翻译以.原文和在同一文件中前于

基于经验模式分解（EMD）的弱小目标检测与算法。EMD引入由过筛的来分解原始图像变换成高频和低频分量的一个确定的数。与EMD算法相比，它是有效的估计关键字引检测和在低信号噪声比（SNR）未知位置和未知速度的弱小目标的是红外搜索的真实世界数据的SNR。在红外场景的背景显示的每个像素和其周围环境之间的空间相：数学形态学是图像处理和分析的一个重要的非线性方法。Hsiao等：结合空间相关性的随机背景模型可以用于提高在自然地形图像目标检测。自适小变换方的限，提供一个效算法小标测。识别数关联分和的行。和神经网络。在中，基于经验模式分解（EMD）的弱小目标检测算法。将原始图像分解成IMF分量（固有模态函数。结果发现，通过残余物产品估计背景，这是由EMD的算法提取有用的。我们可以通过从原始图像中除去背景检测弱小目标。此外，在张量积EMD的分解行为的研究表明其在计算成本方面的效率。本文的结构如下。在第二节，一维EMD描述。二维经验模式分解（BEMD）和弱小目标经验模式分由Huang等人EMD方法。在1998年，它可以分解成数据有限和有意义的固有集，的数量和过零点数目必须相等或相差最多者之一;（b）在任何情况下，由局个IMF并不局限于一个窄频带信号，它可以是幅度和频率调制。所以纯粹频率或幅度调制功能，可以通过的IMF为它们按照传统的定义具有有限的带宽。不幸的是，大部分的数据不是IMF分量。其中涉及多个振荡模式下的数据可以通过使用EMD分解成连续的IMF。凭借IMF分量，分解方法可以简单地使用当地的最大值和最小值分别定义了信封。一旦的标识，所有的局部极大值由三次样条线作为上包络线连接É（T。重复上述局部极小产生下包络ë（T。上和下包络线应该包括它们之间的所有数据。假设X（t）。的平均值被指定为米0（t）和信号之间的差×（t）和米0（T）是第一成分，ħ1（t）即，等式（2.1）和等式（2.2ħ0（T）=X（ （2.1ħ1（T）=H0（T）-M0（T。 （2.2）2.1（b）2.1（c）中所示。2.1（b）则上部和该信号的下包络线和它们的平均值。图2.1（c）所示的信号和局部均值如式之间的区别。次。在第二个筛分的过程中，ħ1（t）1（t）然后ħ2（t）H1（t）1（t）ħ2（t）2.2因此，我们重复这个过程筛选Ĵ次，得到ħĴ（T）的等式 2.3ħĴ（T）=HJ-1（T）-MJ-1（t） IMF1IMF（2.4）（T）=HĴ（ （2.4现在，描述的停止标准筛选过程。为了确保IMF分量保留振幅和频率调制的足 对于一个典型的价值SD0.20.3进行设定。也就是说，当SD满足2<SD03，在筛选过程停止。该标准已实际意思是：当停止条件满足时，ħĴ将满际金组织的标准，充分。也过筛的时间进行控制，并从原始信号的振幅的筛选过程，或不同于小于1，然后过筛过程停止。这个标准是用来通过HHT工具箱V1.0（Hilbert-Huang变换工具箱，专业版V1.0，普林斯顿系统，普林斯顿新泽西州，2000年。作为一个改进的SD标准，瑞霖等提出了前进3阈值标准。他们（T）（E（T）E（T）/2和σ（T）=|M（T）/A（T|m（t）EMDσ（T）θ1α的总时间和σ（t）θ2对剩余的部分。阈值的典型值α=005，θ1=00和θ210θ1由于残基，R1（t）subsequentsŘĴ（t）其结果是方程（2.6：ř2（T）=R1（T）-IMF2（T），...，RÑ（T）=RN-1（T）-IMF（T 取。通过总结筛选过程上面我们最终得到等式（2.7）因此，我们在数据导入的分解得出Ñ经验的模式，以及残基，RÑ（t）量图2.3。原始数据是合并有许多局部极值，并分解成六个部分。虽然EMD算法已收到显著重视，近年来，理论基础还没有完全建立起来。大多数基本的数学问题仍然没有得到处理。最近，有理论研究，试图了解为什么了EMD算法的工作。矩阵ASS。这里的平均包络是上部和们从点的位置是不变的一步EMD。然后如下的筛选算法可以改写：（一）S0=S=X给定的阈值τI=1（四）S=SI-1-ASI-1（五）如果∥ASI-1∥小于给定的阈值τ，终止算法;否则，I=I+ 并转（B由于信封矩阵的本征值都在[0,1]，我们得出这样的结论矩阵序列是收敛的。因此，序列S是收敛的BEMD弱小目标检测与在本节中，基于EMD的弱小目标检测算法。金组织的希尔伯特谱和残留分析显F（XY）mn图像，并且升EMD让řKĶ=F（XY），K=0R=1（一）fř=F（R1N）ř行的图像，这是一个信号。计算第一国际货币IMF（ř）fŘ。（二）让řķ（R，1：N）=RK（R，1：N）-国际金组（ř）řMR=R+1，然后转到（二（一）;否则转到（三C=1（三）fÇ=RK（1MC）Ç图像，这是一个信号列。计算第一国际货IMF（FÇ）fÇ。（四）让řK（1：M，C）=RK（1：M，C）-国际金织（FÇ）ÇNC=C+1，然后转到（三）（c）（四K=K+1，IMFķ（XY）=RK-1，[Rķ=IK-1Rk-1K= K如果ĶL，去（二）;否则算法结束。为方程（3.1： IMFķ（XY）IMFř（XY）是残留物中。为了从所示的红外图像中提取弱小目标图3.1，根据我们的实验中，背景的良好估计是实现L=43.2（a）（d）3.33.2（a）1（XY），其中包含其中包含的背景信息。自然，R4（XY）的灰度值是相当的，这意味着它可能包含目标的信息较少。HHT3.（aIMF43.4（a）中，很容易看BEMD织4超过行。傅里叶变换的关注与沿可变的整个范围所采取的信号的频谱。它不能呈现的信号的时间-频率特性。我们知道国际金组织包含目标的特息。所以包含足够的背景信息，没有的分解需要。随着BEMD图像被分解成固有模态函数和残留ř4（XY。固有模态函数表示的目噪声的去除新形象R4（XY）从原始图像。通过选择新的图像作为阈值的最大灰度感。完整的算法是由两个独立的部分：检测部和部分。（一）背景重建。当前帧分解成固有模态函数和残留ř4（XY）它表示一个（二）背景消除。我们通过消除获得与目标和噪音的新形象ř4（XY）（三）III（A）为实验结（4.1）其中（X，Y）是像素的坐标，F（X，Y）和代表的灰度值（XY）mnf是图像的最确的对象被移除的算法将作的更好。据称较高PNSR数字来指示的平方差更好的性能f和较小。结ContentslistsavailableatSignalProcessing:ImageContentslistsavailableatSignalProcessing:Image Dimtargetdetectionandtrackingbasedonempirical HongLia,ShaohuaXua,LuoqingLiDepartmentofMathematics,HuazhongUniversityofScienceandTechnology,WuhanFacultyofMathematicsandComputerScience,HubeiUniversity,WuhanarticleinfArticleReceived8June2007Receivedinrevisedform8October2008Accepted8October:TargetdetectionandtrackingEmpiricalmode IntrinsicmodefunctionMathematicalmorphologyHilberttransform

