数字图像处理(冈萨雷斯第三版)英文翻译课件

DigitalImageProcessingTianjinUniversityofTechnologyandEducationSchoolofElectronicEngineering2017

DigitalImageProcessingTianSynopsisThecontentsoftheeightweeksareasfollows:Thefirst、secondchapteristheintroductionandthebasicconceptofimageprocessing.Thethird,fourthchapterisspacedomainandfrequencydomaintransformThefifth,eighthchapterisimageenhancementandimagerestoration.ThesixthchapterisimagecodingTheseventh,ninthchapterisimagesegmentationandmorphologyThetenthchapter,otherSynopsisThecontentsoftheeiThefirstchapterisintroduction1.1FromimagetoimageengineeringImageanddigitalimageImagetechnologyandimageengineeringRelateddisciplinesandfields.1.2ImageprocessingandanalysisImageprocessingandanalysissystemImageacquisition,display,storage,communication,processingandanalysismoduleThefirstchapterisintroductimageprocessingimageanalysisImageunderstandingAbstractdegreeDataquantityImagefoundationimageprocessingimageanalysis1.1.1ImageanddigitalimageWhatisanimage?

Animageisavisualrepresentationofpictures,animations,etc..Thedifferencebetweengraphicsandcomputergraphicsisthatcomputergraphicsarefrombuildingmathematicalmodelstogeneratinggraphics,andimagesusuallyrefertographsgeneratedfromoutside.

Theobjectiveworldisathree-dimensionalspace,butthegeneralimageistwo-dimensional.Twodimensionalimagesinevitablylosepartoftheinformationintheprocessofreflectingthethree-dimensionalworld.Evenrecordedinformationcanbedistortedandevendifficulttorecognizeobjects.Therefore,itisnecessarytorecoverandreconstructinformationfromimages,andtoanalyzeandextractmathematicalmodelsofimagessothatpeoplecanhaveacorrectandprofoundunderstandingofwhatisrecordedintheimage.Thisprocessbecomestheprocessofimageprocessing.1.1Fromimagetoimageengineering1.1.1Imageanddigitalimage1Whydoyouneeddigitalimages?

Ordinaryimagescontainenormousamountsofinformationandrequiretheuseofcomputerstoprocessimages.Therefore,itisnecessarytotransformordinaryimagesintodigitalimagesthatthecomputercanprocess.Today'sdigitalcamerascandirectlyconvertvisualimagesintodigitalimages.Adigitalimage,similartorastergraphics,consistingoffiniterowsandfinitecolumns.Eachbasicunitiscalledapixel.Thevoxelofathree-dimensionalimageisalsocalledvoxel.Thetwo-dimensionaldigitalimageusuallyisarectangle,youcanuseatwo-dimensionalarrayofI(x,y)tosaid,wherex,ycoordinatesinatwo-dimensionalspaceisacoordinatesystem,I(x,y)saidintheimagegrayvalueatthepointandotherproperties.ColorcanbepreparedthreeRGBmonochromaticgrayvalue.Generallyspeaking,thesecoordinatesandgrayvaluesarerealnumbers,notonlydependontheselectionofcoordinatesystem,butalsodependonthemeasurementunitofgrayvalue.However,adigitalcomputercanonlyrepresentfinitenumbersoffinitewordlengths.Therefore,thegrayvaluemustbediscretized.Simplyput,adigitalimageisequivalenttoafinitematrixofintegervalues.Digitalimageistheobjectofdigitalimageprocessingandanalysis.WhydoyouneeddigitalimagesTheimageontheleftistheimageprocessingtechnique.UsedtotestcomputeralgorithmsAstandardimageofactualeffects.Thenameofthisimageislenna.Itismadeupofasetofnumbers.OriginalimageThewidthandheightare256pixelseach.Thereareeightbitsinpixels.ItisinBMPformatAbout66Kbytesinsize.TheimageontheleftistheiAbriefhistoryofdigitalimageprocessing

