This book takes readers on a tour through modern methods in image analysis and reconstruction based on level set and PDE techniques, the major focus being on morphological and geometric structures in images. The aspects covered include edge-sharpening image reconstruction and denoising, segmentation and shape analysis in images, and image matching. For each, the lecture notes provide insights into the basic analysis of modern variational and PDE-based techniques, as well as computational aspects and applications.

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 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 its topology or develop singularities, will find this book interesting and useful.

The topic of level sets is currently very timely and useful for creating realistic 3-D images and animations. They are powerful numerical techniques for analyzing and computing interface motion in a host of application settings. In computer vision, it has been applied to stereo and segmentation, whereas in graphics it has been applied to the postproduction process of in-painting and 3-D model construction. Osher is co-inventor of the Level Set Methods, a pioneering framework introduced jointly with James Sethian from the University of Berkeley in 1998. This methodology has been used up to now to provide solutions to a wide application range not limited to image processing, computer vision, robotics, fluid mechanics, crystallography, lithography, and computer graphics. The topic is of great interest to advanced students, professors, and R&D professionals working in the areas of graphics (post-production), video-based surveillance, visual inspection, augmented reality, document image processing, and medical image processing. These techniques are already employed to provide solutions and products in the industry (Cognitech, Siemens, Philips, Focus Imaging). An essential compilation of survey chapters from the leading researchers in the field, emphasizing the applications of the methods. This book can be suitable for a short professional course related with the processing of visual information.

This book publishes a collection of original scientific research articles that address the state-of-art in using partial differential equations for image and signal processing. Coverage includes: level set methods for image segmentation and construction, denoising techniques, digital image inpainting, image dejittering, image registration, and fast numerical algorithms for solving these problems.

The topic of level sets is currently very timely and useful for creating realistic 3-D images and animations. They are powerful numerical techniques for analyzing and computing interface motion in a host of application settings. In computer vision, it has been applied to stereo and segmentation, whereas in graphics it has been applied to the postproduction process of in-painting and 3-D model construction. Osher is co-inventor of the Level Set Methods, a pioneering framework introduced jointly with James Sethian from the University of Berkeley in 1998. This methodology has been used up to now to provide solutions to a wide application range not limited to image processing, computer vision, robotics, fluid mechanics, crystallography, lithography, and computer graphics. The topic is of great interest to advanced students, professors, and R&D professionals working in the areas of graphics (post-production), video-based surveillance, visual inspection, augmented reality, document image processing, and medical image processing. These techniques are already employed to provide solutions and products in the industry (Cognitech, Siemens, Philips, Focus Imaging). An essential compilation of survey chapters from the leading researchers in the field, emphasizing the applications of the methods. This book can be suitable for a short professional course related with the processing of visual information.

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 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 its topology or develop singularities, will find this book interesting and useful.