计算机视觉课件2（英文版）

Course2 ImageFilteringCourse2 ImageFiltering

Imagefilteringisoftenrequiredprioranyothervisionprocessestoremoveimagenoise,overcomeimagecorruptionandchangedistributioninanimage. ——linearfilter ——nonlinearfilter1.Linearsystemdeltafunctionimpulseresponse

Continuouscase: Discretecase:LinearSpaceInvariantSystemLSIh(x,y)inputf(x,y)outputg(x,y)

——convolution(卷积)Fordiscretecase:InFourierdomain:

then:2.MeanFilter——averageintensityvaluesoftheneighborpixelsatapixel.e.g.windowneighbors.where 111111111Thelargerwindowsize,theefficientinreducingnoise,butthemoreblurringoriginalimage(loseimagedetails)——youmustmakeatrade-off!Toreducewindowsboundaryeffectandforasmoothfiltering,filterelementsareoftenweighted.

MeanFilteronGaussiannoisecorruptedimage3.GaussianFilter:impulseresponseofGaussianfilter:——linearsystem——rotationalsymmetric——FourierTransformationisstillaGaussianFor1-Dcase:ItisstillaGaussian!——SeparatibilityItcaneasilybeseenhattheGaussiancorecanbeseparatedinbothspacedomainandFourierdomain,i.e.So,InFourierDomain,——Cascadingoperation:LetIfaGaussianfilterhasalargeparameter,itrequiresalargeoperationmaskandthus,itwilltakelongtimetoprocess.

WecanseparatethelargeGaussianofintotwosmallerGaussianfiltersofparameterandperformthefilteringprocessesincascade.4.DiscreteGuassianFilter

WherewindowsizeToformaGaussianFilter:(1)

ChooseapropersizeNofmaskwindow.(2)

Calculatethevalueofeachmaskelement.

e.g.(3)

Scaleallmaskelementstointegerwiththesamescalingfactor.Scale(4)findthenormalizingfactorkTherefore,foraninputimageoutputofGaussiansmoothis:Bytheway,Atwo-dimenssionalGaussianfiltercanbeextendedbytwoone–dimentionalGaussian (how?Homework).

5.MedianFilter(nonlinear)------Veryefficienttoremovesalt-and–peppernoise.Inawindowofoffiltermask,ordertheintensityvalueofpoints.set(2)Settheimagepixelwithintensity………………………………759936384910199822

Forexample,

Othernonlinearfilters:——minimumfilter(removesaltnoise):——maximumfilter(removepeppernoise)——Midpointfilter(removeGaussiannoiseanduniformnoise)Medianfilteronsalt-and-peppernoisecorruptedimageMinimumfilteronsaltnoisecorruptedimageMorphologicalFiltersReviewof“set〞:Intersection:Union:Complement:Translation:whereareposition,andisavectoroperation.

AB(2)Dilation:givenanimageandstructuringelementdilatation

ofAbyBisdefinedas Dilatationoperationtendstoinflatetheoriginalimage.(3)Erosion:ErosionofAbyBisdefinedbyallpixelthatmakesinsidetheimageA,i.e.or,equivalentlyErosionoperationintendstoshrinkoriginalimage.

Opening:

Openoperationtoanimageiserosionfollowedbydilationwiththesamestructuringelement.Itwillremovetheimageregionsthatatoosmalltocontainthestructuringelement,leavingtheresultedimageapproximatelyunchanged.Closing:

Closingoperationtoanimageisdilationfollowedbyerosion.Itwillfillinholesandconcavitiessmallerthanstructuringelement,leavingtheresultedimageapproximatelyunchanged.6.HistogramModification(ImageEnhancement)Uniformintensitydistributionofanimagecanfithumaninterpretationoftheimage,italsomeetstherequirementsofsomeimageoperations,suchasimagethresholding.

originalintensitydistributionuniformintensitydistributionLetoriginalimagehasintensityandwithprobability.Thetransformedimagehasintensitywithprobability.Then,thetransformationwillmakesresultantimagehaveuniformintensitydistribution,i.e.Prove:Fordiscretecase,lettheoriginalimagehasintensityisthenumberofpixelsatlevelinitshistogram,wewanttomaptheimagetoanewonewiththesameofnumberofintensitylevelbutdifferenthistogram,wherethehistogramispre-designed(e.g.,uniform):findaintensitylevelK,whichthat:

then,mappixelsoflevels