abstracDimtargetdetectionandtrackingalgorithmbasedontheempiricalmode tion(EMD)isproposed.EMDisintroducedto posetheoriginalimageintoadefinitenumberofhighfrequencyandlowfrequencycomponentsbymeansofsifting.WiththeEMDalgorithm,itisvalidtoestimatethebackgroundandgetthedimtargetbyremovingthebackgroundfromtheoriginalimage.Thealgorithmdetectsdimmovingtargeteffectivelyandestimateitstrajectoryaccuray.Thedataysisandexperimentsshowthattheproposedalgorithmisadaptabletorealtimetargetdetectionandtracking.&2008ElsevierB.V.AllrightsDetectionandtrackingofdimtargetofunknownpositionandunknownvelocityatlowsignalnoiseratio(SNR)isanimportantissueininfraredsearchingandtrackingsystem.Whentheinfraredsensorisnotinthedirectcontactwiththetarget,thetargetisimmersedinaheavyclutteredbackground.Duetotheexistenceofatemperaturefield,targetedgesareblurredandcannotbeaccuraydefined.Wecannotgetfeatureinformationabouttheinteriordetailsofatarget.Furthermore,aeroopticdisturbancesandairturbulencemaketheSNRofasingleinfraredimageverylowonrealworlddata.Thebackgroundininfraredsceneshowsspatialcorrelationbetweeneachpixelanditssurroundings.Becauseoftheeffectsofinherentsensornoiseandthephenomenaofnaturethereexistsomehighgrayregionsintheinfraredimageascomplicatedcloudedgeandirregularsunlitspot.Alloftheabovemakethetargetdifficulttodetectandtrack.However,aninfraredimagedescribesthedistribu*Corresponding .:+86 E-mail (L.

