Variational Methods in Image Segmentation: with seven image processing experiments (Progress in Nonlinear Differential Equations and Their Applications, 14, Band 12)

Morel, Jean-Michel and Sergio Solimini:

ISBN 10: 0817637206 / ISBN 13: 9780817637200

Published by Birkhäuser, 1994

About this Item

264 p. Former library copy with spine label and stamps. Cover slightly light-stained and slightly bumped. Clean and very good inside 225 Sprache: Englisch Gewicht in Gramm: 711.

Seller Inventory # 28414

Bibliographic Details

• Title: Variational Methods in Image Segmentation: with seven image processing experiments (Progress in Nonlinear Differential Equations and Their Applications, 14, Band 12)
• Publisher: Birkhäuser
• Publication Date: 1994
• Language: English
• ISBN 10: 0817637206
• ISBN 13: 9780817637200
• Binding: Hardcover
• Condition: Gut
• Seller catalogs:
  • Mathematik

About this title

Synopsis

This book contains both a synthesis and mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmen­ tation of digital images as well as the understanding of visual perception. A common formalism for these theories and algorithms is obtained in a variational form. Thank to this formalization, mathematical questions about the soundness of algorithms 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 seg­ mentation energies, "edge" terms compete with "region" terms in a way which is supposed to impose regularity on both regions and boundaries. This fact was an experimental guess in perception phenomenology and computer vision until it was proposed as a mathematical conjecture by Mumford and Shah. The third part of the book presents a unified presentation of the evi­ dences in favour of the conjecture. It is proved that the competition of one-dimensional and two-dimensional energy terms in a variational for­ mulation cannot create fractal-like behaviour for the edges. The proof of regularity for the edges of a segmentation constantly involves con­ cepts from geometric measure theory, which proves to be central in im­ age 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").

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