形态插值方法应用于图像重构_英文_

1、第25卷第4期中南民族大学学报(自然科学版)Vol.25No.4MorphologicalInterpolationAppliedinImageDuan(CollegeofComputerScience,th2,Wuhan430074)Abstractmaticalmorphologyisanewresearchfield.Thepresentinves2tigationpmtoandimprovetheinterpolatingtechniquebasedongeodesicdistancefunction.Thismethodcoulddealwithbinaryiandthemomedi

2、ansetsbetweentwobinarysetsmages,grayim2ages,colorimages,andmulti2spectralimagescombinewiththetechniqueofmorphologicaltransform,whichin2.Themorphologicalinterpolationalgorithmusedinicreasedthemethodseffectivenessmagepartitionsequencewasproposed,itcouldbesuccessfullyappliedtoimagereconstructionforvari

3、esimage.Keywordsmorphologicalinterpolation;imagereconstruction;morphologicaloperator中图分类号TP751文献标识码A文章编号167224321(2006)0420087205形态插值方法应用于图像重构段汕(中南民族大学计算机科学学院,武汉430074)摘要指出了基于数学形态学的形态插值方法是一项新的研究领域,提出了一种改进二值图像测地距离函数和形态中集函数的方法,并在此基础上建立了一种适用于灰值图像、彩色图像及多光谱图像的形态插值变换.应用插值变换于图像分割序列重构的实验结果表明:该方法可以成功地运用于对各种类

4、型的图像进行有效地插值重构和图像形变.关键词形态插值;图像重构;形态变换DuanShanPhD,Prof,CollegeofComputerScience,SCUFN,Wuhan430074,China.Theprofileandthetextureofhomogeneouszones1IntroductionInthefieldofimageprocessing,imageinter2polationisanimportantcontentandnecessary.Thewaytoobtainhighcompressionratesfortoolimageisaninterestedaimt

5、ogoinfor.Whenusingobject2basedimagecoding,partitionsequencesofimageareproduced.Theimageissegmentedintothefacetsarethencodedandtransmittedseparate2ly.Intheencoderside,demandsampletheimagesequencetechnically,andtransmitonlytheselect2edframes.So,whencodingappliestosequences,thenewimageofthesequenceared

6、eformedandshifted,andnewfacetsmayappear,othersdisap2pear.Inthedecoderside,non2selectedimagesarereconstructedonlyrelyingonthedecodedversion收稿日期2006209213作者简介段汕(19622),女,博士,教授,研究方向:图像处理和模式识别,E2mail:jy5699基金项目中南民族大学自然科学基金资助项目(YZY03005)(自然科学版)中南民族大学学报88第25卷5.Inordertovisualizetheofthetransmittedimagesim

7、age,thereceiverhastoreconstructtheimagese2quencesbasedonthedecodedsequences,andtore2.Onesolutionplacemissingimagesbysometoolswouldconsistininterpolatingmissingimagesfromtransmittedimage.Thepresentinvestigation,in2spiredbyMeyer,works123Inthispaper,thegeodesicsetZoftwosetsXandYismodifiedasthesetlinkXt

8、oYusingtheunionofstraightsegmentswithminimumlength.IfXY= ,thenXYbetweenthetwoobjectsZ;ifXY ,thenZ=XorZ=Y.Sotheal2gorithmcalculatestwointerpolationfunctionscanbedefineduniformlyforandYhavepty,s:(ZSerraandBeuchersbasic,whichconsistingincreationofinterme2diaryimagesbetweengivenoneshavebeendevel2opedsin

9、ce1996,proposesamethodtomodifyimprovetheinterpolatingbasedgeodesichomediansetstwsetsintroducesainterpolationcandealwithbinaryim2ages,grayimages,colorimages,andmulti2spec2tralimages,andalsodiscussanewalgorithmforpartitionimagesequencesinterpolation.,xZZ)+dZ X(x,5Z).(1)+,xZc,xZdZ(x,Y)+dZ Y(x,5Z).IntY(

10、x)=(2)+,xZcZXZYWhenXY ,thentheleftofformula(1)and(2)willbeInt(x)=Int(x),Int(x)=Int(x).XXYYXYTheinterpolatedsetsbetweenXandZ,andbetweenYandZ,canbeobtainedbyasinglethresholdbetween0and1:)=x:Int(x)Thr(Int)(,XXZZ2InterpolationbasedongeodesicdistancefunctionMorphologicalinterpolationisaprocessoftransform

