Image Processing: The Fundamentals, Second Edition

所需积分/C币:18 2014-11-11 16:03:45 16.81MB PDF

Image Processing: The Fundamentals, Second Edition 图像处理基础:第二版 作者:Maria Petrou, Costas Petrou © 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-74586-1 图像处理经典书籍,高清晰版本,质量保证。 本图书仅供私人学习、交流之用,请勿用作商业用途。本书版权归原作者所有
This edition first published 2010 c 2010 John Wiley Sons Ltd Registered office John Wiley Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 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, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books names and product names used in this book are trade names, service marks, trademarks or registered q Designations used by companies to distinguish their products are often claimed as trademarks. All bra trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought Library of Congress Cataloging-in-Publication Data Petrou. Maria Image processing: the fundamentals/ Maria Petrou, Costas Petrou.-2nd ed cm Includes bibliographical references and inde ISBN978-0-470-74586-1( cloth) 1. Image processing- Digital techniques TA1637P482010 621.36′7-dc22 2009053150 ISBN978-0-470-74586-1 A catalogue record for this book is available from the British Library Set in 10/12 Computer Modern by Laserwords Private Ltd, Chennai, India Printed in Singapore by markon This book is dedicated to our mother and grandmother Dionisia, for all her love and sacrifices Contents Preface 1 Introduction Why do we process images? What is an image What is a digital image? What is a spectral band? Why do most image processing algorithms refer to grey images, while most images we come across are colour images How is a digital image formed? If a sensor corresponds to a patch in the physical world, how come we can have more than one sensor type corresponding to the same patch of the scene? What is the physical meaning of the brightness of an image at a pixel position? Why are images often quoted as being512×512,256×256,128×128etc? 3366 How many bits do we need to store an image? What determines the quality of an image What makes an image blurred? What is meant by image resolution What is the purpose of image processing:? What does“ good contrast”mean? How do we do image processing? Do we use nonlinear operators in image processing? ? What is a linear operator 12 How are linear operators defined What is the relationship between the point spread function of an imaging device and that of a linear operator? How does a linear operator transform an image What is the meaning of the point spread function? Box 1.1.The formal definition of a point source in the continuous domal 14 How can we express in practice the effect of a linear operator on an image 18 Can we apply more than one linear operators to an image? 22 Does the order by which we apply the linear operators make any difference to the result? 22 Box 1.2. Since matrix multiplication is not commutative, how come we can change the order by which we apply shift invariant linear operators? 22 VIll Contents Box 1.3. What is the stacking operator 29 What is the implication of the separability assumption on the structure of matrix H? 38 How can a separable transform be written in matrix form? 39 What is the meaning of the separability assumption? 40 Box 1.4. The formal derivation of the separable matrix equation 41 What is the“ take home” message of this chapter What is the significance of equation(1.108) in linear image processing? 43 43 What is this book about? 44 2 Image Transformations What is this chapter about? 47 How can we define an elementary image? 47 What is the outer product of two vectors? How can we expand an image in terms of vector outer products? 47 47 How do we choose matrices hc and hr? 49 What is a unitary matrix What is the inverse of a unitary transform How can we construct a unitary matrix? How should we choose matrices U and V so that g can be represented by fewer bits than f? 50 What is matrix diagonalisation? Can we diagonalise any matrix? 2.1 Singular value decomposition 51 How can we diagonalise an image 51 Box 2. 1. Can we expand in vector outer products any image 54 How can we compute matrices U, V and A needed for image diagonalisation 56 Box 2.2. What happens if the eigenvalues of matrix gg are negative? What is the singular value decomposition of an image? 60 Can we analyse an eigenimage into eigenimages? 61 How can we approximate an image using SVD? 62 Box 2.3. What is the intuitive explanation of SVD? 62 What is the error of the approximation of an image by SVD? 63 How can we minimise the error of the reconstruction? 65 Are there any sets of elementary images in terms of which any image may be expanded? 72 What is a complete and orthonormal set of functions? 72 Are there any complete sets of orthonormal discrete valued functions 73 2.2 Haar. Walsh and hadamard transforms 74 How are the haar functions defined? 74 How are the Walsh functions defined? 74 Box 2. 4. Definition of walsh functions in terms of the rademacher functions 74 How can we use the haar or Walsh functions to create image bases? How can we create the image transformation matrices from the Haar and walsh functions in practice 76 What do the elementary images of the Haar transform look like? Can we define an orthogonal matrix with entries only +1 or-1? Box 2.5. Ways of ordering the Walsh functions 86 What do the basis images of the Hadamard/ Walsh transform look like? Contents What are the advantages and disadvantages of the Walsh and the haar transforms? 92 What is the haar wavelet? 2. 3 Discrete fourier transform 94 What is the discrete version of the Fourier transform(DFT)? 4 Box 2.6. What is the inverse discrete fourier transform 95 How can we write the discrete fourier transform in a matrix form? Is matrix U used for DFT unitary? 99 Which are the elementary images in terms of which DFT expands an image? 101 Why is the discrete Fourier transform more commonly used than the other 105 What does the convolution theorem state 105 Box 2.7. If a function is the convolution of two other functions what is the rela its dft with the dfts of the two functions How can we display the discrete Fourier transform of an image 112 What happens to the discrete Fourier transform of an image if the image is rotated? 113 What happens to the discrete Fourier transform of an image if the image What is the relationship between the average value of the image and its DFT?..114 is shifted 118 What happens to the dft of an image if the image is scaled? Box 2.8. What is the fast Fourier Transform? 124 What are the advantages and disadvantages of dFT? 126 Can we have a real valued DFT? 126 Can we have a purely imaginary DFT? 130 Can an image have a purely real or a purely imaginary valued DFT? 137 2.4 The even symmetric discrete cosine transform (EDCT) 138 What is the even symmetric discrete cosine transform Box 2.9. Derivation of the inverse 1d even discrete cosine transform 143 What is the inverse 2d even cosine transform? 145 What are the basis images in terms of which the even cosine transform expands an Image 146 2.5 The odd symmetric discrete cosine transform (ODCT) 149 What is the odd symmetric discrete cosine transform? 149 Box 2.10. Derivation of the inverse 1d odd discrete cosine transform 152 What is the inverse 2d odd discrete cosine transform? 154 What are the basis images in terms of which the odd discrete cosine transform expands an image 154 2.6 The even antisymmetric discrete sine transform(EDST) 157 What is the even antisymmetric discrete sine transform? 157 Box 2.11. Derivation of the inverse 1d even discrete sine transform 160 What is the inverse 2D even sine transform? 