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Spline Histogram with Multi-Scale Transforms

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Spline Histogram with Multi-Scale Transformswith

    Spline Histogram with Multi-Scale

    Transforms

    V0L.24NO.1ACTAMETEOROLOGICASINICA

    TropicalCycloneCloudImageSegmentationbytheB.Spline

    HistogramwithMultiScaleTransforms

    ZHANGChangjiang''(张长江),WANGXiaodong(汪晓东),andDUANMUchunjiang(

    木春江)

    1StateKeyLaboratoryofSevereWeather,ChineseAcademyofMeteorologicalSciences,Beijin100081

    2CollegeofMathematicsPhysicsandInformationEngineering,ZhejiangNormalUniversity.nhua321004

    (ReceivedApril30,2008;revisedJuly23,2009)

    ABSTRACT

    Anefficienttropicalcyclone(TC)cloudimagesegmentationmethodisproposedbycombiningthe

    curvelettransform,thecubicB

    Splinecurve,andthecontinuouswavelettransform.Inordertoenhancethe globalandlocalcontrastoftheoriginalTCcloudimage,asecond

    generationdiscretecurvelettransform

    isimplementedfortheoriginalTCcloudimage.Basedonourpriorworkthelowfrequencycomponents

    areenhancedbyusinganincompleteBetatransformandthegeneticalgorithminthecurveletdomain.

    ThentheenhancedTCcloudimageisusedtosegmentthemainbodyoftheTCfromtheTCcloudimage.

    First,preprocessingisimplementedbyB

    SplinecurvestotheoriginalTCcloudimagetoremoveunrelated

    smallcloudmasses.Aregionofinterest(ROI)whichincludesthemainbodyofTCcanthusbeobtained.

    Second,thegray-levelhistogramofROIisobtained.Inordertoreduceoscillationsofthehislogram.the

    graylevelhistogramissmoothedbycubicBSplinecurvesandtheB

    Splinehistogramisobtained.Theone

    dimensionalcontinuouswavelettransformisemployedforthecurvaturecurveoftheB

    Splinehistogram.

    Anewsegmentationcostcriterionisgivenbycombiningthreshold,error,andstructuresimilarity.The

    optimallysegmentedimagecanbeobtainedbythecriterioninthecontinuouswaveletdomain.

    Theoptimally

    segmentedimageispost-processedtoobtainthefinalsegmentedTCimage.Theexperimentalresultsshow

    thatthemainbodyofTCcanbeeffectivelysegmentedfromthecomplexbackgroundintheTCcloudimage

    bytheproposedalgorithm.

    Keywords:tropicalcyclonecloudimage,segmentation,B

    Splines,curvelettransform,continuouswavelet

    transforii1

    Citation:ZhangChangjiang,WangXiaodong,andDuanmuChunjiang,2010:Tropicalcyclonecloudimage

    segmentationbytheBSplinehistogramwithmulti

    scaletransforms.ActaMeteor.Sinica,

    24(1),7894.

    1.Introduction

    Withtheimprovementintimeandspatialreso

    lutionsofsatellite,thesatellitecloudimagehasbe

comeanimportanttoolformonitoringtropicalcy

    clones(TCs).TheTCcloudimagesegmentationisan importantissuebutisalsoadifficultone.Acomplete TCcloudmassincludesallkindsofclouds.TheTC cloudmassincludesdifferenttypesofcloudsindiffer

    entdevelopingphases.Therefore,itisverydifficult touseaproperstatisticmethodtoprocessallkinds ofclouds.Currently,nogeneralalgorithmsuitablefor allapplicationsisfound.Ingeneral,differentsegmen

    2010

    tationapproachesareusedtosegmentdifferentkinds ofimages.Inthispaper,weaimtosegmentthemain cloudseriesfromaTCcloudimage.

    Manyresearchershavedonelotsofgoodworkin thisarea.Someresearchershavecarriedoutstudiesto segmentasatelliteimagebyusingshape(Chehdiand Liao,1993;Waldemarketa1.,2000),colour,texture orregioninformation(Shaneta1.,1993;Tateyamaet a1.,2002).Someresearchershavecarriedoutstudies tosegmentasatelliteimagebyusingmathematical morphology(Tateyamaeta1.,2004;Liueta1.,2001, 2004;Wangeta1.,2001;Liueta1.,1997;Lopezeta1., 2004;Intajageta1.,2006).Manyresearchersusedthe SupportedbytheNationalNaturalScienceFoundationofChina(408050481,ZhejiangProvi

    ncialNatura1ScienceFoundation

    (Y506203),ShanghaiTyphoonInstitute/ChinaMeteorologicalAdministration(2008ST01

    ),theStateKeyLaboratoryofSevere

    Weather/ChineseAcademyofMeteorologicalSciences(2008LASW

    B03),andtheResearchFoundationofStateKeyLaboratory ofRemoteSensingSciencejointlysponsoredbytheInstituteofRemoteSensingApplications