tionofheatradiationfromatargetanditsbackgroundandtheinfraredradianceofdimpointtargetisirrelevanttothesurrounding.Generallywesupposethatthetargetiseitherdarkerorbrighterthanitsimmediateadjacentbackground.Thus,dimtargetscanberegardedassingularpointsintheinfraredimage.Thethermalimagesareobtainedbysensingtheradiationintheinfraredspectrum,whichiseitheremittedorreflectedbytheobjectinthescene.Duetothisproperty,infraredimagescanprovideinformationwhichisnotavailableinvisualimages.However,incontrasttovisualimages,theimagesobtainedfromaninfraredsensorhaveextremelylowSNR,whichresultsinlimitedinformationforperformingdetectionortrackingtasks.To ethe imposedifferentconstraintstoprovidesolutionsforalimitednumberofsituations[30].Therearetwobasictargetdetectionandtrackingapproaches:detectbeforetrack(DBT)andtrackbeforedetect(TBD)methods[2].DBTalgorithmsusuallyexhibitpoorperformancewhentheSNRislowandTBDalgorithmsareoftenextremelysensitivetobackgroundornoise.Inaddition,DBTandTBDalgorithmsusuallyassumebackgroundclutterandnoisefollowGaussiandistributions,whereasthisdoesnot0923-5965/$-seefrontmatter&2008ElsevierB.V.AllrightsH.Lietal./SignalProcessing:ImageCommunication23(2008) tomostrealsituation.Ourmainconcernisdeveloaworkingalgorithm,whichtakesintoaccountdetectingthedimtargetfasterandstillhasbetterperformance.Wedescribethedimmovingpointtargettrackingininfraredimagesequence.WepresentapowerfuldetectionandtrackingalgorithmforlowSNRwithouttheassumptionaboutthedistributionsofthebackgroundclutterandnoise.Simulationresultsshowthatthealgorithmisinsensitivetothenoiseandisadaptabletorealtimetargetdetectionandtracking.Varioustechniqueshavebeenproposedforautomaticinfraredtargetdetection.Someoftheimportanttechniquescanbecategorizedinthefollowing.Mathematicalmorphologicmethod:Mathematicalmorphologicisanimportantnonlinearmethodinimageprocessingandysis[24,25].Hsiaoetal.[9]presentedanimagesegmentationalgorithmthatisahybridofmathematicalmorphologyandregiongrowingtechnique.Chietal.[4]proposedanovelapproachforsmalltargetdetectioninsingleframebasedonordermorphologytransformationandimageentropydifference.Statisticalmodel:Stochasticbackgroundmodelsincorporatingspatialcorrelationscanbeusedtoenhancethedetectionoftargetsinnaturalterrainimagery.ChappleandBertilone[3]proposedasimplestochasticmodelforimagesofnaturalbackgroundsbasedonthepointwisenonlineartransformationofGaussianrandomfields,anddemonstrateditseffectivenessandcomputationalefficiencyinmodelingthetexturesfoundinnaturalterrainimageryacquiredfromairborneinfraredsensors.Geneticalgorithm:Geneticalgorithmiseffectiveforfindinganoptimalvalueinthecomplexoptimizationproblembysimulatingthebiologicalevolutionaryproprocessor,whichhasstrongcapabilitytosearchtheoptimizationinallpossiblefieldsandisaneffectivemethodtosolvetheproblemofoptimalcombination.Ithasbeenintroducedtodetectdimtargetincomplexdetectionandrecognitionability,Xiong[29]proposedfilters.AndLi[13]studiedacombinationofgeneticalgorithmandmultistagehypothesistrackingmethod.Wavelettransformation:Thewavelettransformisakindoftimefrequencyysismethod.Itisfittedtoextracthighfrequencyfromlowfrequency.Thedirectionadaptivewavelettransformgoesbeyondthelimitationofdirectionsandprovidesaneffectivealgorithmfordimtargetdetection[14].Highordercorrelation:Highordercorrelationmethodproposedin[15]recursivelycomputesthespatiotemporalcrosscorrelationsbetweendataofconsecutivescans.Thismethodnotonlysignificantlyimprovestheclutterrejectionrate,butalsoincreasesthefeasibilityofthemodifiedhighordercorrelationmethodforotherareassuchastrackidentification,dataassociation,classificationandtracking[16,17].Therearestillmanyotheralgorithmsfortargetdetectionsuchasfeaturematching,rotationandshiftinvariant,adaptivefilterandneuralnetwork[1].Inthepaper,thedimtargetdetectionalgorithmbasedonthe