Thegenerationofdigitalpicturesisfaraheadofthecomputer.Thefirstdigitalimagetransmittedbytelegraph.Insixand70s,withthedevelopmentofcomputerhardwareandthediscoveryoffastFuLiyetransformalgorithm,itwaspossibletousecomputertoprocessimages.Since80s,threedimensionalimageshavebeenprocessed.Since90s,withtheimprovementofcomputerperformanceandextensiveuse,imageprocessingtechnologyhasbeeninvolvedineverycornerofsociety.Theimagehasgraduallydominatedthemediaandproducedmanynewindustriesandnewopportunities.Thefuturedevelopmentoftheimageprocessingislimitless.Digitalimageprocessingbelongstocomputerscience,but90%ofitreliesonmathematics.Fromthispointofview,thedigitalimageprocessingtechnologyisaveryidealdirectionforthestudentsofthisspecialty.1.1.2ImagetechnologyandimageengineeringAbriefhistoryofdigitalimaWhichbelongstoimagetechnology?

Imagetechnologyisageneraltermforthetechnologyconcernedwithimages.Itisakindofcomprehensivetechnicalengineering.Itincludesimageacquisition,acquisition,encoding,storageandtransmission,imagegeneration,displayandoutput,imagetransformation,enhancement,restorationandreconstruction,imagesegmentation,targetdetection,expressionanddescription,featureextraction,imageclassification,imagerecognition,modelingandmatching,imageandsceneunderstanding.Narrowsensedigitalimageprocessingreferstotheenhancement,restorationandreconstructionofanimage.Theobjectofoperationisthepixelofanimage,andtheoutputisanimage.WhichbelongstoimagetechnolWhatisimageengineering?(generalizeddigitalimageprocessing)

Itiscomposedofthreesystems:imageprocessing,imageanalysisandimageunderstanding.Imageprocessingincludesimageacquisitionandtransformationfromimagetoimage,soastoimprovethesubjectivevisualeffectandtodopreliminaryprocessingforimageanalysisandimageunderstanding.Imageanalysisistoextractthedataofinterestfromtheimagetodescribethecharacteristicsofthetargetintheimage.Imageunderstandingisbasedonimageanalysistostudythenatureandrelationshipofeachobject,inordertogettheunderstandingofthecontentoftheimageandexplaintheoriginalscene.Imageprocessing,imageanalysisandimageunderstandingarethreedifferentabstractprocessesfromlowtohigh.Thiscoursefocusesonimageprocessingandanalysissystems.imageprocessingimageunderstandingimageanalysisAbstractdegreeDataquantityImageDataSymbolWhatisimageengineering?(ge1.1.3RelateddisciplinesandfieldsImageengineeringisasystematicstudyofvariousimagetheories,techniquesandapplications.

Fromtheresearchmethod,andmathematics,physics,psychology,biology,electronics,computersciencecanlearnfromeachother,fromthescopeofit,andpatternrecognition,computervision,computergraphicsandotherdisciplines.1.1.3Relateddisciplinesand1.2Imageprocessingandanalysis1.2.1Imageprocessingandanalysissystem

Theimageprocessingandanalysissystemincludesthefollowingmodules:imageacquisitionmodule,imagedisplaymodule,imagestoragemodule,imagecommunicationmoduleandimageprocessingandanalysismodule.1.2.2ModularImageacquisitionmodule

Imagedisplaymodule

Imagestoragemodule

Imagecommunicationmodule

Imageprocessingandanalysismodule1.2Imageprocessingandanaly1.2.1Thedatastructureofanimagefile

Thebasicfunctionsofacompleteimageprocessingprogramare:openimagefiles,displayimages,imagefilesforthespecifiedprocessing,storageofimagefiles.Sinceimagefilesarelarge,theyusuallyneedtobecompressedbeforestorage.Soopeningandstoringimagefilesinvolvestheformatofthefile.Formatofimagefile