11、ationofoneimageintoanotheroneusingthemathematicalmorphology.Itresultsinainter2polationsequence,shapeofwhichisturningfromtheinitialoneintothefinalone.Theinterpolatorbuildbythegeodesicdistanceisafunctionwhichproducestheinterpolatedobject.Therearediffer2entinterpolationlevel,denotedbyarealnumber(01),in

12、dicatesapositionoftheinterpolatedobjectintheinterpolationsequence.Theunderly2ingidea1)=x:Int(x)Thr(Int)(.YYZZ(3)Inthiscase,Thr(Int)(0)=X,Thr(Int)(0)=Y,XYThr(Int)(1)=Thr(Int)(1)=Z.XYTheseformulasshowthatwhenparameterin2)willstartfromcreasingfrom0to1,Thr(Int)(XXgrowandbecomeZ,andatthesametime,ZZZZZtot

13、ransformasetXintoasetYwhen)willstartfromZshrinkandbe2Thr(Int)(1-YcomeY.TheinterpolatedsetbetweenXandY(in2)willbedefinedasfollows:terpolationlevelwith()=IntsetX)Thr(Int)(1-),XY ,Thr(Int)(XYZXYZXYYZthereisanonemptyintersectionbetweenthem:XwillshrinkandbecomeXYandatthesametimeXYwillgrowandbecomeY.Thege

14、odesicsetisanimportantmethodtosolvethecaseofXY=.Thenotionofgeodesicdistanceisusedtobuildthealgorithm.ThegeodesicdistancebetweentwopointsxandyinsetA,denotedasdA(x,y)is4)Thr(Int)(1-),XY= .Thr(Int)(XY(4)definedtheminimumlengthofpathinsetA,whichjoinxandy.Thegeodesicdistancebetweenasinglepointxandacompac

15、tsetBA,denotedbydA(x,B),isdefinedas:dA(x,B)=yinfdA(x,y).B3Multi-valuesimageinterpolationMathematicalmorphologicalofferssomepow2第4期段汕:形态插值方法应用于图像重构89erfultoolsfortheimageinterpolation.WhensetsXandYwithnon2emptyintersection(XY ),theinterpolationsetbetweenXandYcanbe=(XY) (IntsetB)(XY) (B).X(5)Y3,5Umbra

16、M(f,g)=IZWUmbrainf(f,g).4WhereIZWistheSKIZofW=E2Umbrasup(f,g)Umbrainf(f,g).expressedbyfollowingequation:Usingthemethodofreconstructingimage4basedontheumbra,wecanformulatethemedi2Where Bisadilationofsizeand Brepre2,bothwiththeelementarysentsanerosionofsizestructuringelementB.Thisequationconstituforan

17、efficientalgorithmofmediancreati.ButwhenXY= ,ugeodesicset,thesetbetweenX=X (IntsetB)Z (B).XandtheinterpolatedsetbetweenYandZ:=Y (IntsetB)Z (B).YandYinthefollowingway:=IntsetIntset.IntsetXXYYZZZZanfunctionoffandginfollowingway:(k)()M(f,g)=supinf(inf(f,g)(sup(f,g).k(9)kintegervalues,()dilationanderosi

18、onofperformedwithnon2flatstructuringele2ment.Thenotionofmedianimagesforcolorimagesormulti2spectralimagescanbedefinedinthesame.Thedefinitionwayasinthecaseofgrayimagespresentedinformula(9)canbeappliedtoboth.Theonlydifferenceliesingrayandcolorimagesthesupremumandinfinimumoperatorsbecauseofthecolorimage

19、sarethevectorvaluesandmustfol2lowtherulesofvectorcomparison.Oneofthemostpopularwaysofvectordatacomparingisalexicographicordering.Thereducedorderingbasedonthemappingbetweentwovectorspacesisan2otherpopularandpracticalorderingstructure.Theexamplereferstocolormorphologicalin2terpolationoftwoimagesshowni

20、nFig1.Itshowsthatmorphologicalinterpolationimageisatotallynewimage,shapeofwhichishalfwaybetweenthe.Thecolorpixelsshapesofbothtwoinputobjectscomparisonswereperformedinreducedorderingofmulti2valuesimagespace.()(6)(7)WecanformulatetheinterpolatedsetbetweenX(8)Forthegrayimagefunctionsf(x)andg(x)definedi

