Geometric Partial Differential Equations and Image Analysis

Applications covered include image segmentation, shape analysis, image enhancement, and tracking.

Guillermo Sapiro (Author)

9780521685078, Cambridge University Press

Paperback, published 13 February 2006

412 pages
22.9 x 15.4 x 2.1 cm, 0.55 kg

'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

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.

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.

Subject Areas: Image processing [UYT], Differential & Riemannian geometry [PBMP]