PAGE2PAGE2Chapter1■IntoductionDigitalImageProcessingandEdgeDetectionDigitalImageProcessingInterestindigitalimageprocessingmethodsstemsfromtwoprincipalapplica-tionareas:improvementofpictorialinformationforhumaninterpretation;andprocessingofimagedataforstorag,transmission,andrepresentationforau-se.Animagemaybedefinedasatwo-dimensionalfunction,f(x,y),wherexandyarespatial(plane)coordinate,andtheamplitudeoffatanypairofcoordinates(x,y)iscalledtheintensityorgryleveloftheimageatthatpoint.henx,y,andtheamplitudevaluesoffareallfinit,discretequantitie,wecalltheimageadigitalimage.hefieldofdigitalimageprocessingreferstoprocessingdigitalimagesbymeansofadigitalcompute.Notethatadigitalimageiscomdfaerf,hfhsarnvalu.heseelementsarereferredtoaspictureelements,imageelements,pels,andpiels.Pielisthetermmostwidelyusedtodenotetheelementsofadigitalimag.Visionisthemostadvancedofoursenses,soitisnotsurprisingthatimagesplaythesinglemostimportantroleinhumanperception.However,unlikehumans,whoarelimitedtothevisualbandoftheelectromagnetic(EM)spec-trum,imagingmachinescoveralmosttheentireEMspectrum,rangingfromgammatoradiowaves.Theycanoperateonimagesgeneratedbysourcesthathumansarenotaccustomedtoassociatingwithimages.Theseincludeultra-sound,electronmicroscopy,andcomputer-generatedimages.Thus,digitalimageprocessingencompassesawideandvariedfieldofapplications.Thereisnogeneralagreementamongauthorsregardingwhereimageprocessingstopsandotherrelatedareas,suchasimageanalysisandcomputervi-sion,start.Sometimesadistinctionismadebydefiningimageprocessingasadisciplineinwhichboththeinputandoutputofaprocessareimages.Webelievethistobealimitingandsomewhatartificialboundary.Forexample,underthisdefinition,eventhetrivialtaskofcomputingtheaverageintensityofanimage(whichyieldsasinglenumber)wouldnotbeconsideredanimageprocessingoperation.Ontheotherhand,therearefieldssuchascomputervisionwhoseultimategoalistousecomputerstoemulatehumanvision,includinglearningandbeingabletomakeinferencesandtakeactionsbasedonvisualinputs.Thisareaitselfisabranchofartificialintelligence(AI)whoseobjectiveistoemulatehumanintelligence.ThefieldofAIisinitsearlieststagesofinfancyintermsofdevelopment,withprogresshavingbeenmuchslowerthanoriginallyanticipated.Theareaofimageanalysis(alsocalledimageunderstanding)isinbe-tweenimageprocessingandcomputervision.Therearenoclearcutboundariesinthecontinuumfromimageprocessingatoneendtocomputervisionattheother.However,oneusefulparadigmistoconsiderthreetypesofcomputerizedprocessesinthiscontinuum:low-,mid-,andhighlevelprocesses.Low-levelprocessesinvolveprimitiveopera-tionssuchasimagepreprocessingtoreducenoise,contrastenhancement,andimagesharpening.Alow-levelprocessischaracterizedbythefactthatbothitsinputsandoutputsareimages.Mid-levelprocessingonimagesinvolvestaskssuchassegmentation(partitioninganimageintoregionsorobjects),descriptionofthoseobjectstoreducethemtoaformsuitableforcomputerprocessing,andclassification(recognition