Theimagefilereferstothefilecontainingtheimagedata.Inadditiontotheimagedataitself,thedocumentgenerallyhastheimagedescriptioninformationfortheimagetoreadanddisplay.Representsavectororrasterformofanimage.Invectorform,theimageisrepresentedbyaseriesoflinesegmentsorlinesegments,andthegraylevelsofthesegmentscanbedifferent.Eachpartofthecompositebodycanbefilledwithdifferentgraylevels.Avectorformfilehasaseriesofcommandsanddata,andtheresultisanimage.1.2.1Thedatastructureofan

Imagedatafileismainlyrasterform,thatis,theimageisacollectionofimagepoints,moresuitableforcompleximageschange.Itsmaindrawbackisthelackoflinksbetweenobjectsandpixels,andchangesintheimageduringtheexpansionoftheimage.Forexample,commonimagefiletypesareBMP,JPG,andsoon.Theimageprocessingprogrammustconsidertheformatoftheimagefile,otherwiseitisnotpossibletoopenandsavetheimagefileproperly.

PgmformatManyuniversitiesintheUnitedStatesusepgmformattoavoidusingcompressedfileformats,whichisveryconvenientforbeginners.Hereisanimageofthisformat.ImagedatafileismainlyThisisacolorpictureinpgmformatThisisacolorpictureinpgmThisisthepgmformat,colorphotos,16partsystemcode.Theoriginalcodeisnotastringofbranches.It'swrittenintheformofabranch

(attention：LF=SP=newline;space;#=commentline)：0x50

0x35

0x0AexpressP5

(LF);0x230x200x200x49…0x0Aexpess#(SP)(SP)I…(LF);0x360x340x300x200x340x380x300x0A

express640(SP)480(LF);0x320x350x35

0x0A

expess255(LF)0x270x27…

express23,23,…(Pixelgrayvalue)……………………………………Thisisthepgmformat,color数字图像处理(冈萨雷斯第三版)英文翻译课件Thedecodingofthisimagefile:P5#ImportedfromSUNimage:LEGGO_HOUSE_1.0.intensity6404802550x270x270x270x270x270x270x270x270x270x270x270x270x270x260x270x270x270x280x270x270x270x270x270x270x270x270x270x270x270x270x270x270x270x270x270x260x270x260x270x280x270x270x260x270x270x270x280x270x270x270x270x270x270x280x280x270x280x290x280x270x280x280x280x270x270x270x270x270x270x270x280x270x280x280x280x280x280x280x280x280x280x290x290x290x280x280x280x28………………...Thedecodingofthisimagefil

PGMformatdigitalimagefileisacommonformofimageprocessing,teachingandresearchinAmericancomputerscience.Althoughthevolumeoffilesisrelativelylarge,thepixelisdirectlyrelatedtothenumber,soitiseasytocheckandmodify.Itconsistsoftwoparts:1、thefirstpartisthefilehead,whichconsistsofseveralrows:Thefirstlineillustratesthetypeoffile,forexample,P2(forblackandwhiteimages)orP5(forcolorimages);Thenisto#atthebeginningoftheannotation,thecommentlinedoesnotperforminthesoftwarewhentheimageisopened,cannotcomment,orhowto#atthebeginningofthecommentline;Thefirstlineafterthecommentlinespecifiesthesizeofthedigitalimage,forexample,640480(640pixelswide,480pixelshigh,withaspaceinthemiddle);Thenextlinespecifiesthegrayscaleoftheimage,forexample,255.Therearenopunctuationmarksattheendofeachline.2、The2andsecondpartsarebitmaparraysthatarenolongersegmented.Forexample,inthe256grayscale,theP2typeisonepixel,onebyte(8bits),andtheP5typeisonepixel,threebytes(R,G,B,8bitseach).PGMformatdigitalimagefilThesecondchapterisaboutimageandvision2.1IntroductionandreviewThefoundationincludesthreeparts:visionbase,imagingbaseandimagefoundation:Visualbasis(humaneyesandbrightness,vision,color,vision)ImagingFundamentals(model,geometry,andsamplingquantization)Imagebasis(interpixelrelation,imageoperationandimagecoordinatetransformation)Becareful：Visual:referstothestimulationoflighttothesensesandthesenseofthevisualsystem.Visualperception:howtoformanimageoftheexternalworldthroughvision.Thesecondchapterisaboutim2.2Humaneyeandbrightnessvision2.2.1Humaneyeimage