21、nthespaceE,thenotionofmediansetofthemcanalsobeestablishedbyusingumbratheo2ry.Accordingtotheideaofcentermorphological4operator,themedianoff(x)andg(x)isafunc2tion,whichcanbededucedasfollow.Considertheumbrasetofinf(f,g)andsup(f,g),thesetoverthesup(f,g)canbeexpressedasE2Umbrasup(f,g),andthemedianfunctio

22、noffandg,de2noteasM(f,g),satisfythefollowingrelation:(a)(b)(c)(d)Fig1Interpolationimage(c)and(d)oftwoinputJPGimages(a)and(b)(自然科学版)中南民族大学学报90第25卷4InterpolationalgorithmImageinterpolationisnecessarytoreachhighcompressionratesincodingfield.Segmentationimageisthekeystepthatmakespossibletodevel2opsuchan

23、approachforsequenceinterpolation.Asresultofthesegmentationstep,imagesaresplitintoasetofregionsaccordingtothebasicimagecomponentsuchaspixelsandblocks,formapartitionimagesusingtotranscoded.thisimagep,totime,spframagermationareproducedinwhichbringthehightransmissionspeed.Forthetwocomponentsinthesequenc

24、e,thetaskweshoulddoistobuildingtheintermediatepartitionJk+1,Jk+p-1computedusingthefollowingrules:(s)(s-1),Lk(0)=inf(Jk,Jk+p),Lk=(LkHk(s)=(Hk(s-1),Hk(0)=sup(Jk,Jk+p)=Mk(0).Theinterpolationalgorithmdescribedahead,canbeusedforgrayimagesandmulti2valueim2ages,suchcolorimagesandmulti2spectralimages.Butjus

25、toneproblemmutionistheentsinmulti2acethegrayimages.isproblemthecomparativetroducedbyusinglexicographicordering,ormoreuniversally,byusingreducedorderingwillbeagoodscheme.Inthiscase,theinitialmulti2valuespaceneedtoconvertedtothecomparativeonebyusingnnconversionmatrix,wherenisthedimensionnumberofmulti2

26、valuesdataspace.Toillustratetheproposedinterpolationmeth2odsandthealgorithm,twoexamplesaregiven.FirstexampleispresentedofFig2.Itisacolorin2terpolationsequence,whichobtainedbyiterativealgorithmstatedinsection3,basedonFig1(c)and(d).Thecolorpixelscomparisonswereper2formedinreducedorderingofmulti2values

27、imagespace.ThesecondexampleisshowedinFig3,whichgivestwointerpolatedreconstructsequencesbasedontwodifferentinformationofsegmentation.imagesforthegivenparameterk,withnootherinputdatathanthetwoinitialpartitionsJkandJk+pinthesequence.Equation(9)canapplytoconstructtheitera2tivealgorithmofinterpolationmed

28、ianimagecalcu2lationfromJkandJk+p.untilMkIterationsareperformed(sk)(sk)=Mkk(sk+1)k,andfinallywegetreconstruct(s-1)sequenceM,Mk:(s)(s)(s)Mk=supinf(Lk,Hk),M,M(0)(1)k.Theindexesintoprightcornerrepresentthenum2berofiteration.Thes2thiterationvaluesarethenFig2Interpolationimagesequenceofimage(a)and(b)gene

29、ratedbycolormorphologicalinterpolation第4期段汕:形态插值方法应用于图像重构91(a)(b)(c)(e)(f)(g)(h)Fig3Interpolationreconstructimagesequencegeneratedusingmorphologicalmethod5ConclusionThemethodofmorphologicalinterpolationhasbeenpresented.Itcanbeusedforbinaryimage,grayimage,colorimageandmulti2spectralimage.Twointerpola

30、tionmethodsarepresentedaswellinthispaper,basedonthegeodesicdistancefunc2tionapproachandmorphologicalmedianapproach,respectively.Bothcanbeappliedtothegeneration.ofinterpolationsequencesbetweentwoimagesTheinterpolationsequencecontainsarealchangeintheshapeofobjectsonit,notonlythesimplemix2ingofbothimageslikethelinearimageinterpola2tionproduce.sequence.TheproposedmethodcanalsobeusedtoreconstructimagefromthepartitionimageInaddition,theresultsobtainedusingtheproposedmethodareinterestingalsofromtheartisticpointofview,becauseofthetransformationoftheshapelookmysterious.The