13-BasicImageOperations

YongXu(許勇)

SchoolofComputerScience&Engineering2ContentHistogramsPointoperators（點運算）Imagenoise（圖像噪聲）Groupoperations（群運算）Individualbrightnesslevels’(亮度級)occupanciesTheimagecontrastTherangeofbrightnesslevels

Howtomaketheimageclearer?3HistogramsAdvantageSimple,quick,somewhateffectiveDisadvantageCannotdescribespatialinformationCannotdescribetheimagedetails4HistogramsTwocompletelydifferentimagewhichhavesimilarhistograms5PyramidHistogram6PyramidHistogram7DistinguishableSimilarDifferentDifferentInvariant？UseafunctionThepointatthesameplaceintheoriginalimageMathematicalfunctionBasicpointoperations（基本點運算）BecomputedfromtheimageitselfHistogramnormalization（直方圖正規化）Histogramequalization（直方圖均衡化）Histogramspecification（直方圖匹配）Thresholding（閾值處理）9PointOperatorsAlinearbrightnessrelation

k:gain(增益)，l:level(偏移量)

10BasicPointOperationsk=1.2l=10Originalimage11BasicPointOperationsk,l?12BasicPointOperationsk=1,l=0k=-1,l=255k=1,l=35k=1.1,l=-1013BasicPointOperationsThesawtoothoperator（鋸齒算子）AnalternativeformofthelinearoperatorEmphasizelocalcontrastchange14BasicPointOperationsy=xmod50y=xmod100y=xmod90y=xmod80y=xmod70y=xmod6015TheSawtoothOperatory=(xmod50)*255/49y=(xmod60)*255/59y=(xmod70)*255/69y=(xmod80)*255/79y=(xmod90)*255/89y=(xmod100)*255/9916TheSawtoothOperatorOriginalimagemod50mod60mod7017TheSawtoothOperatorOriginalimagemod80mod90mod100ArithmeticfunctionsLogarithm

Darker,asmallrangeofbrightnesslevels18BasicpointoperationsOriginalpictureLogarithm25log(50f(x,y))log(50f(x,y))log(f(x,y))LogarithmLogarithm19BasicPointOperationsExponent30exp(f(x,y)/100)OriginalpictureArithmeticfunctionsExponentBrighter,greatercontrastexp(f(x,y)/100)exp(f(x,y))ExponentExponentStretchandshifttheoriginalhistogramCoverallthe256availablelevels20HistogramNormalizationOriginalimageNormalizedimage21HistogramNormalizationOriginalimageNormalizationimageAnonlinearprocessandirreversibleProduceapicturewithaflatterhistogramAlllevelsareequiprobableThemappingfunctionContinuous22HistogramEqualization

ThemappingfunctionDiscrete23HistogramEqualization1399821373360646820529260

h0312243441516471829300.1210.0820.1630.1640.0450.0460.1670.0480.0890.12

f

p(i)00.1210.2020.3630.5240.5650.6060.7670.8080.8891.00

s(i)OriginalimageHistogram2400.1210.2020.3630.5240.5650.6060.7670.8080.8891.001399821373360646820529260511332552552249251133204133133194019414319422492015392255921940

f

gHistogramEqualization

s(i)

255s(i)round

numbers25HistogramEqualizationOriginalimageEqualizedimage26HistogramEqualizationOriginalimageEqualizationimage27HistogramEqualization28HistogramEqualizationNormalizationEqualization29HistogramEqualizationOriginalimageNormalization

Equalization30HistogramEqualizationOriginalimageNormalization

Equalization31HistogramEqualizationOriginalimageNormalization

Equalization32HistogramEqualizationOriginalimageNormalization

Equalization33HistogramEqualizationOriginalimageNormalization

Equalization34HistogramEqualizationOriginalimageNormalization

EqualizationForthecolorimageDohistogramnormalizationineachchannelDohistogramequalizationineachchannel35HistogramEqualizationChannel1Channel2Channel3OriginalimageNormalization

EqualizationHistogramnormalizationAlinearprocessandreversibleHistogramequalizationAnonlinearprocessandirreversible36HistogramEqualizationTheconvertedimagehasaparticularhistogram.ContinuousDiscrete37HistogramSpecificationOriginal->equalizeDesired->equalizeFinalOriginal->equalizeDesired->equalizeFinal38HistogramSpecificationDesiredequalizeequalizegg-1OriginalFinalminimal39HistogramSpecificationxipx(i)f00.190.1910.250.4420.210.6530.160.8140.080.8950.060.9560.030.9870.021.00gpz(i)zi0.000.0000.000.0010.000.0020.150.1530.350.2040.650.3050.850.2061.000.157zipz(i)00.0010.0020.0030.1940.2550.2160.2470.11Selectspixels

AparticularvalueAspecifiedrangeUniformthresholding（均一閾值處理）Requireknowledgeofthegraylevel