Thehumaneyeisacomplexvisualorgan.Thefrontoftheeyehasalens,thelensofacamera.Theposteriorpartoftheeyeballhastheretina.Therearetwophotoreceptorsonthesurfaceoftheretina:conesandcolumncells.Therearesixandsevenmillionconecellsintheeye,whicharesensitivetobrightlightandcolor.Theeyedividesthedetailswiththeaidofcones,becauseeachconeisconnectedtothenerveending.Thevisionofconesiscalledlightvision.Thereare750thousandto1million500thousandcolumncellsintheeye.Theyarelarge,andseveralcolumncellsareattachedtoonenerveend.Lowresolution,mainlyprovidingoverallvisualimpression.Althoughtheyarenotsensitivetocolor,theyaresensitivetoweaklight.Thevisionofcylindricalcellsiscalleddarkvision.Thecenteroftheretinaisthefovea,anareaofabout1.51.5mm2long,theconecelldensityreached150000/mm2,isthemostsensitiveeyearea.2.2HumaneyeandbrightnessvHumaneyestructureHumaneyestructure人眼成像Densityanddistributionofconesandcolumncells人眼成像Densityanddistributiono2.2.2BrightnessadaptationanddifferentiationSubjectivebrightnessandsubjectiveadaptability,becausethedigitalimagedisplaystheimagewithobjectivebrightness,thehumaneyegetsthevisionwithsubjectivebrightness,sothebrightnessadaptabilityofhumaneyeaffectstheresultofimageprocessing.Thevisualsystemofthehumaneyecanadapttothebrightnesslevelofthelight,fromvisibledarknesstoglare,thedifferencecanreach1010levels.Butthehumaneyedoesnotseeobjectsinsuchalargerangeatthesametime,andcanonlyadapttoasmallrangeofbrightnesschangesatthesametime(level106).2.2.2BrightnessadaptationanUndercertainconditions,thecurrentsensitivityofavisualsystemiscalledthebrightnessadaptationlevel.Thesensitivityisverifiedbyexperiments.Intheexperiment,graduallyincreasethelightintensityofI,changealotforI,toachieveanumberofobserverscanperceive,whenpeopleperceivedhalfoftheincreaseintheI/IWeberratiohasbecomealot,asthesensitivityofthecurrentvisualsystem.Inverystronglight,itisnecessarytochangetheintensityofthelighttoallowmultipleobserverstoperceive;onthecontrary,inacertainintensityoflight,theslightchangesinlightintensitywillmakepeopleperceive.Undercertainconditions,theThesubjectivebrightnessofthehumaneyeisnonlinear,forexample,theMachbandThesubjectivebrightnessoftOpticalillusionsofhumaneyesOpticalillusionsofhumaneye2.3colorvision2.3colorvisionAccordingtothestructureofthehumaneye,allcolorsaredifferentcombinationsofthreebasiccolorsAccordingtothestructureofAllcolorscanberegardedasthesuperpositionofthreebasiccolors,canbeseenasthethreecolor(acolorremovalfromwhite)superpositionAllcolorscanberegardedasThreebasicfeaturesofcolor:gray,hueandsaturation,andthelatterarecalledchromaticity.Thegrayscaleisproportionaltothereflectivityoftheobject;thehueisrelatedtothemainspectruminthelight;thesaturationisrelatedtothepurityofthehue.ThethreestimulithatmakeupthecolorCareX,Y,Z,andthepercentagesarex,y,ZX=X/(X+Y+Z),y=Y/(X+Y+Z),z=1-X-Y.Threebasicfeaturesofcolor:数字图像处理(冈萨雷斯第三版)英文翻译课件2.5imagingtransformationLetW(X,Y,Z)bethecoordinatesofanypointinthe3Dspace,Z>=Accordingtothepropertiesofsimilartriangles,x/=X/(-Z), y/=Y/(-Z),x=X/(-Z), y=Y/(-Z)Makeuseofpointwhhomogeneouscoordinates(kX,kY,kZ,K)