empiricalmode position(EMD)isproposed.Theoriginalimageis posedintoIMFs(intrinsicmodefunctions).Itisfoundthattheresidueitemisusefultoestimatethebackground,whichisextractedbyEMDalgorithm.Wecoulddetectthedimtargetbyremovingthebackgroundfromtheoriginalimage.Furthermore,thestudyofthebehaviorofthe positionontensorproductEMDshowsitsefficiencyintermsofcomputationalcost.Thepaperisorganizedasfollows.InSection2,onedimensionEMDisdescribed.Thebidimensionalempiricalmode position(BEMD)anddimtargetdetectionandtrackingarediscussedinSection3.Section4illustratesouralgorithmbysimulationexperiments.AconclusionisgiveninSection5.Empirical EMDTheEMDmethodwasproposedbyHuangetal.in1998[12].Itcan intrinsicmodefunctionsadaptively.IMFisafunctionthatsatisfiestwoconditions:(a)inthewholedataset,thenumberofextremeandthenumberofzerocrossingsthemeanvalueoftheenvelopedefinedbythelocalaandtheenvelopedefinedbythelocalminimaiszero.ThefirstconditionissimilartothetraditionalnarrowbandrequirementsforastationaryGaussianprocess.Thesecondconditionmodifiestheclassicalglobalrequirementtoalocalone.AnIMFaftertheHilberttransformgivesthebestinstantaneousfrequencywithphysicalmeaning.Withthisdefinition,anIMFisnotrestrictedtoanarrowbandsignalanditcanbebothoramplitudemodulatedfunctionscanbeIMFsfortheyhavefinitebandwidthaccordingtothetraditionaldefinition.Unfortunay,mostofthedataarenotIMFs.The posedintosuccessiveIMFsbyusingEMD.ByvirtueoftheIMFs,the positionmethodcansimplyusetheenvelopesdefinedbythelocal aandminimaseparay.Oncetheextremeareidentified,allthelocal aareconnectedbyacubicsplinelineastheupperenvelopeemaxðtÞ.RepeatthelocalminimatoproducethelowerenvelopeeminðtÞ.Theupperandlowerenvelopesshouldcoverallthedatabetweenthem.SupposethesignalisxðtÞ.Themeanisdesignatedasm0ðtÞ,andthedifferencebetweenthesignalxðtÞandm0ðtÞisthefirstcomponent,h1ðtÞ,i.e.,h0ðtÞ¼ h1ðtÞ¼ Theprocessdescribedaboveiscalled‘‘siftingprocess’’.Heretodemonstrateouralgorithmweshallconsideroneroworcolumnofimage‘‘Lena’’astheoriginalsignal.Fig.1(a)showsthesignalextractedfromimage‘‘Lena’’.TheprocedureisillustratedinFig.1(b)and(c).Fig.1(b)

0

H.Lietal./SignalProcessing:ImageCommunication23(2008) IMF1; tion1before IMF1; tion1after Fig.1.Sifting0 Fig.2.ResultofthesecondsiftingexhibitstheupperandthelowerenvelopesofthesignalsignalandthelocalmeanasinEq.(2.2),i.e.,h1ðtÞ.Ideally,h1ðtÞdescribedaboveseemstosatisfyalltherequirementsofIMF.Inreality,however,overshootsundershootsmayexist,andtheygeneratenewextremaIllustrativeexamplesthatexhibitundershootsandovershootscanbefoundatthe25,120and160pointsinmeanandnottheenvelopes,thatwillenterthesifting