)ofindividualobjects.Amidlevelprocessischaracterizedbythefactthatitsinputsgenerallyareimages,butitsoutputsareattributesextractedfromthoseimages(e.g.,edges,contours,andtheidentityofindividualobjects).Finally,higherlevelprocessinginvolves“makingsense”ofanensembleofrecognizedobjects,asinimageanalysis,and,atthefarendofthecontinuum,performingthecognitivefunctionsnormallyassociatedwithvision.Basedontheprecedingcomments,weseethatalogicalplaceofoverlapbetweenimageprocessingandimageanalysisistheareaofrecognitionofindividualregionsorobjectsinanimage.Thus,whatwecallinthisbookdigitalimageprocessingencompassesprocesseswhoseinputsandoutputsareimagesand,inaddition,encompassesprocessesthatextractattributesfromimages,uptoandincludingtherecognitionofindividualobjects.Asasimpleillustrationtoclarifytheseconcepts,considertheareaofautomatedanalysisoftext.Theprocessesofacquiringanimageoftheareacontainingthetext,preprocessingthatimage,extracting(segmenting)theindividualcharacters,describingthecharactersinaformsuitableforcomputerprocessing,andrecognizingthoseindividualcharactersareinthescopeofwhatwecalldigitalimageprocessinginthisbook.Makingsenseofthecontentofthepagemaybeviewedasbeinginthedomainofimageanalysisandevencomputervision,dependingonthelevelofcomplexityimpliedbythestatement“makingsense.”Aswillbecomeevidentshortly,digitalimageprocessing,aswehavedefinedit,isusedsuccessfullyinabroadrangeofareasofexceptionalsocialandeconomicvalue.Theareasofapplicationofdigitalimageprocessingaresovariedthatsomeformoforganizationisdesirableinattemptingtocapturethebreadthofthisfield.Oneofthesimplestwaystodevelopabasicunderstandingoftheextentofimageprocessingapplicationsistocategorizeimagesaccordingtotheirsource(e.g.,visual,X-ray,andsoon).Theprincipalenergysourceforimagesinusetodayistheelectromagneticenergyspectrum.Otherimportantsourcesofenergyincludeacoustic,ultrasonic,andelectronic(intheformofelectronbeamsusedinelectronmicroscopy).Syntheticimages,usedformodelingandvisualization,aregeneratedbycomputer.Inthissectionwediscussbrieflyhowimagesaregeneratedinthesevariouscategoriesandtheareasinwhichtheyareapplied.ImagesbasedonradiationfromtheEMspectrumarethemostfamiliar,es-peciallyimagesintheX-rayandvisualbandsofthespectrum.Electromagnet-icwavescanbeconceptualizedaspropagatingsinusoidalwavesofvaryingwavelengths,ortheycanbethoughtofasastreamofmasslessparticles,eachtravelinginawavelikepatternandmovingatthespeedoflight.Eachmasslessparticlecontainsacertainamount(orbundle)ofenergy.Eachbundleofenergyiscalledaphoton.Ifspectralbandsaregroupedaccordingtoenergyperphoton,weobtainthespectrumshowninfig.below,rangingfromgammarays(highestenergy)atoneendtoradiowaves(lowestenergy)attheother.ThebandsareshownshadedtoconveythefactthatbandsoftheEMspectrumarenotdistinctbutrathertransitionsmoothlyfromonetotheother.Imageacquisitionisthefirstprocess.Notethatacquisitioncouldbeassimpleasbeinggivenanimagethatisalreadyindigitalform.Generally