1000 P=0100 0010 00-1/1ch=Pwh=P·(kX,kY,kZ,k)=(kX,kY,kZ,-(k/)Z+k）=(x,y,z,1)x=kX/(-k/Z+k)=X/(-Z),thesamewaytogetyandZxZ(X,Y,Z)02.5imagingtransformationLetwh=P-1ch 1000 P-1=0100 0010 001/1wh=P-1·

(x,y,0,1)=(x,y,0,1).ThereisnocoordinatecomponentZ,sothepointof3DcannotberepresentedIfadditionaldepthinformationZisknown,thenthepointof3Dcanberepresented,(X,Y,Z,1)=wh=P-1(x,y,z,1)=(x,y,z,z/+1).其中，X=x/(+z),Y=y/(+z),Z=z/(+z)wh=P-1ch2.6samplingandquantificationAnimageneedstobediscretizedtobecomeadigitalimagebeforeitcanbeprocessedbyacomputer.Thediscretizationofspatialcoordinatesofimagesiscalledspatialsampling,andthediscretizationofgrayscaleiscalledgrayscalequantization.Samplingisdividedintouniformsamplingandquantificationandnonuniformsamplingandquantification.Supposetheimageisarectangle.TakeMlongNthesameasthesizeofthegridintheplane,andthegraylevelisdividedintoG.Theclosestgraynumberateachpointineachgridistakenasthegraylevelofthegrid.Usually,takeM=2m,N=2n,andG=2k.Thenumberofbitsneededtostoreanimageisequaltob=MNk.Forexample,animageof128long128,64graylevelneeds220,512long512,256imagegraylevelto226.Thenumberofsamplingandtheselectionofgraylevelarerelatedtotheresolutionandstorageability,whichneedtobeconsideredcomprehensively.Suchas:Theeffectofchangesinimagespatialresolution.Theeffectofchangesinimagegrayscaleresolution.Theeffectofsimultaneouschangesinimagespaceandgrayscaleresolution.2.6samplingandquantificatioTheeffectofchangesinimagespatialresolutionTheeffectofchangesinimageTheeffectofchangesinimagegrayscaleresolutionTheeffectofchangesinimageEffectofchangesinimagegrayscaleresolution(2)EffectofchangesinimagegraNonuniformsamplingandquantization

Giventhespatialresolution,thequalityoftheimagecanbeimprovedbyadaptivesamplingprocessaccordingtotheimagecharacteristics.Forexample,areaswithlargevariationsingraylevelsshouldbesampledmoreclosely.Also,forexample,thefrequencyofallgrayvaluescanbecalculated.Ifarangeofgrayvaluesappearfrequently,andinotherareas,thegrayvaluesappearmoresparse,theninthisrange,thequantizationgrayscaleismoredense,andinotherareaslessdilute.Nonuniformsamplingandquanti2.7PixelconnectionPixelshavefourneighborhoodN4andeightneighborhoodN8。Pixelconnectivityconsistsof4-connections,8-connections,andhybridconnections(m-connections).CallpointsRandParemixedconnections,ifRandPare4-connections,orRandPare8-connected,butnot4-connected.Thehybridconnectionavoidsambiguityarisingfrom8-connectivity.2.7PixelconnectionPixelshav2.8

Arithmeticandlogic

Thefouroperationsoftheimagearedoneonebyoneasimagepoints.Theadditionisusedtoremovenoisecommonlyusedinmedicalimaging,subtraction,multiplicationanddivisionisoftenusedtocorrecttheimageofthegrayshadow.

