IMAGE PROCESSING FOR ENGINEERS

438 Pages·2018·57.958 MB·English

by  Andrew E. Yagle, Fawwaz T. Ulaby

Image Processing
For Engineers
by Andrew E. Yagle and Fawwaz T. Ulaby
Book companion website:
: ip.eecs.umich.edu
“book” — 2016/3/15 — 6:35 — page iii — #3
IMAGE
PROCESSING
FOR ENGINEERS
Andrew E. Yagle
The University of Michigan
Fawwaz T. Ulaby
The University of Michigan
Copyright  2018 Andrew E. Yagle and Fawwaz T. Ulaby
This book is published by Michigan Publishing under an agreement with the authors.
It is made available free of charge in electronic form to any student or instructor
interested in the subject matter.
Published in the United States of America by
Michigan Publishing
Manufactured in the United States of America
ISBN 978-1-60785-488-3 (hardcover)
ISBN 978-1-60785-489-0 (electronic)
“book” — 2016/3/15 — 6:35 — page v — #5
This book is dedicated to the memories of
Professor Raymond A. Yagle and Mrs. Anne Yagle
Contents
Preface Chapter 4 Image Interpolation 128
Chapter 1 Imaging Sensors 1 4-1 Interpolation Using Sinc Functions 129
4-2 Upsampling and Downsampling Modalities 130
1-1 Optical Imagers 3 4-3 Upsampling and Interpolation 133
1-2 Radar Imagers 13 4-4 Implementation of Upsampling Using 2-D DFT
1-3 X-Ray Computed Tomography (CT) 18 in MATLAB 137
1-4 Magnetic Resonance Imaging 19 4-5 Downsampling 140
1-5 Ultrasound Imager 23 4-6 Antialias Lowpass Filtering 141
1-6 Coming Attractions 27 4-7 B-Splines Interpolation 143
4-8 2-D Spline Interpolation 149
Chapter 2 Review of 1-D Signals and Systems 38
4-9 Comparison of 2-D Interpolation Methods 150
2-1 Review of 1-D Continuous-Time Signals 41 4-10 Examples of Image Interpolation Applications 152
2-2 Review of 1-D Continuous-Time Systems 43
Chapter 5 Image Enhancement 159
2-3 1-D Fourier Transforms 47
2-4 The Sampling Theorem 53 5-1 Pixel-Value Transformation 160
2-5 Review of 1-D Discrete-Time Signals and 5-2 Unsharp Masking 163
Systems 59 5-3 Histogram Equalization 167
2-6 Discrete-Time Fourier Transform (DTFT) 66 5-4 Edge Detection 171
2-7 Discrete Fourier Transform (DFT) 70 5-5 Summary of Image Enhancement Techniques 176
2-8 Fast Fourier Transform (FFT) 76
2-9 Deconvolution Using the DFT 80 Chapter 6 Deterministic Approach to Image 180
2-10 Computation of Continuous-Time Fourier Restoration
Transform (CTFT) Using the DFT 82
6-1 Direct and Inverse Problems 181
6-2 Denoising by Lowpass Filtering 183
Chapter 3 2-D Images and Systems 89
6-3 Notch Filtering 188
3-1 Displaying Images 90 6-4 Image Deconvolution 191
3-2 2-D Continuous-Space Images 91 6-5 Median Filtering 194
3-3 Continuous-Space Systems 93 6-6 Motion-Blur Deconvolution 195
3-4 2-D Continuous-Space Fourier Transform
Chapter 7 Wavelets and Compressed Sensing 202
(CSFT) 94
3-5 2-D Sampling Theorem 107
7-1 Tree-Structured Filter Banks 203
3-6 2-D Discrete Space 113
7-2 Expansion of Signals in Orthogonal Basis
3-7 2-D Discrete-Space Fourier Transform (DSFT) 1 18
Functions 206
3-8 2-D Discrete Fourier Transform (2-D DFT) 119
7-3 Cyclic Convolution 209
3-9 Computation of the 2-D DFT Using MATLAB 121
7-4 Haar Wavelet Transform 213
7-5 Discrete-Time Wavelet Transforms 218 Chapter 10 Color Image Processing 334
7-6 Sparsification Using Wavelets of Piecewise-
Polynomial Signals 223 10-1 Color Systems 335
7-7 2-D Wavelet Transform 228 10-2 Histogram Equalization and Edge Detection 340
7-8 Denoising by Thresholding and Shrinking 232 10-3 Color-Image Deblurring 343
7-9 Compressed Sensing 236 10-4 Denoising Color Images 346
7-10 Computing Solutions to Underdetermined
Chapter 11 Image Recognition 353
Equations 238
7-11 Landweber Algorithm 241 11-1 Image Classification by Correlation 354
7-12 Compressed Sensing Examples 242 11-2 Classification by MLE 357