Asdescribedabove,thesiftingprocessistoseparatethefinestlocalmodefromthedatafirstbasedonlyonthecharacteristictimescale.Thesiftingprocess,however,hastwoeffects:(a)toeliminateridingwaves;and(b)tosmoothunevenamplitudes.Now,weshalldescribethestopcriterionforsiftingprocess.TomakesuretheIMFcomponentsretainenoughphysicalsenseofbothamplitudeandfrequencymodulations,acriterionforthesiftingprocesstostopshouldbetoCauchyconvergencecriterion:process.Anexamplecanbefoundforthehump160inthedatainFig.1(b).Afterthefirstitionofsiftingprocess,

SD

1ZTjhJðtÞhJ

thehump esalocal umatthesametimelocationasinFig.1(c).Newextremageneratedinthisway

T jhJ—1actuallyrecoverthepropermodeslostintheinitialexamination.Infact,thesiftingprocesscanrecoverlowamplituderidingwaveswithrepeatedsiftings.Thesiftingprocessservestwopurposes:toeliminateridingwavesandtomakethewaveprofilesmoresymmetric.Towardthisend,thesiftingprocesshastoberepeatedmoretimes.Inthesecondsiftingprocess,h1ðtÞistreatedasthesignalandthemeanisdesignatedasm1ðtÞ,thenh2ðtÞ¼h1ðtÞm1ðtÞ.Thesignalh2ðtÞshowninFig.2hasstilllocal aandminima.Therefore,werepeatthissiftingprocedureJtimesandgethJðtÞ:hJðtÞ¼hJ mJ Then,itisdesignatedasimf1,thefirstIMFfromtheimf1ðtÞ¼hJ

AtypicalvalueforSDcanbesetbetween0.2and0.3.Thatis,whenSDsatisfies02SD03thesiftingprocessstops.Thecriterionhasphysicallymeaning:whenthestopcriterionissatisfied,hJwillsatisfythecriterionofIMFsufficiently.AlsothetimesofsiftingiscontrolledandtheamplitudefluctuationsfromtheoriginalsignalcanbeIn1999,Huangproposedanewstopcriterion[10].Iftheextremumnumberequalsthenumberofzerocrosspointsinthreecontinuoussiftingprocess,ordifferslessthanone,thensiftingprocessstop.ThiscriterionwasusedbyHHTtoolboxv1:0(HilbertHuangTransformToolbox,ProfessionalEditionv1:0,PrincetonSaliteSystems,Princeton,NJ,2000).AsanimprovementtoSDcriterion,Rilling,etal.[23]proposedforward3criterion.TheydefineaðtÞ¼ðemaxðtÞeminðtÞÞ=2and¼jmðtÞ=aðtÞj,wheremðtÞismeanenvelope.EMDperformsthesiftingprocessuntilðÞforfractionH.Lietal./SignalProcessing:ImageCommunication23(2008) 1aofthetotaltimeandsÞyfortheremainingfraction.Thetypicalvalueofthethresholdsarea¼0:05,y1¼0:05andy2¼10y1.Overall,thefirstIMF,imf1ðtÞ,ispresentedbyEq.(2.4)accordingtothestopcriterion.Wecanseparatefromtherestofthedatar1ðtÞ¼xðtÞ Sincetheresidue,r1ðtÞ,stillcontainsinformationoflongerperiodcomponents,itistreatedasthenewdataandsubjectedtothesamesiftingprocessasdescribedabove.ThisprocedurecanberepeatedonallthesubsequentsrjðtÞ,andtheresultisr2ðtÞ¼r1ðtÞimf2ðtÞ;...;rNðtÞ¼rN1ðtÞimfNðtÞ.Thesiftingprocesscanbestoppedbyanyofthefollowingpredeterminedcriteria:(i)whentheIMFcomponent,imfNðtÞ,ortheresidue,rNðtÞ, essosmallthatitislessthanthepredeterminedvalueofsubstantialconsequence;(ii)whentheresidue,rNðtÞ, functionfromwhichnoIMFcanbeextracted.BysummingupthesiftingprocessabovewefinallyobtainxðtÞ¼imfkðtÞþ k

