Variational Methods in Image Segementation: v. 14 (Progress in Nonlinear Differential Equations and Their Applications) - Hardcover

Morel, J-. M.; Solimini, S.

Hardcover

ISBN 10: 3764337206 ISBN 13: 9783764337209

Publisher: Birkhauser Verlag AG, 1994

Synopsis

This text contains a synthesis and a mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmentation of digital images as well as the understanding of visual perception. A common formalism for these theories and algorithms is obtained in variational form. Thanks to the formalization, mathematical questions about the soundness can be raised and answered. Perception theory has to deal with the complex interaction between regions and "edges" (or boundaries) in an image; in the variational segmentation energies, "edge" terms compete with "region" terms in a way which is intended to impose regularity on both regions and boundaries. The first part of the book presents a unified presentation of the evidence in favour of the conjecture. It is proven that the competition of one-dimensional and two-dimensional energy terms in a variational formulation cannot create fractal-like behaviour for the edges. The proof of regularity for the edges of a segmentation constantly involves concepts from geometric measure theory, which proves to be central in image processing theory. The second part of the book provides a fast and self-contained presentation of the classical theory of rectifiable sets (the "edges") and unrectifiable sets ("fractals").

About this title

Review

"Well-written and very user-friendly. Each chapter is introduced by a brief summary of its aims... A very readable introduction to the mathematical theory of image segmentation."

--ZAA

Edition details

• Publisher: Birkhauser Verlag AG
• Publication date: 1994
• ISBN 10: 3764337206
• ISBN 13: 9783764337209
• Binding: Hardcover
• Language: English
• Number of pages: 264