11-3 Classification by MAP 358
Chapter 8 Random Variables, Processes, and 254
11-4 Classification of Spatially Shifted Images 360
Fields
11-5 Classification of Spatially Scaled Images 361
8-1 Introduction to Probability 255 11-6 Classification of Rotated Images 366
8-2 Conditional Probability 259 11-7 Color Image Classification 367
8-3 Random Variables 261 11-8 Unsupervised Learning and Classification 373
8-4 Effects of Shifts on Pdfs and Pmfs 263 11-9 Unsupervised Learning Examples 377
8-5 Joint Pdfs and Pmfs 265 11-10 K-Means Clustering Algorithm 380
8-6 Functions of Random Variables 269
Chapter 12 Supervised Learning and 389
8-7 Random Vectors 272
Classification
8-8 Gaussian Random Vectors 275
8-9 Random Processes 278 12-1 Overview of Neural Networks 390
8-10 LTI Filtering of Random Processes 282 12-2 Training Neural Networks 396
8-11 Random Fields 285 12-3 Derivation of Backpropagation 403
12-4 Neural Network Training Examples 404
Chapter 9 Stochastic Denoising and 291
Deconvolution Appendix A Review of Complex Numbers 411
9-1 Estimation Methods 292 Appendix B MATLAB® and MathScript 415
9-2 Coin-Flip Experiment 298
9-3 1-D Estimation Examples 300 Index 421
9-4 Least-Squares Estimation 303
9-5 Deterministic versus Stochastic Wiener
Filtering 307
9-6 2-D Estimation 309
9-7 Spectral Estimation 313
9-8 1-D Fractals 314
9-9 2-D Fractals 320
9-10 Markov Random Fields 322
9-11 Application of MRF to Image Segmentation 327
Preface
“Apictureisworthathousandwords.” • An introduction to discrete wavelets, and application of
wavelet-baseddenoisingalgorithmsusingthresholdingand
Thisisanimageprocessingtextbookwithadifference.Instead
shrinkage,includingexamplesandproblems.
ofjustapicturegalleryofbefore-and-afterimages,weprovide
(on the accompanying website) MATLAB programs (.m files) • An introduction to compressed sensing, including exam-
and images (.mat files) for each of the examples. These allow
plesandproblems.
thereadertoexperimentwithvariousparameters,suchasnoise
strength,andseetheireffectontheimageprocessingprocedure. • An introduction to Markov random fields and the ICM
We also provide general MATLAB programs, and Javascript algorithm.
versionsofthem,formanyoftheimageprocessingprocedures
• An introduction to supervised and unsupervised learning
presented in this book. We believe studying image processing
andneuralnetworks.
withoutactuallyperformingitislikestudyingcookingwithout
turningonanoven. • Coverageofbothdeterministic(least-squares)andstochas-
Designedforacourseonimageprocessing(IP)aimedatboth
tic (a priori power spectral density) image deconvolution,
graduatestudentsaswellasundergraduatesintheirsenioryear,
andhowthelattergivesbetterresults.
in any field of engineering, this book starts with an overview
in Chapter 1 of how imaging sensors—from cameras to radars • InterpolationusingB-splines.
toMRIs and CAT—form images, and then proceeds tocover a
• A review of probability, random processes, and MLE,
wide array of image processing topics. The IP topics include:
MAP,andLSestimation.
imageinterpolation,magnification,thumbnails,andsharpening,
edge detection, noise filtering, de-blurring of blurred images,
supervisedandunsupervisedlearning,andimagesegmentation, BookCompanionWebsite:ip.eecs.umich.edu
among many others. As a prelude to the chapters focused on
The book website is a rich resource developed to extend the
imageprocessing(Chapters3–12),thebookoffersinChapter2
educational experience of thestudent beyond the materialcov-
a review of 1-D signals and systems, borrowed from our 2018
ered in the textbook. It contains MATLAB programs, standard
book Signals and Systems: Theory and Applications, by Ulaby
imagestowhichthereadercanapplytheimageprocessingtools
andYagle.
