Image-Fusion-Algorithms-and-Applications.pdf

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Image Fusion

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Image Fusion: Algorithms and Applications Edited by Tania Stathaki Amsterdam • Boston • Heidelberg • London • New York Oxford • Paris • San Diego • San Francisco • Singapore Sydney • Tokyo Academic Press is an imprint of Elsevier

Academic Press is an imprint of Elsevier 84 Theobald’s Road, London WC1X 8RR, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA First edition 2008 Copyright © 2008 Elsevier Ltd. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) (0) 1865 843830; fax: (+44) (0) 1865 853333; email: permissions@elsevier.com. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent veriﬁcation of diagnoses and drug dosages should be made Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-12-372529-5 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library For information on all Academic Press publications visit our web site at www.books.elsevier.com Printed and bound in Great Britain 08 09 10 10 9 8 7 6 5 4 3 2 1

Contents Preface List of contributors 1 Current trends in super-resolution image reconstruction Antonis Katartzis and Maria Petrou 1.1 Introduction.................................................................................................. 1.2 Modelling the imaging process.................................................................... 1.2.1 Geometric transformation models.................................................... 1.2.2 Image degradation models ............................................................... 1.2.3 Observation model – Mathematical formulation ............................. 1.3 State-of-the-art SR methods......................................................................... 1.3.1 Frequency domain methods ............................................................. 1.3.2 Projection Onto Convex Sets (POCS).............................................. 1.3.3 Bayesian/variational methods .......................................................... 1.3.4 Interpolation-based approaches ....................................................... 1.4 A new robust alternative for SR reconstruction ........................................... 1.4.1 Sub-pixel registration....................................................................... 1.4.2 Joint Bayesian registration/reconstruction....................................... 1.5 Comparative evaluations .............................................................................. 1.6 Conclusions.................................................................................................. Acknowledgements............................................................................................... References............................................................................................................. 2 Image fusion through multiresolution oversampled decompositions Bruno Aiazzi, Stefano Baronti and Massimo Selva 2.1 Introduction.................................................................................................. 2.2 Multiresolution analysis............................................................................... 2.2.1 Fundamental principles.................................................................... 2.2.2 Undecimated discrete wavelet transform......................................... 2.2.3 Multi-level decomposition of wavelet transforms ........................... 2.2.4 Translation-invariant wavelet decomposition of a 2-D image ......... 2.2.5 ‘À trous’ wavelet decomposition of an image.................................. 2.2.6 Laplacian pyramid ........................................................................... 2.3 MTF-tailored multiresolution analysis ........................................................ 2.4 Context-driven multiresolution data fusion ................................................. 2.4.1 Undecimated wavelet-based data fusion scheme............................. 2.4.2 Pyramid-based data fusion scheme.................................................. v xiii xv 1 1 2 3 4 6 7 7 9 11 13 14 15 15 19 21 22 23 27 27 30 30 33 33 34 36 38 40 41 43 44

