Geometric Partial Differential Equations and Image Analysis

Guillermo Sapiro (University of Minnesota)

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English

Cambridge University Pres
17 March 2006

Mathematics & Sciences; Differential calculus & equations; Differential & Riemannian geometry; Applied optics; Image processing

This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area 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 in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practitioners. It is intended to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.

By: Guillermo Sapiro (University of Minnesota)
Imprint: Cambridge University Pres
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 154mm, Spine: 21mm
Weight: 550g
ISBN: 9780521685078
ISBN 10: 0521685079
Pages: 412
Publication Date: 17 March 2006
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Guillermo Sapiro is a Professor of Electrical and Computer Engineering at the University of Minnesota, where he works on differential geometry and geometric partial differential equations, both in theory and applications in computer vision and image analysis.

Reviews for Geometric Partial Differential Equations and Image Analysis

' ... 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 fur 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