outlined in the book, and Javascript image processing modules
withselectableparameters.Italsocontainssolutionsto“concept
Bookhighlights:
questions” and “exercises,” and, for instructors, solutions to
• A section in Chapter 1 called “Coming Attractions,” of- homeworkproblems.
fering a sampling of the image processing applications
coveredinthebook. Acknowledgments: Mr. Richard Carnes—our friend, our pi-
ano performance teacher, and our LATEX super compositor—
• MATLABprogramsandimages(.mand.matfiles)onthe
deserves singular thanks and praise for the execution of this
book’swebsiteforallexamplesandproblems.Allofthese
book.Wearetrulyindebtedtohimforhismeticulouscareand
alsorunonNILabVIEWMathscript.
attention.WealsothankMs.RoseAndersonfortheelegantde-
• Coverageofstandardimageprocessingtechniques,includ- signofthecoverandforcreatingtheprintableAdobeInDesign
versionofthebook.
ing upsampling and downsampling, rotation and scaling,
histogram equalization, lowpass filtering, classification,
edgedetection,andanintroductiontocolorimageprocess- ANDREWYAGLEANDFAWWAZULABY,2018
ing.
1
Chapter
1 IImmaaggiinngg SSeennssoorrss
Contents
Lens of diameter D
Overview, 2
1-1 Optical Imagers, 3
y
1-2 Radar Imagers, 13
1-3 X-Ray Computed Tomography (CT), 18 Source s
1-4 Magnetic Resonance Imaging, 19 x
θ
1-5 Ultrasound Imager, 12
1-6 Coming Attractions, 27
Problems, 36 Object plane Image plane

Objectives Image processing has applications in medicine,
robotics, human-computer interface, and manufac-
turing, among many others. This book is about the
Learn about:
mathematical methods and computational
algorithms used in processing an image from its raw
■ How a digital camera forms an image, and what
form—whether generated by a digital camera, an
determines the angular resolution of the camera.
ultrasound monitor, a high-resolution radar, or any
other 2-D imaging system—into an improved form
■ How a thermal infrared imager records the distribu-
suitable for the intended application. As a prelude,
tion of energy emitted by the scene.
this chapter provides overviews of the image
■ How a radar can create images with very high formation processes associated with several sensors.
resolution from satellite altitudes.
■ How an X-ray system uses computed tomography
(CT) to generate 3-D images.
■ How magnetic resonance is used to generate 3-D
MRI images.
■ How an ultrasound instrument generates an image of
acoustic reflectivity, much like an imaging radar.
■ The history of image processing.
■ The types of image-processing operations examined
in detail in follow-up chapters.
2 CHAPTER1 IMAGINGSENSORS
Overview
sectional images (called slice) of the attenuation for specific
areasofinterest. A ratherdifferentprocessoccursin magnetic
In today’s world we use two-dimensional (2-D) images gen- resonanceimaging(MRI).
erated by a variety of different sensors, from optical cameras Fortheseandmanyothersensingprocesses,theformationof
and ultrasound monitors to high-resolution radars and others. the2-Dimageisonlythefirststep.AsdepictedinFig.1-1,we
A camera uses light rays and lenses to form an image of the callsuchanimagetherawimage,becauseoftenwesubjectthe
brightness distribution across the scene observed by the lens, raw image to a sequence of image processing steps designed
ultrasoundimagersusesoundwavesandtransducerstomeasure to transform the image into a product more suitable for the
the reflectivity of the scene or medium exposed to the sound intendedapplication(Table1-1).Thesestepsmayservetofilter
waves, and radar uses antennas to illuminate a scene with out(mostof)thenoisethatmayhaveaccompaniedthe(desired)
microwaves and then detect the fraction of energy scattered signal in the image detection process, rotate or interpolate the
back toward the radar. The three image formation processes imageifcalledforbytheintendedapplication,enhancecertain
are markedly different, yet their output product is similar: a image features to accentuate recognitionof objects of interest,
2-D analog or digital image. An X-ray computed tomography orcompressthe numberofpixelsrepresentingthe imageso as
(CT) scanner measures the attenuation of X-rays along many toreducedatastorage(numberofbits),aswellasotherrelated
directions through a 3-D object, such as a human head, and actions.
then processes the data to generate one or more 2-D cross-
Raw Improved
Image image Image image
Image display
formation processing
Image storage/
Sensor transmission
Image Formation and Processing
Image analysis
Figure1-1 Afteranimageisformedbyasensor,imageprocessingtoolsareappliedformanypurposes,includingchangingitsscaleand
orientation,improvingitsinformationcontent,orreducingitsdigitalsize.