Mathematical Models for Registration and Applications to Medical Imaging
Image registration is an emerging topic in image processing with many applications in medical imaging, picture and movie processing. The classical problem of image registration is concerned with ?nding an appropriate transformation between two data sets.
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MATHEMATICS IN INDUSTRY Editors Hans-Georg Bock Frank de Hoog Avner Friedman Arvind Gupta Helmut Neunzert William R. Pulleyblank Torgeir Rusten Fadil Santosa Anna-Karin Tornberg
THE EUROPEAN CONSORTIUM FOR MATHEMATICS IN INDUSTRY SUBSERIES Managing Editor Vincenzo Capasso Editors Robert Mattheij Helmut Neunzert Otmar Scherzer
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Otmar Scherzer
Mathematical Models for Registration and Applications to Medical Imaging With 54 Figures, 12 in Color, and 12 Tables
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Editor Otmar Scherzer .. Universitat Innsbruck .. Institut fur Informatik, Technikerstr. 21A A -- 6020 Innsbruck, Austria e-mail: [email protected]
Library of Congress Control Number: 2006926829
Mathematics Subject Classification (2000): 65J15, 65F22, 94a08, 94J40, 94K24 ISBN-10 3-540-25029-8 Springer Berlin Heidelberg New York ISBN-13 978-3-540-25029-6 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2006 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset by the editors & SPI Publisher Services Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: design & production GmbH, Heidelberg Printed on acid-free paper SPIN: 11397403 46/3100/SPI - 5 4 3 2 1 0
Preface
Image registration is an emerging topic in image processing with many applications in medical imaging, picture and movie processing. The classical problem of image registration is concerned with finding an appropriate transformation between two data sets. This fuzzy definition of registration requires a mathematical modeling and in particular a mathematical specification of the terms appropriate transformations and correlation between data sets. Depending on the type of application, typically Euler, rigid, plastic, elastic deformations are considered. The variety of similarity measures ranges from a simple Lp distance between the pixel values of the data to mutual information or entropy distances. This goal of this book is to highlight by some experts in industry and medicine r
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