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Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik Variational Methods in Image Segmentation
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Variational Methods in Image Segmentation
Jean-Michel Morel (Gebundene Ausgabe, Deutsch)
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Beschreibung
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"). Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
22.12.1994
Sprache
Deutsch
EAN
9780817637200
Herausgeber
Birkhäuser Boston
Serien- oder Bandtitel
Progress in Nonlinear Differential Equations and Their Applications
Sonderedition
Nein
Autor
Jean-Michel Morel
Seitenanzahl
248
Einbandart
Gebundene Ausgabe
Buch Untertitel
with seven image processing experiments
Bandzählung
14
Schlagwörter
behavior, interaction, fractal, interpolation, form, image segmentation, proof, wavelet, computer vision, presentation, mathematical analysis, Mathematica, measure theory, constant, algorithms
Thema-Inhalt
PBKS - Numerische Mathematik
PBV - Kombinatorik und Graphentheorie
PBWH - Mathematische Modellierung
TBJ - Mathematik für Ingenieure
PBW - Angewandte Mathematik
Höhe
235 mm
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