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DigitalImageProcessingSecondEditionInstructorsManualRafaelC.GonzalezRichardE.WoodsPrenticeHallUpperSaddleRiver,NJhistory10987654321Copyrightc1992-2002byRafaelC.GonzalezandRichardE.WoodsPrefaceThismanualcontainsdetailedsolutionstoallproblemsinDigitalImageProcessing,2ndEdition.Wealsoincludeasuggestedsetofguidelinesforusingthebook,anddiscusstheuseofcomputerprojectsdesignedtopromoteadeeperunderstandingofthesubjectmatter.Thenotationusedthroughoutthismanualcorrespondstothenotationusedinthetext.Thedecisionofwhatmaterialtocoverinacourserestswiththeinstructor,anditde-pendsonthepurposeofthecourseandthebackgroundofthestudents.Wehavefoundthatthecourseoutlinessuggestedherecanbecoveredcomfortablyinthetimeframesindicatedwhenthecourseisbeingtaughtinanelectricalengineeringorcomputersci-encecurriculum.Ineachcase,nopriorexposuretoimageprocessingisassumed.Wegivesuggestedguidelinesforone-semestercoursesattheseniorandfirst-yeargraduatelevels.Itispossibletocovermostofthebookinatwo-semestergraduatesequence.Thebookwascompletelyrevisedinthisedition,withthepurposenotonlyofupdatingthematerial,butjustasimportant,makingthebookabetterteachingaid.Tothisend,theinstructorwillfindtheneworganizationtobemuchmoreflexibleandbetterillustrated.Althoughthebookisselfcontained,werecommenduseofthecompanionwebsite,wherethestudentwillfinddetailedsolutionstotheproblemsmarkedwithastarinthetext,reviewmaterial,suggestedprojects,andimagesfromthebook.Oneoftheprincipalreasonsforcreatingthewebsitewastofreetheinstructorfromhavingtopreparematerialsandhandoutsbeyondwhatisrequiredtoteachfromthebook.Computerprojectssuchasthosedescribedinthewebsiteareanimportantpartofacourseonimageprocessing.Theseprojectsgivethestudenthands-onexperiencewithalgorithmimplementationandreinforcethematerialcoveredintheclassroom.Theprojectssuggestedatthewebsitecanbeimplementedonalmostanyreasonably-equippedmulti-userorpersonalcomputerhavingahardcopyoutputdevice.1IntroductionThepurposeofthischapteristopresentsuggestedguidelinesforteachingmaterialfromthisbookattheseniorandfirst-yeargraduatelevel.Wealsodiscussuseofthebookwebsite.Althoughthebookistotallyself-contained,thewebsiteoffers,amongotherthings,complementaryreviewmaterialandcomputerprojectsthatcanbeassignedinconjunctionwithclassroomwork.Detailedsolutionstoallproblemsinthebookalsoareincludedintheremainingchaptersofthismanual.TeachingFeaturesoftheBookUndergraduateprogramsthatofferdigitalimageprocessingtypicallylimitcoveragetoonesemester.Graduateprogramsvary,andcanincludeoneortwosemestersofthema-terial.Inthefollowingdiscussionwegivegeneralguidelinesforaone-semesterseniorcourse,aone-semestergraduatecourse,andafull-yearcourseofstudycoveringtwosemesters.Weassumea15-weekprogrampersemesterwiththreelecturesperweek.Inordertoprovideflexibilityforexamsandreviewsessions,theguidelinesdiscussedinthefollowingsectionsarebasedonforty,50-minutelecturespersemester.Theback-groundassumedonthepartofthestudentissenior-levelpreparationinmathematicalanalysis,matrixtheory,probability,andcomputerprogramming.Thesuggestedteachingguidelinesarepresentedintermsofgeneralobjectives,andnotastimeschedules.Thereissomuchvarietyinthewayimageprocessingmaterialistaughtthatitmakeslittlesensetoattemptabreakdownofthematerialbyclassperiod.Inparticular,theorganizationofthepresenteditionofthebookissuchthatitmakesitmucheasierthanbeforetoadoptsignificantlydifferentteachingstrategies,dependingoncourseobjectivesandstudentbackground.Forexample,itispossiblewiththeneworganizationtoofferacoursethatemphasizesspatialtechniquesandcoverslittleornotransformmaterial.Thisisnotsomethingwerecommend,butitisanoptionthatoftenisattractiveinprogramsthatplacelittleemphasisonthesignalprocessingaspectsofthefieldandprefertofocusmoreontheimplementationofspatialtechniques.2Chapter1IntroductionThecompanionwebsitewww:
prenhall:
com=gonzalezwoodsorwww:
imageprocessingbook:
