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Image segmentation consists of dividing an image domain into disjoint regions according to a characterization of the image within or in-between the regions. Therefore, segmenting an image is to divide its domain into relevant components. The efficient solution of the key problems in image segmentation promises to enable a rich array of useful applications. The current major application areas include robotics, medical image analysis, remote sensing, scene understanding, and image database retrieval. The subject of this book is image segmentation by variational methods with a focus on formulations which use closed regular plane curves to define the segmentation regions and on a level set implementation of the corresponding active curve evolution algorithms. Each method is developed from an objective functional which embeds constraints on both the image domain partition of the segmentation and the image data within or in-between the partition regions. The necessary conditions to optimize the objective functional are then derived and solved numerically. The book covers, within the active curve and level set formalism, the basic two-region segmentation methods, multiregion extensions, region merging, image modeling, and motion based segmentation. To treat various important classes of images, modeling investigates several parametric distributions such as the Gaussian, Gamma, Weibull, and Wishart. It also investigates non-parametric models. In motion segmentation, both optical flow and the movement of real three-dimensional objects are studied.

Geometric measure theory. --- Image processing -- Digital techniques -- Mathematics. --- Image segmentation --- Electrical & Computer Engineering --- Engineering & Applied Sciences --- Electrical Engineering --- Telecommunications --- Applied Physics --- Mathematics --- Image processing --- Level set methods. --- Digital techniques. --- Mathematics. --- Level sets (Mathematics) --- Osher-Sethian level set methods --- Sethian level set methods, Osher --- -Digital image processing --- Engineering. --- Image processing. --- Signal, Image and Speech Processing. --- Image Processing and Computer Vision. --- -Interfaces (Physical sciences) --- Digital image processing --- Digital electronics --- Computer vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Signal processing. --- Speech processing systems. --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical equipment

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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.

Level set methods. --- Implicit functions. --- Fonctions implicites --- Level set methods --- Implicit functions --- 514.8 --- 681.3*G18 --- Level sets (Mathematics) --- Osher-Sethian level set methods --- Sethian level set methods, Osher --- -Interfaces (Physical sciences) --- Functions, Implicit --- Functions of several real variables --- Geometric study of objects of mechanics and physics --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Physics --- Atomic Physics --- Mathematical Theory --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 514.8 Geometric study of objects of mechanics and physics --- -Functions, Implicit --- Mathematics. --- Image processing. --- Computer mathematics. --- Continuum physics. --- Mechanics. --- Mechanics, Applied. --- Computational Mathematics and Numerical Analysis. --- Classical Continuum Physics. --- Image Processing and Computer Vision. --- Theoretical and Applied Mechanics. --- 681.3 *G18 --- Computer science --- Computer vision. --- Mechanics, applied. --- Classical and Continuum Physics. --- Optical data processing. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Classical field theory --- Continuum physics --- Continuum mechanics --- Computer mathematics --- Optical equipment --- Méthodes d'ensembles de niveaux --- Representation des surfaces --- Méthodes d'ensembles de niveaux