vi Contents 2.4.3 ‘À trous’ wavelet data fusion scheme .............................................. 2.4.4 Enhanced Spectral Distortion Minimising (ESDM) model ............. 2.4.5 Enhanced Context-Based (ECB) model........................................... 2.5 Quality.......................................................................................................... 2.5.1 Quality assessment of fusion products............................................. 2.5.2 Quality indices ................................................................................. 2.6 Experimental results..................................................................................... 2.6.1 Data set and compared methods ...................................................... 2.6.2 Performance comparison on QuickBird data................................... 2.6.3 Performance comparison on Ikonos data......................................... 2.7 Concluding remarks..................................................................................... Acknowledgements............................................................................................... References............................................................................................................. 3 Multisensor and multiresolution image fusion using the linear mixing model Jan G.P.W. Clevers and Raul Zurita-Milla 3.1 Introduction.................................................................................................. 3.2 Data fusion and remote sensing ................................................................... 3.3 The linear mixing model.............................................................................. 3.4 Case study .................................................................................................... 3.4.1 Introduction...................................................................................... 3.4.2 Study area and data .......................................................................... 3.4.3 Quality assessment........................................................................... 3.4.4 Results and discussion ..................................................................... 3.5 Conclusions.................................................................................................. References............................................................................................................. 46 47 48 48 48 50 52 52 54 57 62 63 63 67 67 69 70 73 73 73 74 76 81 81 85 4 Image fusion schemes using ICA bases Nikolaos Mitianoudis and Tania Stathaki 4.1 4.2 85 Introduction.................................................................................................. 88 ICA and Topographic ICA bases ................................................................. 88 4.2.1 Deﬁnition of bases ........................................................................... 92 4.2.2 Training ICA bases .......................................................................... 93 4.2.3 Properties of the ICA bases.............................................................. 95 4.3 Image fusion using ICA bases ..................................................................... 96 4.4 Pixel-based and region-based fusion rules using ICA bases........................ 97 4.4.1 A Weight Combination (WC) pixel-based method.......................... 97 4.4.2 Region-based image fusion using ICA bases................................... 98 4.5 A general optimisation scheme for image fusion ....................................... 4.5.1 Laplacian priors ............................................................................... 99 4.5.2 Verhulstian priors............................................................................. 100 4.6 Reconstruction of the fused image............................................................... 102 4.7 Experiments ................................................................................................. 105 4.7.1 Experiment 1: Artiﬁcially distorted images..................................... 106 4.7.2 Experiment 2: Out-of-focus image fusion ...................................... 108 4.7.3 Experiment 3: Multi-modal image fusion........................................ 109

Contents vii 4.8 Conclusion ................................................................................................... 111 Acknowledgements............................................................................................... 115 References............................................................................................................. 116 5 Statistical modelling for wavelet-domain image fusion 119 Alin Achim, Artur Łoza, David Bull and Nishan Canagarajah 5.1 Introduction.................................................................................................. 119 5.2 Statistical modelling of multimodal images wavelet coefﬁcients................ 121 5.2.1 Heavy-tailed distributions ................................................................ 121 5.2.2 Modelling results of wavelet subband coefﬁcients .......................... 124 5.3 Model-based weighted average schemes ..................................................... 125 5.3.1 Saliency estimation using Mellin transform .................................... 128 5.3.2 Match measure for SαS random variables: The symmetric covariation coefﬁcient...................................................................... 131 5.4 Results.......................................................................................................... 132 5.5 Conclusions and future work ....................................................................... 135 Acknowledgements............................................................................................... 136 References............................................................................................................. 136 6 Theory and implementation of image fusion methods based on the á trous 139 algorithm Xavier Otazu 6.1 6.2 Introduction.................................................................................................. 139 6.1.1 Multiresolution-based algorithms .................................................... 140 Image fusion algorithms .............................................................................. 141 6.2.1 Energy matching .............................................................................. 141 6.2.2 Spatial detail extraction. The à trous algorithm............................... 142 6.2.3 Spatial detail injection...................................................................... 144 6.3 Results.......................................................................................................... 150 Acknowledgements............................................................................................... 153 References............................................................................................................. 153 7 Bayesian methods for image fusion 157 Jürgen Beyerer, Michael Heizmann, Jennifer Sander and Ioana Ghe¸ta 7.1 Introduction: fusion using Bayes’ theorem.................................................. 158 7.1.1 Why image fusion? .......................................................................... 158 7.1.2 Three basic requirements for a fusion methodology........................ 160 7.1.3 Why Bayesian fusion? ..................................................................... 162 7.2 Direct application of Bayes’ theorem to image fusion problems ................ 163 7.2.1 Bayesian solution of inverse problems in imaging .......................... 163 7.2.2 Bayesian image fusion exempliﬁed for Gaussian distributions ....... 165 7.2.3 Bayes estimators .............................................................................. 167 7.2.4 Multi-stage models........................................................................... 170 7.2.5 Prior modelling ................................................................................ 171 7.3 Formulation by energy functionals .............................................................. 173 7.3.1 Energy terms .................................................................................... 174 7.3.2 Connection with Bayes’ methodology via Gibbs’ distributions ...... 178

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