ofChineseAcademyofSciencesand

    BeijingNormalUniversity(2O09KFJJ013). Correspondingauthor:zcj74922@zjnu.edu.ca. No.1ZHANGChangjiang,WANGXiaodongandDUANMUChunj'iang clusteringalgorithmtosegmentasatelliteimage fXueeta1.,2006;BaraldiandParmiggiani,1998; Thitimashima,2000;OoiandLira,2006;Rekiketa1., 20061.Someotherresearchershavesegmentedasatel

    liteimagebyusingtheartificialintelligentalgorithm (VannoorenbergheandFlouzat,2006;Yeeta1.,2006; NeagoeandFratila,1999;Shieta1.,2001).Mostof theaboveworksareengagedinhighresolutionsatel

    liteimages.SegmentationofTCcloudimageisvery importantinweatherforecasting,however,relevantre

    searchinthisrespectislittle(Liueta1.,2004;Wanget a1.,2001;Liueta1.,1997;Lopezeta1.,2004;Baraldi andParmiggiani,1998).Mostofthesegmentation methodsforTCcloudimagesarebasedonintensity ortextureofsatellitecloudimages,withoutconsider

    ingtheradianinformationoftheTC.Therefore,this mayresultininaccuratesegmentationforsomeTC cloudimages.

    Recently,themultiscalegeometryanalysis

    (MGA)methodhasbeenwidelyusedinimagepro- cessing.Discretecurvelettransformisanefficient MGAmethod(Jeaneta1.,2002).Ithasmanyadvan

    tagescomparedwiththewavelettransform.Forexam

    ple,ithasbetterdirectionalproperties.Thismethod hasbeenusedwidelyinimagedenoising,enhance

    ment,segmentation,fusion,andCompression(Long

eta1..2005).itisdividedintotwocategories:first

    generationcurvelettransformandsecondgeneration

    curvelettransform.Thecomputationburdenofthe secondgenerationcurvelettransformislessthanthat ofthefirstgeneration.

    Inthispaper,weusethesecondgenerationdis

    cretecurvelettransform,anincompleteBetatrans

    form,andthegeneticalgorithm(GA)toenhancethe globalandlocalcontrastofanoriginalTCcloudim

    age.Theenhancedimageisusedtosegmentthemain bodyoftheTC.Preprocessingisdonetotheorig

    inalTCcloudimagetogetridofunrelatedsmall cloudmasses.Weusetheonedimensionalcontin

    uouswavelettransform(CWT)andcubicBSpline

    curvestosegmentthepre?processedTCcloudimage. Firstly,aBSplinecurveisusedtosmooththeos

    cillationsoforiginalgraylevelhistogramandtheB

    Splinehistogramisobtained.Thecurvaturecurveof theB??Splinehistogramisdecomposedwiththeone.. dimensionalCWT.Secondly,basedonourpriorwork 79

    (Zhangeta1.,2007a),anoptimallysegmentedTC cloudimageisobtained.Anewcostcriterionispro

    posedbycombiningJungcriterion(Changeta1.,1997) withstructuresimilarity(Wangeta1.,2004)tode- terminetheoptimalsegmentationscaleintheCWT domain.Postprocessingisimplementedtotheopti

    mallysegmentedTCcloudimagetoobtainthefinal segmentedTCcloudimage.

2.PreprocessingforTCcloudimage

    TheoriginalTCcloudimagemaybefuzzyorof badcontrastforvariousreasons.Itisnecessaryto enhancethecontrastofTCcloudimageinorderto efficientlysegmentthemainbodyofTCfromasatel

    litecloudimage.Basedonourpriorwork(Zhanget a1.,2007a),thediscretecurvelettransform,theincom- pleteBetatransform,andtheGAareusedtoenhance theglobalcontrastoftheTCcloudimage.Letthe enhancedTCcloudimagebeG(Zhangeta1.,2007a). MedianfilterisusedtosuppressthenoiseintheTC cloudimage,thusafilteredimageMisobtained.Let FshowtheoriginalTCcloudimage.Inordertoen

    hancethelowfrequencycomponentsoftheTCcloud image.anewTCcloudimageLcanbeobtainedas folows:

    (,Y):G(x,Y)F(x,Y)f1)

    Similarly,inordertoenhancethehighfrequency componentsoftheTCcloudimage,anothernewTC cloudimageHcanbeobtainedasfollows:

    H(x,Y)=a(x,Y)M(x,)

    Therefore,anultimateenhancedTCcloudimage Hcanbeobtainedby

    U(x,Y)=aL(x,Y)+M(x,Y)+(,),

    where=1,2,3,,;=1,2,3,,R.Vari-

    blesCandRrespectivelyrepresentthecolumnsand rowsoftheTCcloudimage.andareconstants whichcontroltheenhancedextentforlowandhigh frequencycomponentsoftheTCcloudimage.Here weset0==1.

