Paragios N., Handbook Of Mathematical Models In Computer Vision.pdf

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HANDBOOK OF MATHEMATICAL
MODELS IN COMPUTER VISION
HANDBOOK OF
MATHEMATICAL MODELS
IN COMPUTER VISION
Edited by
Nikos Paragios
Ecole Nationale des Fonts et Chaussees
Yunmei Chen
University of Florida
Olivier Faugeras
INRIA
Springer
Library of Congress Cataloging-in-Publication Data
A CLP. Catalogue record for this book is available from the Library of
Congress.
Handbook of Mathematical Models in Computer Vision,
Edited by Nikos Paragios,
Yunmei Chen and Olivier Faugeras
p.cm.
ISBN-10: (HB) 0-387-26371-3
ISBN-13: (HB) 978-0387-26371-7
ISBN-10: (eBook) 0-387-28831-7
ISBN-13: (eBook) 978-0387-28831-4
Printed on acid-free paper.
Copyright © 2006 by Springer Science+Business Media, Inc.
All rights reserved. This work may not be translated or copied m whole or in part without
the written permission of the publisher [Springer Science+Business Media, Inc., 233 Spring
Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or
scholarly analysis. Use in connection with any form of information storage and retrieval,
electronic adaptation, computer software, or by similar or dissimilar methodology now
known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks and similar terms,
even if they are not identified as such, is not to be taken as an expression of opinion as to
whether or not they are subject to proprietary rights.
Printed in the United States of America.
9 8 7 6 5 4 3 2 1
springeronline.com
SPIN 11055662 (HC) / 11552987 (eBook)
Contents
Preface
List of Contributors
xix
xxiii
I Image Reconstruction
1
Diffusion Filters and Wavelets: What Can They Learn from Each
Other?
J. Weickert, G. Steidl, P. Mrazek, M. Welk, and T. Brox
1.1
Introduction
1.2
Basic Methods
1.2.1 Wavelet Shrinkage
1.2.2 Nonlinear Diffusion Filtering
1.3
Relations for Space-Discrete Diffusion
1.3.1 Equivalence for Two-Pixel Signals
1.3.2 A Wavelet-Inspired Scheme for TV Diffusion of
Signals
1.3.3 Generalisations to Images
1.4
Relations for Fully Discrete Diffusion
1.4.1 Diffusion-Inspired Shrinkage Functions
1.4.2 Wavelet Shrinkage with Improved Rotation Invariance .
1.4.3 Diffusion-Inspired Wavelet Shrinkage of Colour
Images
1.5
Wavelets with Higher Vanishing Moments
1.6
Summary
Total Variation Image Restoration: Overview and Recent Develop-
ments
T. Chan, S. Esedoglu, F. Park and A. Yip
2.1
Introduction
2.2
Properties and Extensions
2.2.1 BV Space and Basic Properties
2.2.2 Multi-channel TV
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