,theimageacquisitionstageinvolvespreprocessing,suchasscaling.Imageenhancementisamongthesimplestandmostappealingareasofdigitalimageprocessing.Basically,theideabehindenhancementtechniquesistobringoutdetailthatisobscured,orsimplytohighlightcertainfeaturesofinterestinanimage.Afamiliarexampleofenhancementiswhenweincreasethecontrastofanimagebecause“itlooksbetter.”Itisimportanttokeepinmindthatenhancementisaverysubjectiveareaofimageprocessing.Imagerestorationisanareathatalsodealswithimprovingtheappearanceofanimage.However,unlikeenhancement,whichissubjective,imagerestorationisobjective,inthesensethatrestorationtechniquestendtobebasedonmathematicalorprobabilisticmodelsofimagedegradation.Enhancement,ontheotherhand,isbasedonhumansubjectivepreferencesregardingwhatconstitutesa“good”enhancementresult.ColorimageprocessingisanareathathasbeengaininginimportancebecauseofthesignificantincreaseintheuseofdigitalimagesovertheInternet.Itcoversanumberoffundamentalconceptsincolormodelsandbasiccolorprocessinginadigitaldomain.Colorisusedalsoinlaterchaptersasthebasisforextractingfeaturesofinterestinanimage.Waveletsarethefoundationforrepresentingimagesinvariousdegreesofresolution.Inparticular,thismaterialisusedinthisbookforimagedatacompressionandforpyramidalrepresentation,inwhichimagesaresubdividedsuccessivelyintosmallerregions.Compression,asthenameimplies,dealswithtechniquesforreducingthestoragerequiredtosaveanimage,orthebandwidthrequiredtotransmiit.Althoughstoragetechnologyhasimprovedsignificantlyoverthepastdecade,thesamecannotbesaidfortransmissioncapacity.ThisistrueparticularlyinusesoftheInternet,whicharecharacterizedbysignificantpictorialcontent.Imagecompressionisfamiliar(perhapsinadvertently)tomostusersofcomputersintheformofimagefileextensions,suchasthejpgfileextensionusedintheJPEG(JointPhotographicExpertsGroup)imagecompressionstandard.Morphologicalprocessingdealswithtoolsforextractingimagecomponentsthatareusefulintherepresentationanddescriptionofshape.Thematerialinthischapterbeginsatransitionfromprocessesthatoutputimagestoprocessesthatoutputimageattributes.Segmentationprocedurespartitionanimageintoitsconstituentpartsorobjects.Ingeneral,autonomoussegmentationisoneofthemostdifficulttasksindigitalimageprocessing.Aruggedsegmentationprocedurebringstheprocessalongwaytowardsuccessfulsolutionofimagingproblemsthatrequireobjectstobeidentifiedindividually.Ontheotherhand,weakorerraticsegmentationalgorithmsalmostalwaysguaranteeeventualfailure.Ingeneral,themoreaccuratethesegmentation,themorelikelyrecognitionistosucceed.Representationanddescriptionalmostalwaysfollowtheoutputofasegmentationstage,whichusuallyisrawpixeldata,constitutingeitherthebound-aryofaregion(i.e.,thesetofpixelsseparatingoneimageregionfromanother)orallthepointsintheregionitself.Ineithercase,convertingthedatatoaformsuitableforcomputerprocessingisnecessary.Thefirstdecisionthatmustbemadeiswhetherthedatashouldberepresentedasaboundaryorasacompleteregion.Boundaryrepresentationisappropriatewhenthefocusisonexternalshapecharacteristics,suchascornersandinflections.Regionalrepresentationisappropriatewhenthefocusisoninternalproperties,suchastextureorskeletalshape.Insomeapplications,theserepresentationscomplementeachother.Choosingarepresentationisonlypartofthesolutionfortrans-formingrawdataintoaformsuitableforsubsequentcomputerprocessing.Amethodmustalsobespecifiedfordescribingthedatasothatfeaturesofinterestarehighlighted.Description,alsocalledfeatureselection,dealswithextractingattributesthatresultinsomequantitativeinformationofinterestorarebasicfordifferentiatingoneclassofobjectsfromanother.Recognitionistheprocessthatassignsalabel(e.g.,“vehicle”)toanobjectbasedonitsdescriptors.Asdetailedbefore,weconcludeourcoverageofdigitalimageprocessingwiththedevelopmentofmethodsforrecognitionofindividualobjects.SofarwehavesaidnothingabouttheneedforpriorknowledgeorabouttheinteractionbetweentheknowledgebaseandtheprocessingmodulesinFig2above.Knowledgeaboutaproblemdomainiscodedintoanimageprocessingsystemintheformofaknowledgedatabase.Thisknowledgemaybeassim-pleasdetailingregionsofanimagewheretheinformationofinterestisknowntobelocated,thuslimitingthesearchthathastobeconductedinseekingthatinformation.Theknowledgebasealsocanbequitecomplex,suchasaninterrelatedlistofallmajorpossibledefectsinamaterialsinspectionproblemoranimagedatabasecontaininghigh-resolutionsatelliteimagesofaregionincon-nectionwithchange-detectionapplications.Inadditiontoguidingtheoperationofeachprocessingmodule,theknowledgebasealsocontrolstheinteractionbetweenmodules.ThisdistinctionismadeinFig2abovebytheuseofdouble-headedarrowsbetweentheprocessingmodulesandtheknowledgebase,asop-posedtosingle-headedarrowslinkingtheprocessingmodules.EdgedetectionEdgedetectionisaterminologyin\o"Imageprocessing"imageprocessingand\o"Computervision"computervision,particularlyintheareasof\o"Featuredetection(computervision)"featuredetectionand\o"Featureextraction"featureextraction,toreferto\o"Algorithm"algorithmswhichaimatidentifyingpointsina\o"Digitalimage"digitalimageatwhichthe\o"Luminousintensity"imagebrightnesschangessharplyormoreformallyhasdiscontinuities.Althoughpointandlinedetectioncertainlyareimportantinanydiscussiononsegmentation,edgedectectionisbyfarthemostcommonapproachfordetectingmeaningfuldiscountiesingraylevel.Althoughcertainliteraturehasconsideredthedetectionofidealstepedges,theedgesobtainedfromnaturalimagesareusuallynotatallidealstepedges.Insteadtheyarenormallyaffectedbyoneorseveralofthefollowingeffects:1.focalblurcausedbyafinite\o"Depth-of-field"depth-of-fieldandfinite\o"Pointspreadfunction"pointspreadfunction;2.\o"Penumbra"penumbralblurcausedbyshadowscreatedbylightsourcesofnon-zeroradius;3.