Thuswearriveata positionofthedataintoNempiricalmodes,andaresidue,rNðtÞ,whichcanbeeitherthemeantrendoraconstant.Toillustratethe positionprocess,wepresentalltheIMFsobtainedfromtherepeatedsiftingprocessesinFig.3.Theoriginaldataarecomplicatedwithmanylocalextremaandare posedintosixcomponents.ConvergentpropertyofAlthoughEMDalgorithmhasreceivedsignificantattentioninrecentyears,thetheoreticalbasehasnotbeenfullyestablished[11].Mostoftheunderlyingmathematicalproblemshasstillnotbeentreated.Recently,therearetheoreticalstudiestryingtounderstandwhytheEMDalgorithmswork,see,e.g.,WediscusssomeresultsoftheconvergentpropertyofEMDbasedon[28].Theyconstructanenvelopematrixoperatorto ysisthesiftingprocessbasedondiscretetime.Inthepaper,wealsodiscussEMDalgorithminthediscretetimesetting.GivenasignalS,matrixAiscalledenvelopematrixifASismeanenvelopoftimeseriesS.Heremeanenvelopeislocalaverageoftheupperandlowerenvelope,whichispresentedinsifting0000000

Fig.3.TheEMDcomponentsofimage H.Lietal./SignalProcessing:ImageCommunication23(2008)Theyobtainasignificantconclusion:eigenvaluesofenvelopematrixareinInordertodiscusstheconvergentproperty,weassumethatthepositionofextremepointisinvariantwhensiftingprocessitessufficiently.WeinvestigateEMDfromthestepthatthepositionofextremepointisinvariant.Thenthesiftingalgorithmcouldberewrittenasfollows[28]:SetS0¼S¼x,givenathresholdtandi¼FindthelocalextremalConstructamatrixAthatcomputesthemeanvalueoftheupperandlowerenvelops.ComputeSi¼i ASIfki1kislessthanthegiventhresholdt,terminatethealgorithm;otherwise,i¼iþ1andgotoStep(b).ItiseasytoseeiS0Si¼AðIAÞkS0ifkPkconcludethatthematrixsequencei-1AðIAÞkS0kconvergent.ThereforethesequenceSiisDimtargetdetectionandtrackingbasedonInthissection,dimtargetdetectionalgorithmbasedonEMDisproposed.TheHilbertspectraoftheIMFsandresidueareyzedtoshowthevalidityofthestopcriterion.Theresidueisusedtoestimatethebackgroundortolocatethetarget.ThemathematicalmorphologyfilterisalsousedtoremovethenoisesoftheBidimensionalempirical Toextract2DIMFsofanimageduringthesiftingprocess,Nunesetal.[20]andSinclairetal.[26]usedtheFig.4.Aframeinimage

imageextrematocomputethesurfaceinterpolation.Liuetal.[18,19]studiedtextureclassificationandsynthesisthroughEMD.Flandrinetal.reportedinthepaper[8]thatthebuiltinadaptivityofEMDmakesitbehavespontaneouslyasa‘‘waveletlike’’filterbank.WeextendonedimensionalEMDtoBEMDbasedontensorproductmethod.We poserowsandcolumnsoftheimageandextractthelocalinformation.Thealgorithmisdescribedindetailfollowedbytheexampleofaninfraredimage.Supposefðx;yÞisthemxnimage,andlistheempiricalvaluewhichcontrolshowtostopEMDalgorithm.LetRk¼Ik¼fðx;yÞ,k¼Letr¼fr¼fðr;1:nÞistherrowoftheimage,whichisasignal.CalculatethefirstIMFimfðfrÞofthesignalfr.LetRkðr;1:nÞ¼Rkðr;1:nÞimfðfrÞ,ifrr¼rþ1,andgoto(II)(a);otherwisegotoLetc¼fc¼Rkð1:m;cÞistheccolumnoftheimage,whichisasignal.CalculatethefirstIMFimfðfcÞofthesignalfc.LetRkð1:m;cÞ¼Rkð1:m;cÞimfðfcÞ,ifcnc¼cþ1,andgoto(III)(c);otherwisegotoLetk¼kþ1,imfkðx;yÞ¼R1,Rk¼Ik1R1,Ik¼Rk.Ifkgoto(II);otherwisefinishtheThealgorithmgivesapossibleconstructionforIMFs.Thus,everyimagefðx;yÞcanbe posedasfðx;yÞ¼imfkðx;yÞþRlðx; kwhereimfkðx;yÞareIMFsandRlðx;yÞistheInordertoextractthedimtargetfromtheinfraredimageshowninFig.4,accordingtoourexperiment,agoodestimationofbackgroundisachievedwhenl¼4.Fig.5(a)(d)showthefourintrinsicmodefunctions,andFig.6depictsthe residue.Amongthem,Fig.5(a)isimf1ðx;yÞ,whichcontainsthefinestscaleandhighestfrequency,thefeatureinformationofthetargetandnoise.Fig.6isR4ðx;yÞ,theresidue,whichcontainsinformationofbackground.Naturally,R4ðx;yÞcanbeusedastheestimationofthebackground.Thegrayvalueofthepositionoftargetisquitedark,whichmeansitmaycontainlessinformationoftarget.Fig.5.IntrinsicmodeH.Lietal./SignalProcessing:ImageCommunication23(2008) Fig.6.Theresidue:Fig.7.TheHilbertandFourierspectralofimfover