comisavaluableteachingaid,inthesensethatitincludesmaterialthatpreviouslywascov-eredinclass.Inparticular,thereviewmaterialonprobability,matrices,vectors,andlinearsystems,waspreparedusingthesamenotationasinthebook,andisfocusedonareasthataredirectlyrelevanttodiscussionsinthetext.Thisallowstheinstructortoassignthematerialasindependentreading,andspendnomorethanonetotallecturepe-riodreviewingthosesubjects.Anothermajorfeatureisthesetofsolutionstoproblemsmarkedwithastarinthebook.Thesesolutionsarequitedetailed,andwerepreparedwiththeideaofusingthemasteachingsupport.Theon-lineavailabilityofprojectsanddigitalimagesfreestheinstructorfromhavingtoprepareexperiments,data,andhandoutsforstudents.Thefactthatmostoftheimagesinthebookareavailablefordownloadingfurtherenhancesthevalueofthewebsiteasateachingresource.OneSemesterSeniorCourseAbasicstrategyinteachingaseniorcourseistofocusonaspectsofimageprocessinginwhichboththeinputsandoutputsofthoseprocessesareimages.Inthescopeofaseniorcourse,thisusuallymeansthematerialcontainedinChapters1through6.Dependingoninstructorpreferences,wavelets(Chapter7)usuallyarebeyondthescopeofcoverageinatypicalseniorcurriculum).However,werecommendcoveringatleastsomematerialonimagecompression(Chapter8)asoutlinedbelow.Wehavefoundinmorethantwodecadesofteachingthismaterialtoseniorsinelectricalengineering,computerscience,andothertechnicaldisciplines,thatoneofthekeystosuccessistospendatleastonelectureonmotivationandtheequivalentofonelectureonreviewofbackgroundmaterial,astheneedarises.ThemotivationalmaterialisprovidedinthenumerousapplicationareasdiscussedinChapter1.Thischapterwastotallyrewrittenwiththisobjectiveinmind.Someofthismaterialcanbecoveredinclassandtherestassignedasindependentreading.Backgroundreviewshouldcoverprobabilitytheory(ofonerandomvariable)beforehistogramprocessing(Section3.3).Abriefreviewofvectorsandmatricesmayberequiredlater,dependingonthematerialcovered.Thereviewmaterialincludedinthebookwebsitewasdesignedforjustthispurpose.OneSemesterSeniorCourse3Chapter2shouldbecoveredinitsentirety.Someofthematerial(suchaspartsofSections2.1and2.3)canbeassignedasindependentreading,butadetailedexplanationofSections2.4through2.6istimewellspent.Chapter3servestwoprincipalpurposes.Itcoversimageenhancement(atopicofsignif-icantappealtothebeginningstudent)anditintroducesahostofbasicspatialprocessingtoolsusedthroughoutthebook.Foraseniorcourse,werecommendcoverageofSec-tions3.2.1through3.2.2;Section3.3.1;Section3.4;Section3.5;Section3.6;Section3.7.1,3.7.2(throughExample3.11),and3.7.3.Section3.8canbeassignedasindepen-dentreading,dependingontime.Chapter4alsodiscussesenhancement,butfromafrequency-domainpointofview.Theinstructorhassignificantflexibilityhere.Asmentionedearlier,itispossibletoskipthechapteraltogether,butthiswilltypicallyprecludemeaningfulcoverageofotherareasbasedontheFouriertransform(suchasfilteringandrestoration).Thekeyincoveringthefrequencydomainistogettotheconvolutiontheoremandthusdevelopatiebetweenthefrequencyandspatialdomains.AllthismaterialispresentedinveryreadableforminSection4.2.“Light”coverageoffrequency-domainconceptscanbebasedondiscussingallthematerialthroughthissectionandthenselectingafewsimplefilteringexamples(say,low-andhighpassfilteringusingButterworthfilters,asdiscussedinSections4.3.2and4.4.2).Atthediscretionoftheinstructor,additionalmaterialcanincludefullcoverageofSections4.3and4.4.Itisseldompossibletogobeyondthispointinaseniorcourse.Chapter5canbecoveredasacontinuationofChapter4.Section5.1makesthisaneasyapproach.Then,itispossiblegivethestudenta“flavor”ofwhatrestorationis(andstillkeepthediscussionbrief)bycoveringonlyGaussianandimpulsenoiseinSection5.2.1,andacoupleofspatialfiltersinSection5.3.Thislattersectionisafrequentsourceofconfusiontothestudentwho,basedondiscussionsearlierinthechapter,isexpectingtoseeamoreobjectiveapproach.Itisworthwhiletoemphasizeatthispointthatspatialenhancementandrestorationarethesamethingwhenitcomestonoisereductionbyspatialfiltering.Agoodwaytokeepitbriefandconcludecoverageofrestorationistojumpatthispointtoinversefiltering(whichfollowsdirectlyfromthemodelinSection5.1)andshowtheproblemswiththisapproach.Then,withabriefexplanationregardingthefactthatmuchofrestorationcentersaroundtheinstabilitiesinherentininversefiltering,itispossibletointroducethe“interactive”formoftheWienerfilterinEq.(5.8-3)andconcludethechapterwithExamples5.12and5.13.Chapter6oncolorimageprocessingisanewfeatureofthebook.Coverageofthis4Chapter1Introductionchapteralsocanbebriefattheseniorlevelbyfocusingonenoughmaterialtogivethestudentafoundationonthephysicsofcolor(Section6.1),twobasiccolormodels(RGBandCMY/CMYK),andthenconcludingwithabriefcoverageofpseudocolorprocessing(Section6.3).Wetypicallyconcludeaseniorcoursebycoveringsomeofthebasicaspectsofimagecompression(Chapter8).InterestonthistopichasincreasedsignificantlyasaresultoftheheavyuseofimagesandgraphicsovertheIntern
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