162 What are the basis images in terms of which the even sine transform expands an age What happens if we do not remove the mean of the image before we compute its EDST? 166 2. 7 The odd antisymmetric discrete sine transform (ODST) 167 What is the odd antisymmetric discrete sine transform 167 Content Box 2.12. Derivation of the inverse 1d odd discrete sine transform 171 What is the inverse 2d odd sine transform? 172 What are the basis images in terms of which the odd sine transform expands an Image 173 What is the“ take home” message of this chapter 176 3 Statistical Description of Images 177 What is this chapter about? 177 Why do we need the statistical description of images? 177 3.1 Random fields 178 What is a random field? 178 What is a random variable? .178 What is a random experiment? How do we perform a random experiment with computers? 178 how do we describe random variables? 178 What is the probability of an event? 179 What is the distribution function of a random variable 180 What is the probability density function of a random variable? -2lue? What is the probability of a random variable taking a specific va 181 How do we describe many random variables Fandom variable? 181 184 What relationships may n random variables have with each other? 184 How do we define a random field? 189 How can we relate two random variables that appear in the same random field?.. 190 How can we relate two random variables that belong to two different random fields? 193 If we have just one image from an ensemble of images, can we calculate expectation values 195 When is a random field homogeneous with respect to the mean? 195 When is a random field homogeneous with respect to the autocorrelation function? 195 How can we calculate the spatial statistics of a random field? 196 How do we compute the spatial autocorrelation function of an image in practice?. 196 When is a random field ergodic with respect to the mean 197 When is a random field ergodic with respect to the autocorrelation function What is the implication of ergodicity? 199 Box 3.1. Ergodicity, fuzzy logic and probability theory 200 How can we construct a basis of elementary images appropriate for expressing in an optimal way a whole set of images? 200 3.2 Karhunen-Loeve transform 201 What is the Karhunen-Loeve transform 201 Why does diagonalisation of the autocovariance matrix of a set of images define a How can we transform an image so its autocovariance matrix becomes diagonal?. 201 desirable basis for expressing the images in the set? 204 What is the form of the ensemble autocorrelation matrix of a set of images, if the How do we go from the lD autocorrelation function of the vector representation of l0 ensemble is stationary with respect to the autocorrelation? an image to its 2D autocorrelation matrix 211 How can we transform the image so that its autocorrelation matrix is diagonal? 213 Contents How do we compute the K-l transform of an image in practice? 214 How do we compute the Karhunen-Loeve(K-L)transform of an ensemble of ages 215 Is the assumption of ergodicity realistic 215 Box 3.2. How can we calculate the spatial autocorrelation matrix of an image, when t is represented by a vector 215 Is the mean of the transformed image expected to be really 0? 220 How can we approximate an image using its K-L transform? What is the error with which we approximate an image when we truncate Its -l 220 expansion 220 What are the basis images in terms of which the Karhunen-Loeve transform expands an image? 221 Box 3.3. What is the error of the approximation of an image using the Karhunen Loeve transform? 226 3.3 Independent component analysis 234 What is Independent Component Analysis(ICA) 234 What is the cocktail party problem? 234 How do we solve the cocktail party problem 235 What does the central limit theorem say? 235 What do we mean by saying that "the samples of ai(t) are more Gaussianly dis- tributed than either si(t)or s2(t) "in relation to the cocktail party problem? Are we talking about the temporal samples of 1(t), or are we talking about all possible versions of 1(t) at a given time? 235 How do we measure non-Gaussianity? 239 How are the moments of a random variable computed? 239 How is the kurtosis defined? 240 How is negentropy defined? 243 How is entropy defined? 243 Box 3.4. From all probability density functions with the same variance, the gaussian has the maximum entropy 246 How is negentropy computed? 246 Box 3.5. Derivation of the approximation of negentropy in terms of moments 252 Box 3.6. Approximating the negentropy with nonquadratic functions 254 Box 3.7. Selecting the nonquadratic functions with which to approximate the ne- entropy How do we apply the central limit theorem to solve the cocktail party problen? 257 264 How may Ica be used in image processing? 264 How do we search for the independent components? 264 How can we whiten the data? 266 How can we select the independent components from whitened data? 267 Box 3.8. How does the method of Lagrange multipliers work? 268 Box 3.9. How can we choose a direction that maximises the negentropy? 269 How do we perform ICA in image processing in practice 274 How do we apply Ica to signal processing? What are the major characteristics of independent component analysis? 289 What is the difference between ICA as applied in image and in signal processing?. 29 What is the"take home"message of this chapter? 292 Contents 4 Image Enhancement 293 What is image enhancement? ..293 How can we enhance an image? 293 What is linear filtering 293 4.1 Elements of linear filter theory 294 how do we define a 2d filter? 294 How are the frequency response function and the unit sample response of the filter related? 294 Why are we interested in the filter function in the real domain 294 Are there any conditions which h(h, l) must fulfil so that it can be used as a convo lution filter? 294 Box 4.1. What is the unit sample response of the 2D ideal low pass filter? 296 What is the relationship between the 1D and the 2D ideal lowpass filters? 300 How can we implement in the real domain a filter that is infinite in extent? 301 Box 4.2. -transforms Can we define a filter directly in the real domain for convenience? 301 .309 Can we define a filter in the real domain, without side lobes in the frequency 4.2 Reducing high frequency noise domain 309 311 What are the types of noise present in an image 311 What is impulse noise? 311 What is Gaussian noise? .311 What is additive noise? 311 What is multiplicative noise? 311 What is homogeneous noise? 311 What is zero-mean noise? 312 What is biased noi 312 What is independent noise 312 What is uncorrelated noise? 312 What is white noise? 313 What is the relationship between zero-mean uncorrelated and white noise? 313 What is iid noise 313 Is it possible to have white noise that is not iid? 315 Box 4.3. The probability density function of a function of a a random variable 320 Why is noise usually associated with high fred quencies? 324 How do we deal with multiplicative noise? 325 Box 4.4. The fourier transform of the delta function 325 Box 4.5. Wiener-Khinchine theorem 325 Is the assumption of gaussian noise in an image justified? 326 how do we remove shot noise? 326 What is a, rank order filter? 326 What is median filtering 326 What is mode filtering? ...328 Can we filter an image by using the linear methods we learnt in Chapter 2? ters? 328 How do we reduce Gaussian noise? Can we have weighted median and mode filters like we have weighted mean filt 333 335 How do we deal with mixed noise in images 337

