Level Set Methods and Dynamic Implicit Surfaces

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 fr 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)

Implicit Surfaces.- Implicit Functions.- Signed Distance Functions.- 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.- Image Processing and Computer Vision.- Image Restoration.- Snakes, Active Contours, and Segmentation.- Reconstruction of Surfaces from Unorganized Data Points.- 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.