mathematic文档.docx
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mathematic文档.docx
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mathematic文档
Mathematica>
Mathematica教程
BinarizeBlurColorConvertColorNegateColorQuantizeCommonestFilterDarkerDilationDistanceTransformErosionFalseGaussianFilterGeodesicDilationGeodesicErosionImageImageAddImageAdjustImageApplyImageChannelsImageConvolveImageCropImageDataImageDimensionsImageFilterImageHistogramImageLevelsImageMultiplyImagePadImageQImageReflectImageResizeImageRotateImageSubtractImageTakeImageTypeImportLighterMeanFilterMedianFilterMinFilterMorphologicalComponentsOptionsSharpenThumbnailTrue
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ConvolutionsandCorrelations
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ImageProcessing
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ImageProcessing
Mathematicanowprovidesbuilt-insupportforbothprogrammaticandinteractiveimageprocessing—fullyintegratedwithMathematica'spowerfulmathematicalandalgorithmiccapabilities.Youcancreateandimportimages,manipulatethemwithbuilt-infunctions,applylinearandnonlinearfilterstothem,andvisualizetheminanynumberofways.
ImageCreationandRepresentation
Imagescanbecreatedfromnumericalarrays,fromMathematicagraphicsviacut-and-pastemethods,andfromexternalsourcesviaImport.
Image[data]
rasterimagewithpixelvaluesgivenbydata
Import["file"]
importdatafromafile
Imagecreationfunctions.
ThesimplestmethodforcreatinganimageobjectistowrapImagearoundamatrixofrealvaluesrangingfrom0to1.
Hereisaone-channelimagecreatedfromamatrixofnumbers.
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dYoucanalsocopyandpasteordraganddropanimagefromotherapplications.YoucanuseImporttoobtainanimagefromafileonthelocalfilesystemoranyaccessibleremotelocation.
ThisimportsanimagefromtheMathematicadocumentationdirectoryExampleData.
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Usefulpropertiesofanimagecanbeobtainedbycallingthefollowingfunctions.
ImageDimensions[image]
givethepixeldimensionsoftherasterassociatedwithimage
ImageChannels[image]
givethenumberofchannelspresentinthedataforimage
ImageType[image]
givethetypeofvaluesusedforeachpixelelementinimage
ImageQ[image]
giveTrueifimagehastheformofavalidImageobjectandFalseotherwise
Options[symbol]
givethelistofdefaultoptionsassignedtoasymbol
ImageData[image]
thearrayofpixelvaluesinimage
Imageproperties.
Thisreturnstheimagedimensions.
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HereisthesettingoftheColorSpaceoption.
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Theimage'sarrayofpixelvaluescanbeeasilyextractedusingthefunctionImageData.Bydefault,thefunctionreturnsrealvalues,butyoucanaskforaspecifictypeusingtheoptional"type"argument.
Thisreturnsafragmentoftheimageasamatrixofrealvaluesscaledtotherange0to1.
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Hereisthesamefragmentasamatrixofintegersintherange0to255.
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Inthecaseofmultichannelimages,therawpixeldataisrepresentedbya3DarrayarrangedinoneoftwopossiblewaysasdeterminedbytheoptionInterleaving.
Thisimportsacolorimage.
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WiththedefaultsettingInterleaving->True,thedataisorganizedasa2Darrayoflistsofcolorvalues,atripletinthecommoncaseofimagesinRGBcolorspace.
Thisshowsthedefaultdataorganization.
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TheoptionsettingInterleaving->Falsecanbeusedtostoreandretrievetherawdataasalistofmatrices,oneforeachofthecolorchannels.
Hereisafragmentoftheexampleimagearrangedasalistofchannelmatrices.
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Amultichannelimagecanbesplitintoalistofsingle-channelimagesand,conversely,amultichannelimagecanbecreatedfromanynumberofsingle-channelimages.
ThissplitstheexampleRGBcolorimageintothreegrayscaleimages.
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BasicImageManipulation
Considertheimagemanipulationoperationsthatchangetheimagedimensionsbycroppingorpadding.Theseoperationsserveavarietyofusefulpurposes.Croppingallowsyoutocreateanewimagefromaselectedportionofalargerone,whilepaddingistypicallyusedtoextendanimageattheborderstoensureuniformtreatmentoftheborderpixelsinmanyimageprocessingtasks.
ImageTake[image,n]
giveanimageconsistingofthefirstnrowsofimage
ImageCrop[image]
cropimagebyremovingbordersofuniformcolor
ImagePad[image,m]
padimageonallsideswithmbackgroundpixels
Imagecroppingandpaddingoperations.
Thisselectsthefirst50rowsoftheexampleimage.