Fig.8.(a)TheHilbertamplitudeoftheresidue.(b)TheFouriertransformofresidue.Fig.9.DetectedresultofFig.HHTisasuperiortoolfortimefrequency ysisofnonlinearandnonstationarydata[10,12].Itisbasedonanadaptivebasis,andthefrequencyisdefinedthroughtheHilberttransform[5].BasedontheHilberttransform,wecouldobtainthelocalpropertyofthesignal,whichisnotobtainedbyFouriertransform.Fig.7(a)showsonedimensionaltimeamplitudeofintrinsicmodefunctionimf4overrows.Itisknownthatthetargetandnoiseisinhighfrequency.FromFig.7(a),itiseasytoseethatthehighfrequencyislocatedaccurayafterHilberttransform.ItnotonlyilluminatestheefficiencyoftheBEMDmethod,butalsoshowsthelocal ysischaracteristicsoftheHilberttransform.Forcomparison,Fig.7(b)showsonedimensionalFouriertransformofintrinsicmodefunctionofthesignaltakenalongthewholerangeofvariable.Itcannotpresenttimefrequencycharacteristicsofthesignal.Weknowthatimf4containsfeatureinformationoftarget.Sotheresiduewillcontainenoughinformationofbackground,nomore positionisneed.ThesuperiorityofHilberttransformisshowninFig.BackgroundWithBEMDtheimageis posedintointrinsicmodefunctionsandresidueR4ðx;yÞ.Intrinsicmodefunctionsrepresenttargetandnoiseinhighfrequency,whileR4ðx;yÞrepresentsthebackgroundwithalittlenoise.ThereforeweobtainanewimagewithtargetandnoisebyremovingR4ðx;yÞfromtheoriginalimage.Bychoosinganappropriaterateofthe umgrayvalueofthenewimageasthreshold,noisecanbeeffectivelyremoved.Ifthenoisestillexistsinsomeimages,itiseasytoremovebymathematicalmorphologybecausemorphologicalsizedistributioncouldbeusedtoisolatefeaturesfromnoiseonthecorrespondingscale.[21]proposedanewalgorithmforimagenoisereductionusingmathematicalmorphology.Fig.9showsthedetectedresultofFig.4.Itshowsthatthetargetisintherightpositionandhasareasonablesize.

DetectionandtrackingThoughagreatdealofefforthasbeenexpendedondetectingandtrackingobjectsinvisualimages,therehasbeenonlylimitedamountofworkoninfraredimagesinthecomputervisioncommunity.Currentlytherearetwobasictargettrackingapproaches:DBTandTBDmethods.DBTcanhaveareasonableperformanceforhighsignaltonoise/clutterratiowhileTBDtechniquesareespeciallyusefulforverylowSNRscenarios[2].Muchoftherecentworkontargettrackinghasfocusedonimprovingtheseapproaches.HereweprovideanalgorithmbasedonBEMDwhichcandetectthetargetfromthesingleframeprecisely.ThealgorithmhasbetterperformanceforlowSNRandisalsoinsensitivetonoise.Thecompletealgorithmiscomposedoftwoseparateparts:thedetectionpartandthetrackingpart.BackgroundThecurrentframeis posedintointrinsicmodefunctionsandresidueR4ðx;yÞwhichrepresentsthebackgroundwithalittlenoise.BackgroundWeobtainanewimagewithtargetandnoisebyremovingR4ðx;yÞfromtheoriginalimage.Bychoosinganappropriaterateoftheumgrayvalueofthenewimageasthreshold,targetcanbeeffectivelydetected.Ifthenoisestillexistsinsomeimages,itiseasytoremovebymathematicalIfthetargethasbeendetected,markitandgotostepII.Otherwise,gotostepI(a)forthenextOncethetargetisdetected,thealgorithmexecutesthefollowingstepstoperformtracking.Loadinganewframe,wefindapatchwhichcentersonthedetectedtargetinthepreceding H.Lietal./SignalProcessing:ImageCommunication23(2008)Trackingthetargetinthepatch,thenwemarkthetargetincurrentframe.ExperimentInthissectionweconsiderimagesequenceof96frames,eachimageis127x128.Wedetectdimtargettheimagesequencebyusingthemethodproposedinthispaper.Fig.10showstheserial4frameswithdim