Commonlyusedlogicaloperationsare （1）（AND） （2）（OR） （3）（NOT)Theaboveoperationscanbeusedeitherforthewholeimageorforneighborhoodoperations.Forexample,thearithmeticmeanofonepointandits8-neighborhoodisusedasthenewvalueofthispoint.Now,theunitALUofarithmeticandlogicoperationsisusedtospeedupoperations.2.8ArithmeticandlogicThethirdchapteristhespatialrelationofpixelsImagesaremadeupofpixels.Animageisconstructedinpixels.Usuallyx,axialleft,Yaxisdown.Thecoordinatetransformationofanimageisthecoordinatetransformationofapixel.Theso-calledspatialtransformationisthetransformationofpixelsfromonespacetoanother.Oneoftheapplicationsofcoordinatetransformationistocorrectthegeometricdistortionofanimage.ThethirdchapteristhespatiTheneighborhoodofapixelreferstothesetofpixelsaroundthepixel.ApixelPissurroundedbyeightpixels,whichtogetherformthe8-neighborhoodN8(P)ofthepixel.The4-neighborhoodN4(P)consistsofonepixelandfourpixelsintheupperandlowerparts.ApixelconsistsoffourdiagonalpixelscalleddiagonalneighborhoodND(P).Adjacency,connectionandconnectivitybetweenpixelsofthesamegrayscale:

Thetwopixelsfallintoeachother's4-neighborhood,calledthe4-connectionThetwopixelsfallintoeachother's8-neighborhood,calledthe8-connectionIftwopixelsor4-connections,ornot4-connections,fallintoeachother'sdiagonalneighborhoodND(P),thentheyarecalledhybridconnections(m-connections).3.1pixelconnectionTheneighborhoodofapixelreMixedconnectionscanavoidmultipathproblemscausedby8-connections.Theconnectivityoftwosetsofpixelsmeansthattheyhaveapathwithinthespecifiedneighborhood。Forexample,theupperleftcornerandthelowerrightcornerofthefigureTheconnectionby4-isdisconnected;Theconnectionbym-isconnected;The8-connectionisconnected,butthepathisnotunique.ThedistancebetweentwopixelsPandQ,i.e.,afunctionthatsatisfiesthefollowingthreeconditionsD：

D(p,q)

0，ifandonlyifp=q,D(p,q)=0. D(p,q)=D(q,p), D(p,q)+D(q,r)D(p,r).MixedconnectionscanavoidmuDE(p,q)representstheEuclideandistancebetweenp=(x_p,y_p)

andq=(x_q,y_q)

DE(p,q)=[(x_p–x_q)2+(y_p–y_q)2]1/2D4(p,q)representsthedistanceunderthe1-norm

D4(p,q)=|x_p–x_q|+

|y_p–y_q|.D8(p,q)reresentshedistanceunderthe-norm

D4(p,q)=max{|x_p–x_q|,|y_p–y_q|}.10111.4011112222011111111111111111111111Whatisthedistancefrompixeltoboundaryintherightmostgraph?EachpixeltocenterdistanceD：DE(p,q)representstheEuclid3.2basiccoordinatetransformationIthasalreadybeentoldincomputergraphics.Thebasiccoordinatetransformationsaretranslation,expansion,androtation.Complexcoordinatetransformationsaretheircascade.Iscutanderrortheproductofthreefundamentaltransformations?3.2basiccoordinatetransform3.3morphologicaltransformation3.3.1transformsystem1,.morphologicaltransformationanditsclassification