40ThresholdingOriginalimageT=160OriginalimageT=125Adaptivethresholding（自適應閾值處理）Otsu’smethodMaxthefollowingvaluewhere41ThresholdingContrast42ThresholdingOriginalimageT=160OstuT=127OstuT=117T=125OriginalimageRandomvariationofbrightnessorcolorinformationElectronicnoiseAddspuriousandextraneousinformationProduceThesensor

Circuitryofa

scanner

or

digitalcamera…TypesGaussiannoise（高斯噪聲）Saltandpeppernoise（椒鹽噪聲）43ImageNoisePrincipalsourcesSensornoisePoorilluminationHightemperatureElectroniccircuitnoiseNoiseIndependentateachpixelIndependentofthesignalintensityGaussian-distributed44GaussianNoiseg(x,y,i)=f(x,y,i)+noisef(x,y,i)eachpixelineachchanneloftheoriginalimagex,y:location,i:channelg(x,y,i):eachpixelineachchanneloftheGaussiannoiseimagex,y:location,i:channel

Noise

obeys

a

Gaussian

distributionG(μ,σ)45GaussianNoiseImageGaussiannoiseOriginalimageG(0,1)PrincipalsourcesAnalog-to-digitalconvertererrorsBiterrorsintransmissionNoiseSaltnoiseNoisepoints’valuesare255.PeppernoiseNoisepoints’valuesare0.RandomThenoisedensityisaconstant.46SaltandPepperNoiseIneverychanneloftheoriginalimage

Randomchangesomepixels’values(set0or255)Letthenoisedensityisaconstant47SaltandPepperNoiseImageSaltandpeppernoiseOriginalimageNoisedensity=0.05Useapixel’sneighborhoodTemplateconvolution（模板卷積）Averagingoperator（平均算子）Gaussianaveraging（高斯平均）Medianfilter（中值濾波）Modefilter（眾數濾波）ComparisonofstatisticaloperatorsMathematicalmorphology（數學形態學）48GroupOperationsTemplate--asetofweightingcoefficientsPlacethetemplateatthepointofinterest

Theconvolutionnotation49TemplateConvolutionThetemplateweightingfunctionsareunityAdvantageReducenoiseDisadvantageCauseblurringReducedetail50AveragingOperatorOndifferenttemplatesizeTemplatesareusuallyofodddimension.LargeraveragingoperatorsSmooththeimagemoreRemovemoredetail

51AveragingOperator52AveragingOperator3×35×57×7GaussiannoiseSaltandpeppernoiseOriginalimage53AveragingOperatorOriginalimage3×35×57×7ThresholdingT=10054GaussianAveragingOperatorCalculatecoefficients

Templateforthe5×5Gaussianaveragingoperator(σ=1.0).55GaussianAveragingOperator3×35×57×7GaussiannoiseSaltandpeppernoiseOriginalimageTheGaussianfiltervs.directaveragingMorefeaturesareretainedwhilethenoiseisremoved.56GaussianAveragingOperatorAveragingoperatorGaussianaveragingoperator57GaussianAveragingOperator3×35×57×7GaussiannoiseOriginalimageAveragingoperatorGaussianaveragingoperator58GaussianAveragingOperator3×35×57×7OriginalimageAveragingoperatorGaussianaveragingoperatorSaltandpeppernoise

Alternativetemplateshapes59MedianFilterCrossHorizontallineVerticallineAbilitiesRemovesaltandpeppernoiseRetainedges60MedianFilter61MedianFilterGaussiannoiseSaltandpeppernoiseOriginalimage3×35×57×7Findthebackground62MedianFilter--Application

Averaging(g)

select

middle

value

ofimage1~image6Usethemostfrequentlyoccurringpixelvalue63ModeFilter01221481773150115812191Pixels’frequency77487715877219221500774877777721922150001221481773150115812191Theorderofthemean,themedian,andthemode64ModeFilter774851158170219221500Whatshouldwedo？Thetruncatedmedianfilter（截斷中值濾波）IfthemedianislessthanthemeanIfthemedianisgreaterthanthemean65TruncatedMedianFilters=median–min,upper=median+supperminmedianmeanmaxupperminmedianmeanmaxtruncateupperminmedianmeanminmedianmeanmaxupperminmedianmeanmodeThemedianoftheremainingdistributionapproachesthemode.s=max–median,lower=median-smaxmedianmeanminmaxlowermedianmeanminmaxlowermedianmeanmintruncatemaxlowermedianmeanmaxlowermedianmeanmodeThemedianoftheremainingdistributionapproachesthemode.CharacteristicsRemovesaltandpeppernoiseRetainfeatureboundariesExperience66TruncatedMedianFilter67TruncatedMedianFilterGaussiannoiseSaltandpeppernoiseOriginalimage3×35×57×7AveragingoperatorRemovemuchnoisebutblurfeatureboundariesG