showninFigs.12and13,respectively.ThemethodusedinFig.12iswavelettransformationbackgroundsuppressionalgorithm[27],whichissimilartoBEMDmethod.ThemethodusedinFig.13iswavelettransformtargetextractionmethod[14].Thepeaksignalnoiseratio(PSNR)ismostcommonlyusedasameasureofreconstructionqualityinimagecompression.PSNRisdefinedas 1PmPn½fðx; andbackgroundchangesintensity.Grayleveloftargetissimilartothelowergraylevelofthebackground.

PSNR¼10log10

x1yff

itishardtofixoneortwothresholdtopicktargetouteventhoughcertaintransformationisused.WecandetectthetargetaccuraybytheproposedalgorithmasshowninFig.11.Forcomparison,wegiveanotherthedetectionresultsbyusingtwokindofwavelettransformmethodsas

whereðx;yÞisthepixel’scoordinate,fðx;yÞandf˜ðx;yÞrepresentthegrayvalueofðx;yÞintheoriginalimageandtheimageafterremovedtheobject,respectively.mxnisthesizeoftheimages,maxfisthe umpixelvalueoftheimage.ThePSNRisbasedonthedifferencebetweenFig.10.Theoriginalserial4Fig.11.ThetargetdetectionresultsbyFig.12.ThetargetdetectionresultsbywaveletbackgroundFig.13.ThetargetdetectionresultsbywavelettargetH.Lietal./SignalProcessing:ImageCommunication23(2008) theoriginalimageandtheoriginalwithobjectremoved.Itwouldseemthatthemoreaccuraytheobjectisremovedthebetterthealgorithmwouldbeoperating.ThehigherPNSRnumbersareclaimedtoindicatebetterperformanceforthesquareddifferenceoffandf˜isAccordingtothedefinitionofPSNR,thesuperiorityoftheBEMDmethodiseasytoobtainbycomparingtheresultsinTable1.ComparedtowavelettransformbasedontargetextractionalgorithmshowninFig.12,theBEMDmethodismoreaccurate,sincethetargetdetectedbywavelettransformislargerthantheoriginaltarget,andhasinterstice.thetargetwhosegraylevelissimilartothebackground,suchasFig.14.Thecharacteristicsofthepicturearethatthetargetistoosmalltobedistinguishedandmovesfast,whilethegraylevelofthetargetissimilartotheTableThePSNRvaluesoftwokindsofmethods:BEMDandwaveletbackgroundsuppression(unit:dB)123456789Fig.14.(a)Imagewithdimtarget.(b)Detected

ineveryframe.ThefinalresultisshowninFig.Inordertoillustratetheeffectivenessoftheproposedmethod,wegivethetrackingresultsofimagesequenceof30frames.Fig.15showsthetrackingresultsofselectedsixsuccessivereferenceframes.Table2givesthecorrespondingpositionsofthetarget.Asseenfromtheresults,thesystemisabletotrackthetargetsuccessfully.Furthermore,thetrackingcurveanderrorcurveofthereferenceimagesequencearegivenintheFig.16(a)and(b),respectively.ItcanbeseenfromFig.theordinateerrorislessthan0.6255pixels.Asseenfromtheexperimentalresults,thetargetarecorrectlyInthispaper,wehavepresentedanalgorithmbasedonBEMDforthedetectingandtrackingdimmovingpointtargetinarealinfraredimagesequencewithlowSNR.Imagesare posedintotheIMFsandresiduebyBEMDmethod.Byregardingtheresiduesastheestimationofbackground,targetdetectionresultsareobtained.Oncethetar