Morphologicaltransformationisthetransformationofaplaneregionintoaplaneregion.MorphologicaltransformationTablesandrulesAnalyticformulaDiscontinuouscontinuityUnsmoothsmoothlinearNonlinearAffinetransformationeuclideantransformationRigidbodytransformationSimilaritytransformationTranslationtransformationRotationtransformationScalingtransformation3.3morphologicaltransformatiProjectiontransformationfrompointPtoQcanbewrittenWhereAisthe2long2matrix.Theprojectivetransformationcanbewrittenintheformofnonsingularthreeorderhomogeneousmatrices.Note:ingeneral,theprojectionisanonlineartransformationofthetwoorder,butitcanbewritteninthehomogeneousformofthethreeordermatrix.Affinetransformationisanonsingularlineartransformationcoupledwithatranslationtransformation:orProjectiontransformationfromThepropertyofaffinetransformationTheaffinetransformationmapstheoriginto(T1,t2,1),andisnolongertheorigin.Sothegeneralaffinetransformationisnotlineartransformation.IfyoudoatranslationtransformationandmaketheT=0intheupperformula,thentheaffinetransformationisanynonsingularmatrixA.Ontheotherhand,theformofaffinetransformationimpliesthatitdoesnotincludeprojectionprojection.Therefore,itistheproductofthreekindsofbasictransformation,andhasthefollowingproperties.（1）Affinetransformationmapsfinitepointsintofinitepoints.（2）Affinetransformationturnsastraightlineintoastraightline.（3）Affinetransformationsmapparallellinesintoparallellines.（4）WhentheregionPandQaredegeneratetriangles,thereisauniqueaffinetransformation,A,whichturnsPintoQ.ThepropertyofaffinetransfoSpecialaffinetransformations:similartransformationsIntheaffinetransformation,A=sRiscalledasimilaritytransformation,inwhichsistherealnumberandRistherotationtransformation.Whens=andR1ampisanorthogonalmatrixtheaffinetransformationiscalledrigidtransformation,whichbelongstotheisometrictransformation.Whens=1andRareorthogonalmatrices,theaffinetransformationiscalledEuclideantransformation.Anothertermofaffinetransformation:atranslationofnonsingularlineartransformations.Specialaffinetransformations3.4geometricdistortioncorrectionIntheprocessofsampling,thespatialpositionsofpixelsintheimagemaychange,resultingingeometricdistortions.Weneedtocorrectthegeometricdistortion.Setintheoriginalimage(x,y)ofthegrayf(x,y),distortioninto(x',y'inthegrayg(x)',y').Thus,thecorrectedgeometricdistortionconsistsoftwoparts:spacetransformpoint(x',y')backtotheposition(x,y)(2)theGgraygrayinterpolation(x',y')backtof(x,y).3.4geometricdistortioncorreSpacetransformationSetup(x',y')and(x,y)istherelationshipbetweentheThesimplestcaseislinear:Themorecomplicatedsituationisthetwo:IfyouknowtheanalyticexpressionsofS(x,y)andt(x,y),youcanInversefunctiontogetXandy.SpacetransformationSetup(xForaquadrilateralspacetransformation,fourcorrespondingverticescanbedeterminedfirst,Then,themethodofbilinearinterpolationisused:Question:howcanIuselinearinterpolationoftwotimes?Iftheareaofgeometricdistortionisrelativelylarge,then,iftheblocksareused.What'stheeffectofthecorrection?ForaquadrilateralspacetranGrayinterpolation

Although(x',y')coordinatecomponentsthatareinteger,butthenewcalculated(x,y)maynothaveintegercomponent,anddeterminethegrayvalueatthenew.Therearetwoschemes:forwardmappingandbackwardmappingForwardmapping:assigningthegrayvaluesofpixelsofadistortedimagefromtheactualcollectiontotheoriginalPixelsofundistortedimages.IfthepixelPofthedistortedimageismappedtoQ,theQfallsThegrayvaluesofthesefourpointsaretakenbetweenthepixelsoffouroriginalundistortedimagesThebilinearinterpolationisusedasthegrayvalueofthepixelQ.GrayinterpolationAlthoughBackwardmapping:thegrayvalueofpixelsfromtheoriginalimagewithoutdistortionPmappingtotheactualacquisitionofdistortedimagepixelsonP'.IfthepixelQactualacquisitionfallsonthefourpixelsP'(noninteger),graytookthesefourpointsP