80

    3.TheB-Splinehistogram

    ACIMETE0RoL0GICASINICA

    Beziercurveisakindofparameterscurvebased onapproximation,whichwasconstructedbyBezier inFrenchin1962(Sun,1998).Beziercurvehasbeen usedtosmooththehistogramofsatellitecloudim. ageinourpriorresearch(Zhangeta1.,2007a).Bezier curvehasmanyadvantages.However,ithastwoshort. comings:(1)RankofBeziercurveisdeterminedby thenumbernofverticesofcharacteristicpolygon. Theabilitythatthecharacteristicpolygoncontrolsthe Beziercurvewillbecomeweakwhenislarge.f2)

    LocalmodificationcannotbeimplementedinBezier curve,i.e.,thewholecurvewillbeinfluencedifposi

    tionofonecontrolknobischanged.In1972,Gordon expandedtheBeziercurve.BSplinefunctionwasused

    toreplaceBernsteinfunction.BSplinecurvecanim

    provethedefectsoftheBeziercurve.W_euseeven B?-Splinefunctiontosmooththehistogramofthepre.

    processedTCcloudimages.ReferringtotheBezier curveequation,BSplinecurvewhichhasn+1con-

    trolknots(i=0,1,,)canbewrittenby

    ()=??i,(),i=0

    VoL.24

    functionofthecubicBSplinecurvecanbewrittenby

    Ni,3("):[?1,3(u)N2,3(u)N3,3()N4,3()](7)

    where

    N1,3(u):

    N2,3(u)=

N3,3()=

    N4,3(u)=

    (1/6)(u.+3u3u+1),

    (1/6)(3u.6u+4),

    (1/6)(3u.+3u.+3u+1), (1/6)(u.),0??1.

    (8)

    (9)

    (10)

    (11)

    ThusthebasefunctionofthecubicBSplinecan bewrittenbythefollowingmatrix:

    

    (12)

    TwoneighboringcubicBSplinecurvescanbe

    writtenby

    Ci,3(u)=N1,3(u)只一1+?2,3()

    +?3,3()+1+N4,3()+2,

    Ci+l,

    3()=N1,3()+N2,3()+1

    +N3,3()+2+N4,3(u)Pi+3. (13)

    (14)

    where,()isthebasefunction,anditcaD.bedeTherefore,ithcubicB

    SplinecurveCaD.bewritten finedas

    +

    .o(U)=

    ,k(u)=t

i+k——ti

    (+1)V+1,l(U)

    ti+k+l——ti+l

    (??tn+1)(6)

    wheretiistheknotvalue.and'= ft0,1,,tL+2k+1](L=nk)formstheknotvector ofthekthorderBSplinefunction.Equation(6)isthe evenBSplinefunctionwhenti+lti=constant.We havetousethediscretematrixformoftheBSpline

    curvetosmooththehistogramofTCcloudimages.

    HereweusecubicBSplinecurvetocompletethe task.ApieceofcubicBSplinecurvecanbeobtained byextractingneighboringfourknotseverytimefrom

    n+1contr51knots(i=0,1,,n).Thebase

    4

    c()=?,3()2.

    J=1

    (15)

    Thematrixform,correspondingtoEq.(15),can

    beexpressedas

    i,3():(1/6)[u..1]

    

    1

    3

    

    3

    1

    3

    

    6

0

    4

    3

    3

    3

    1

    1

    0

    0

    0

    wherei=1,2,,n-2.Directsplineinterpolationof noisyhistogramofthepreprocessedTCcloudimage

    mayresultinacurvewithunwantedoscillations.This isparticularlybadbecausethecurvatureofthecurve isimportanttodeterminethesegmentationthresh- olds.Abetterapproachistoreducethedegreesof 1???????J

    l000

    NO.1ZHANGChangjiang,WANGXiaodongandDUANMUChunjiang freedomforthesplineandusethemethodofleast squarestofitthesplinetothenoisyhistogram(Hans, 1998).Thedegreesoffreedomareconnectedtothe numberofbreaks(knots).Splineinterpolationuses alldatapointsasbreaks,whilesplinefittingusesa lowernumberofbreaks.Thesmoothingeffectiscon

    trolledbythebreaks.Breaksareselectedindepen- dentlyofdatapointsorasasubsetofdatapoints. DetailsaboutthefittingsplinecanbefoundinHans (1998).

    Lettheoriginalthermalimagebequantifiedinto

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