\o"Shading"shadingatasmoothobjectedge;4.local\o"Specularity"specularitiesor\o"Diffuseinterreflection"interreflectionsinthevicinityofobjectedges.Atypicaledgemightforinstancebetheborderbetweenablockofredcolorandablockofyellow.Incontrasta\o"Line(mathematics)"line(ascanbeextractedbya\o"Ridgedetection"ridgedetector)canbeasmallnumberofpixelsofadifferentcoloronanotherwiseunchangingbackground.Foraline,theremaythereforeusuallybeoneedgeoneachsideoftheline.Toillustratewhyedgedetectionisnotatrivialtask,letusconsidertheproblemofdetectingedgesinthefollowingone-dimensionalsignal.Here,wemayintuitivelysaythatthereshouldbeanedgebetweenthe4thand5thpixels.

5

7

6

4

152

148

149

Iftheintensitydifferenceweresmallerbetweenthe4thandthe5thpixelsandiftheintensitydifferencesbetweentheadjacentneighbouringpixelswerehigher,itwouldnotbeaseasytosaythatthereshouldbeanedgeinthecorrespondingregion.Moreover,onecouldarguethatthiscaseisoneinwhichthereareseveraledges.Hence,tofirmlystateaspecificthresholdonhowlargetheintensitychangebetweentwoneighbouringpixelsmustbeforustosaythatthereshouldbeanedgebetweenthesepixelsisnotalwaysasimpleproblem.Indeed,thisisoneofthereasonswhyedgedetectionmaybeanon-trivialproblemunlesstheobjectsinthesceneareparticularlysimpleandtheilluminationconditionscanbewellcontrolled.Therearemanymethodsforedgedetection,butmostofthemcanbegroupedintotwocategories,search-basedand\o"Zerocrossing"zero-crossingbased.Thesearch-basedmethodsdetectedgesbyfirstcomputingameasureofedgestrength,usuallyafirst-orderderivativeexpressionsuchasthegradientmagnitude,andthensearchingforlocaldirectionalmaximaofthegradientmagnitudeusingacomputedestimateofthelocalorientationoftheedge,usuallythegradientdirection.Thezero-crossingbasedmethodssearchforzerocrossingsinasecond-orderderivativeexpressioncomputedfromtheimageinordertofindedges,usuallythezero-crossingsofthe\o"Laplacian"Laplacianorthezero-crossingsofanon-lineardifferentialexpression,aswillbedescribedinthesectionon\o"Edgedetection"differentialedgedetectionfollowingbelow.Asapre-processingsteptoedgedetection,asmoothingstage,typicallyGaussiansmoothing,isalmostalwaysapplied(seealso\o"Noisereduction"noisereduction).Theedgedetectionmethodsthathavebeenpublishedmainlydifferinthetypesofsmoothingfiltersthatareappliedandthewaythemeasuresofedgestrengtharecomputed.Asmanyedgedetectionmethodsrelyonthecomputationofimagegradients,theyalsodifferinthetypesoffiltersusedforcomputinggradientestimatesinthex-andy-directions.Oncewehavecomputedameasureofedgestrength(typicallythegradientmagnitude),thenextstageistoapplyathreshold,todecidewhetheredgesarepresentornotatanimagepoint.Thelowerthethreshold,themoreedgeswillbedetected,andtheresultwillbeincreasinglysusceptibleto\o"Imagenoise"noise,andalsotopickingoutirrelevantfeaturesfromtheimage.Converselyahighthresholdmaymisssubtleedges,orresultinfragmentededges.Iftheedgethresholdingisappliedtojustthegradientmagnitudeimage,theresultingedgeswillingeneralbethickandsometypeofedgethinningpost-processingisnecessary.Foredgesdetectedwithnon-maximumsuppressionhowever,theedgecurvesarethinbydefinitionandtheedgepixelscanbelinkedintoedgepolygonbyanedgelinking(edgetracking)procedure.Onadiscretegrid,thenon-maximumsuppressionstagecanbeimplementedbyestimatingthegradientdirectionusingfirst-orderderivatives,thenroundingoffthegradientdirectiontomultiplesof45degrees,andfinallycomparingthevaluesofthegradientmagnitudeintheestimatedgradientdirection.Acommonlyusedapproachtohandletheproblemofappropriatethresholdsforthresholdingisbyusing\o"Adaptivethresholding"thresholdingwith\o"Hysteresis"hysteresis.Thismethodusesmultiplethresholdstofindedges.Webeginbyusingtheupperthresholdtofindthestartofanedge.Oncewehaveastartpoint,wethentracethepathoftheedgethroughtheimagepixelbypixel,markinganedgewheneverweareabovethelowerthreshold.Westopmarkingouredgeonlywhenthevaluefallsbelowourlowerthreshold.Thisapproachmakestheassumptionthatedgesarelikelytobeincontinuouscurves,andallowsustofollowafaintsectionofanedgewehavepreviouslyseen,withoutmeaningthateverynoisypixelintheimageismarkeddownasanedge.Still,however,wehavetheproblemofchoosingappropriatethresholdingparameters,andsuitablethresholdingvaluesmayvaryovertheimage.Someedge-detectionoperatorsareinsteadbaseduponsecond-orderderivativesoftheintensity.Thisessentiallycapturesthe\o"Rateofchange"rateofchangeintheintensitygradient.Thus,intheidealcontinuouscase,detectionofzero-crossingsinthesecondderivativecaptureslocalmaximainthegradient.Wecancometoaconclusionthat,tobeclassifiedasameaningfuledgepoint,thetransitioningraylevelassociatedwiththatpointhastobesignificantlystrongerthanthebackgroundatthatpoint.Sincewearedealingwithlocalcomputations,themethodofchoicetodeterminewhetheravalueis“significant”ornotidtouseathreshold.Thuswedefineapointinanimageasbeingasbeinganedgepointifitstwo-dimensionalfirst-orderderivativeisgreaterthanaspecifiedcriterionofconnectednessisbydefinitionanedge.Thetermedgesegmentgenerallyisusediftheedgeisshortinrelationtothedimensionsoftheimage.Akeyprobleminsegmentationistoassembleedgesegmentsintolongeredges.Analternatedefinitionifweelecttousethesecond-derivativeissimplytodefinetheedgeponitsinanimageasthezerocrossingsofitssecondderivative.Thedefinitionofanedgeinthiscaseisthesameasabove.Itisimportanttonotethatthesedefinitionsdonotguaranteesuccessinfindingedgeinanimage.Theysimplygiveusaformalismtolookforthem.First-orderderivativesinanimagearecomputedusingthegradient.Second-orderderivativesareobtainedusingtheLaplacian.數字圖像處理與邊緣檢測數字圖像處理數字圖像處理方法的研究源于兩個主要應用領域：其一是為了便于人們分析而對圖像信息進行改進：其二是為使機器自動理解而對圖像數據進行存儲、傳輸及顯示。一幅圖像可定義為一個二維函數f(x,y)，這里x和y是空間坐標，而在任何一對空間坐標（x,y）上的幅值f稱為該點圖像的強度或灰度。當x,y和幅值f為有限的、離散的數值時，稱該圖像為數字圖像。數字圖像處理是指借用數字計算機處理數字圖像，值得提及的是數字圖像是由有限的元素組成的，每一個元素都有一個特定的位置和幅值，這些元素稱為圖像元素、畫面元素或像素。像素是廣泛用于表示數字圖像元素的詞匯。視覺是人類最高級的感知器官，所以，毫無疑問圖像在人類感知中扮演著最重要的角色。然而，人類感知只限于電磁波譜的視覺波段，成像機器則可覆蓋幾乎全部電磁波譜，從伽馬射線到無線電波。它們可以對非人類習慣的那些圖像源進行加工，這些圖像源包括超聲波、電子顯微鏡及計算機產生的圖像。因此，數字圖像處理涉及各種各樣的應用領域。圖像處理涉及的范疇或其他相關領域（例如，圖像分析和計算機視覺）的界定在初創人之間并沒有一致的看法。有時用處理的輸入和輸出內容都是圖像這一特點來界定圖像處理的范圍。我們認為這一定義僅是人為界定和限制。例如，在這個定義下，甚至最普通的計算一幅圖像灰度平均值的工作都不能算做是圖像處理。