...展开详情
试读 127P Image Processing: The Fundamentals, Second Edition
img
idbj_real

关注 私信 TA的资源

上传资源赚积分,得勋章
    最新推荐
    Image Processing: The Fundamentals, Second Edition 18积分/C币 立即下载
    1/127
    Image Processing: The Fundamentals, Second Edition第1页
    Image Processing: The Fundamentals, Second Edition第2页
    Image Processing: The Fundamentals, Second Edition第3页
    Image Processing: The Fundamentals, Second Edition第4页
    Image Processing: The Fundamentals, Second Edition第5页
    Image Processing: The Fundamentals, Second Edition第6页
    Image Processing: The Fundamentals, Second Edition第7页
    Image Processing: The Fundamentals, Second Edition第8页
    Image Processing: The Fundamentals, Second Edition第9页
    Image Processing: The Fundamentals, Second Edition第10页
    Image Processing: The Fundamentals, Second Edition第11页
    Image Processing: The Fundamentals, Second Edition第12页
    Image Processing: The Fundamentals, Second Edition第13页
    Image Processing: The Fundamentals, Second Edition第14页
    Image Processing: The Fundamentals, Second Edition第15页
    Image Processing: The Fundamentals, Second Edition第16页
    Image Processing: The Fundamentals, Second Edition第17页
    Image Processing: The Fundamentals, Second Edition第18页
    Image Processing: The Fundamentals, Second Edition第19页
    Image Processing: The Fundamentals, Second Edition第20页

    试读已结束,剩余107页未读...

    18积分/C币 立即下载 >