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Geometric Partial Differential Equations and Image Analysis


This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. It brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. The volume provides information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.

• Covers both theory and applications, with a good coverage of the state-of-the-art literature • First to cover many aspects of the topic, not just the numerical or filtering component • Useful resource both for experts and newcomers into the field

1. Basic mathematical background; 2. Geometric curve and surface evolution; 3. Geodesic curves and minimal surfaces; 4. Geometric diffusion of scalar images; 5. Geometric diffusion of vector valued images; 6. Diffusion on non-flat manifolds; 7. Contrast enhancement; 8. Additional theories and applications.

' … enjoyable to read … an excellent introduction for someone interested in pursuing research in this area, with ample references to current work sprinkled throughout.' SIAM Review

' … every person interested in image analysis by partial differential equations or related fields, such as differential geometry and curve evolution, should read this book.' Mathematics of Computation

'… this book will certainly be accepted as a standard text … A student who had worked through everything here would be very well equipped to develop powerful image processing software.' Alex M. Andrew, Robotica

'… a useful introduction to the subject.' John Urbas, Zentralblatt für Mathematik

'For those who are prepared to also take the mathematics, a marvellous world will open. This is applied mathematics at its best. Recommended for researchers and practitioners.' Bulletin of the Belgian Mathematical Society

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Tags: image, processing, number, include, shape, Analysis, Image