另一方面，有些領域（如計算機視覺）研究的最高目標是用計算機去模擬人類視覺，包括理解和推理并根據視覺輸入采取行動等。這一領域本身是人工智能的分支，其目的是模仿人類智能。人工智能領域處在其發展過程中的初期階段，它的發展比預期的要慢的多，圖像分析（也稱為圖像理解）領域則處在圖像處理和計算機視覺兩個學科之間。從圖像處理到計算機視覺這個連續的統一體內并沒有明確的界線。然而，在這個連續的統一體中可以考慮三種典型的計算處理（即低級、中級和高級處理）來區分其中的各個學科。低級處理涉及初級操作，如降低噪聲的圖像預處理，對比度增強和圖像尖銳化。低級處理是以輸入、輸出都是圖像為特點的處理。中級處理涉及分割（把圖像分為不同區域或目標物）以及縮減對目標物的描述，以使其更適合計算機處理及對不同目標的分類（識別）。中級圖像處理是以輸入為圖像，但輸出是從這些圖像中提取的特征（如邊緣、輪廓及不同物體的標識等）為特點的。最后，高級處理涉及在圖像分析中被識別物體的總體理解，以及執行與視覺相關的識別函數（處在連續統一體邊緣）等。根據上述討論，我們看到，圖像處理和圖像分析兩個領域合乎邏輯的重疊區域是圖像中特定區域或物體的識別這一領域。這樣，在研究中，我們界定數字圖像處理包括輸入和輸出均是圖像的處理，同時也包括從圖像中提取特征及識別特定物體的處理。舉一個簡單的文本自動分析方面的例子來具體說明這一概念。在自動分析文本時首先獲取一幅包含文本的圖像，對該圖像進行預處理，提取（分割）字符，然后以適合計算機處理的形式描述這些字符，最后識別這些字符，而所有這些操作都在本文界定的數字圖像處理的范圍內。理解一頁的內容可能要根據理解的復雜度從圖像分析或計算機視覺領域考慮問題。這樣，我們定義的數字圖像處理的概念將在有特殊社會和經濟價值的領域內通用。數字圖像處理的應用領域多種多樣，所以文本在內容組織上盡量達到該技術應用領域的廣度。闡述數字圖像處理應用范圍最簡單的一種方法是根據信息源來分類（如可見光、X射線，等等）。在今天的應用中，最主要的圖像源是電磁能譜，其他主要的能源包括聲波、超聲波和電子（以用于電子顯微鏡方法的電子束形式）。建模和可視化應用中的合成圖像由計算機產生。建立在電磁波譜輻射基礎上的圖像是最熟悉的，特別是X射線和可見光譜圖像。電磁波可定義為以各種波長傳播的正弦波，或者認為是一種粒子流，每個粒子包含一定（一束）能量，每束能量成為一個光子。如果光譜波段根據光譜能量進行分組，我們會得到下圖1所示的伽馬射線（最高能量）到無線電波（最低能量）的光譜。如圖所示的加底紋的條帶表達了這樣一個事實，即電磁波譜的各波段間并沒有明確的界線，而是由一個波段平滑地過渡到另一個波段。圖像獲取是第一步處理。注意到獲取與給出一幅數字形式的圖像一樣簡單。通常，圖像獲取包括如設置比例尺等預處理。圖像增強是數字圖像處理最簡單和最有吸引力的領域。基本上，增強技術后面的思路是顯現那些被模糊了的細節，或簡單地突出一幅圖像中感興趣的特征。一個圖像增強的例子是增強圖像的對比度，使其看起來好一些。應記住，增強是圖像處理中非常主觀的領域，這一點很重要。圖像復原也是改進圖像外貌的一個處理領域。然而，不像增強，圖像增強是主觀的，而圖像復原是客觀的。在某種意義上說，復原技術傾向于以圖像退化的數學或概率模型為基礎。另一方面，增強以怎樣構成好的增強效果這種人的主觀偏愛為基礎。彩色圖像處理已經成為一個重要領域，因為基于互聯網的圖像處理應用在不斷增長。就使得在彩色模型、數字域的彩色處理方面涵蓋了大量基本概念。在后續發展，彩色還是圖像中感興趣特征被提取的基礎。小波是在各種分辨率下描述圖像的基礎。特別是在應用中，這些理論被用于圖像數據壓縮及金字塔描述方法。在這里，圖像被成功地細分為較小的區域。壓縮，正如其名稱所指的意思，所涉及的技術是減少圖像的存儲量，或者在傳輸圖像時降低頻帶。雖然存儲技術在過去的十年內有了很大改進，但對傳輸能力我們還不能這樣說，尤其在互聯網上更是如此，互聯網是以大量的圖片內容為特征的。圖像壓縮技術對應的圖像文件擴展名對大多數計算機用戶是很熟悉的（也許沒注意），如JPG文件擴展名用于JPEG（聯合圖片專家組）圖像壓縮標準。形態學處理設計提取圖像元素的工具，它在表現和描述形狀方面非常有用。這一章的材料將從輸出圖像處理到輸出圖像特征處理的轉換開始。分割過程將一幅圖像劃分為組成部分或目標物。通常，自主分割是數字圖像處理中最為困難的任務之一。復雜的分割過程導致成功解決要求物體被分別識別出來的成像問題需要大量處理工作。另一方面，不健壯且不穩定的分割算法幾乎總是會導致最終失敗。通常，分割越準確，識別越成功。表示和描述幾乎總是跟隨在分割步驟的輸后邊，通常這一輸出是未加工的數據，其構成不是區域的邊緣（區分一個圖像區域和另一個區域的像素集）就是其區域本身的所有點。無論哪種情況，把數據轉換成適合計算機處理的形式都是必要的。首先，必須確定數據是應該被表現為邊界還是整個區域。當注意的焦點是外部形狀特性（如拐角和曲線）時，則邊界表示是合適的。當注意的焦點是內部特性（如紋理或骨骼形狀）時，則區域表示是合適的。則某些應用中，這些表示方法是互補的。選擇一種表現方式僅是解決把原始數據轉換為適合計算機后續處理的形式的一部分。為了描述數據以使感興趣的特征更明顯，還必須確定一種方法。描述也叫特征選擇，涉及提取特征，該特征是某些感興趣的定量信息或是區分一組目標與其他目標的基礎。識別是基于目標的描述給目標賦以符號的過程。如上文詳細討論的那樣，我們用識別個別目標方法的開發推出數字圖像處理的覆蓋范圍。到目前為止，還沒有談到上面圖2中關于先驗知識及知識庫與處理模塊之間的交互這部分內容。關于問題域的知識以知識庫的形式被編碼裝入一個圖像處理系統。這一知識可能如圖像細節區域那樣簡單，在這里，感興趣的信息被定位，這樣，限制性的搜索就被引導到尋找的信息處。知識庫也可能相當復雜，如材料檢測問題中所有主要缺陷的相關列表或者圖像數據庫（該庫包含變化檢測應用相關區域的高分辨率衛星圖像）。除了引導每一個處理模塊的操作，知識庫還要控制模塊間的交互。這一特性上面圖2中的處理模塊和知識庫間用雙箭頭表示。相反單頭箭頭連接處理模塊。邊緣檢測邊緣檢測是\o"圖像處理"圖像處理和\o"計算機視覺"計算機視覺中的術語，尤其在特征檢測和特征抽取領域，是一種用來識別數字圖像亮度驟變點即不連續點的算法。盡管在任何關于分割的討論中，點和線檢測都是很重要的，但是邊緣檢測對于灰度級間斷的檢測是最為普遍的檢測方法。雖然某些文獻提過理想的邊緣檢測步驟，但自然界圖像的邊緣并不總是理想的階梯邊緣。相反，它們通常受到一個或多個下面所列因素的影響：1.有限\o"場景深度（尚未撰寫）"場景深度帶來的聚焦模糊；2.非零半徑光源產生的陰影帶來的\o"半影"半影模糊；3.光滑物體邊緣的\o"陰影"陰影；4.物體邊緣附近的局部\o"鏡面反射"鏡面反射或者\o"漫反射（尚未撰寫）"漫反射。一個典型的邊界可能是（例如