



Summary: excellent
Rating: 5

This book is ABSOLUTELY among the best in the area of computational mathematics. It covers from the basics to the trendy applications, which is the biggest satisfaction I got from spending money on it. It is more than a collection of papers (no kidding!), since the contents have a good interior coherence if you read it carefully rather than browsing it like a novel. And for the those fancy pictures in the book, all I can say is that 'a picture is worth than thousands of words' - it is especially true in the area of graphics. You guys who care about SIGGRAPH should know better. More than that, this book does give you the numerical recipe for you to DIY these simulations on your own computer, besides the mathematics behind all those sexy results. Anyway, this book is worth every penny you spent!