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ImageCropconvenientlycomplementsImageTake.Insteadofspecifyingtheexactnumberofrowsorcolumnstobeextracted,itallowsyoutodefinethedesireddimensionsoftheresultingimage,namely,thenumberofrowsorcolumnsthataretoberetained.Bydefault,thecroppingoperationiscentered,thusanequalnumberofrowsandcolumnsisdeletedfromtheedgesoftheimage.
Herea100×100pixelregionisextractedfromthecenteroftheexampleimage.
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WhileImageCropisprimarilyusedtoreducethedimensionsofthesourceimage,itisfrequentlydesirabletopadanimagetoincreaseitsdimensions.Allthemostcommonpaddingmethodsaresupported.
Thisshowsfourdifferentpaddingmethodsappliedtotherightedgeoftheexampleimage.
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Itisfrequentlynecessarytochangethedimensionsofanimagebyresamplingortorepositionitinsomemanner.Functionsthatperformthesebasicgeometrictasksarereadilyavailable.
ImageResize[image,w]
givearesizedversionofimagethatiswpixelswide
Thumbnail[image]
giveathumbnailversionofimage
ImageRotate[image]
rotateimagecounterclockwiseby90°
ImageReflect[image]
reverseimagebytop-bottommirrorreflection
Spatialoperations.
Here,ImageResizeisusedtoincreaseanddiminishthesizeoftheoriginalimage,respectively.
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ImageRotateisanothercommonspatialoperation.Itresultsinanimagewhosepixelpositionsareallrotatedcounter-clockwisewithrespecttoapivotpointcenteredontheimage.
Thisrotatestheexampleimageby30degrees.
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Severalusefulimageprocessingtasksrequirenothingmorethansimplearithmeticoperationsbetweentwoimagesoranimageandaconstant.Forexample,youcanchangebrightnessbymultiplyinganimagebyaconstantfactororbyadding(subtracting)aconstantto(from)animage.Moreinterestingly,thedifferenceoftwoimagescanbeusedtodetectchangeandtheproductoftwoimagescanbeusedtohideorhighlightregionsinanimageinaprocesscalledmasking.Forthispurpose,threebasicarithmeticfunctionsareavailable.
ImageAdd[image,x]
addanamountxtoeachchannelvalueinimage
ImageSubtract[image,x]
subtractaconstantamountxfromeachchannelvalueinimage
ImageMultiply[image,x]
multiplyeachchannelvalueinimagebyafactorx
Arithmeticoperations.
Hereisanexampleofimageblendingusingadditionandmultiplication.
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ImageProcessingbyPointOperations
Pointoperationsconstituteasimplebutimportantclassofimageprocessingoperations.Theseoperationschangetheluminancevaluesofanimageandthereforemodifyhowanimageappearswhendisplayed.Theterminologyoriginatesfromthefactthatpointoperationstakesinglepixelsasinputs.Thiscanbeexpressedas
g(i,j)=T[f(i,j)]
whereTisagrayscaletransformationthatspecifiesthemappingbetweentheinputimagefandtheresultg,andi,jdenotestherow,columnindexofthepixel.Pointoperationsareaone-to-onemappingbetweentheoriginal(input)andmodified(output)imagesaccordingtosomefunctiondefiningthetransformationT.
ContrastModification
Contrast-modifyingpointoperationsfrequentlyencounteredinimageprocessingincludenegation(grayscaleorcolor),gammacorrection,whichisapower-lawtransformation,andlinearornonlinearcontraststretching.
Lighter[image,...]
givealighterversionofanimage
Darker[image,...]
giveadarkerversionofanimage
ColorNegate[image]
givethenegativeofimage,inwhichallcolorshavebeennegated
ImageAdjust[image]
adjustthelevelsinimage,rescalingthemtocovertherange0to1
ImageApply[f,image]
applyftothelistofchannelvaluesforeachpixelinimage
Selectedpointoperators.
Oneofthesimplestexamplesofapointtransformationisnegation.Foragrayscaleimagef,thetransformationisdefinedby
g(i,j)=1-f(i,j).
Itisappliedtoeverypixelinthesourceimage.Inthecaseofmultichannelimages,thesametransformationisappliedtoeachcolorvalue,ofeverypixel.
Thisshowtheoriginalexampleimageanditsdigitalnegative.
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ThefunctionImageAdjustcanbeusedtoperformmostofthecommonlyneededcontraststretchingandpower-lawtransformations,whileImageApplyenablesyoutorealizeanydesiredpointtransformationwhatsoever.
Thisincreasescontrastusinglinearscaling.
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Asanexampleofanonlinearcontraststretchingoperation,considerthefollowingtransformationcalledsigmascaling.Assumingthedefaultrangeof0to1,thetransformationisdefinedby
.
Thisdefinesthetransformation.
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Hereareseveralplotsofthetransformationfordifferentvaluesofthevarianceparameter.
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Thisshowstheeffectofthetransformationonth
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