翻譯以.原文和在同一文件中前于

基于經(jīng)驗模式分解（EMD）的弱小目標檢測與算法。EMD引入由過篩的來分解原始圖像變換成高頻和低頻分量的一個確定的數(shù)。與EMD算法相比，它是有效的估計關(guān)鍵字引檢測和在低信號噪聲比（SNR）未知位置和未知速度的弱小目標的是紅外搜索的真實世界數(shù)據(jù)的SNR。在紅外場景的背景顯示的每個像素和其周圍環(huán)境之間的空間相：數(shù)學形態(tài)學是圖像處理和分析的一個重要的非線性方法。Hsiao等：結(jié)合空間相關(guān)性的隨機背景模型可以用于提高在自然地形圖像目標檢測。自適小變換方的限，提供一個效算法小標測。識別數(shù)關(guān)聯(lián)分和的行。和神經(jīng)網(wǎng)絡(luò)。在中，基于經(jīng)驗模式分解（EMD）的弱小目標檢測算法。將原始圖像分解成IMF分量（固有模態(tài)函數(shù)。結(jié)果發(fā)現(xiàn)，通過殘余物產(chǎn)品估計背景，這是由EMD的算法提取有用的。我們可以通過從原始圖像中除去背景檢測弱小目標。此外，在張量積EMD的分解行為的研究表明其在計算成本方面的效率。本文的結(jié)構(gòu)如下。在第二節(jié)，一維EMD描述。二維經(jīng)驗模式分解（BEMD）和弱小目標經(jīng)驗模式分由Huang等人EMD方法。在1998年，它可以分解成數(shù)據(jù)有限和有意義的固有集，的數(shù)量和過零點數(shù)目必須相等或相差最多者之一;（b）在任何情況下，由局個IMF并不局限于一個窄頻帶信號，它可以是幅度和頻率調(diào)制。所以純粹頻率或幅度調(diào)制功能，可以通過的IMF為它們按照傳統(tǒng)的定義具有有限的帶寬。不幸的是，大部分的數(shù)據(jù)不是IMF分量。其中涉及多個振蕩模式下的數(shù)據(jù)可以通過使用EMD分解成連續(xù)的IMF。憑借IMF分量，分解方法可以簡單地使用當?shù)氐淖畲笾岛妥钚≈捣謩e定義了信封。一旦的標識，所有的局部極大值由三次樣條線作為上包絡(luò)線連接é（T。重復上述局部極小產(chǎn)生下包絡(luò)?（T。上和下包絡(luò)線應該包括它們之間的所有數(shù)據(jù)。假設(shè)X（t）。的平均值被指定為米0（t）和信號之間的差×（t）和米0（T）是第一成分，?1（t）即，等式（2.1）和等式（2.2?0（T）=X（ （2.1?1（T）=H0（T）-M0（T。 （2.2）2.1（b）2.1（c）中所示。2.1（b）則上部和該信號的下包絡(luò)線和它們的平均值。圖2.1（c）所示的信號和局部均值如式之間的區(qū)別。次。在第二個篩分的過程中，?1（t）1（t）然后?2（t）H1（t）1（t）?2（t）2.2因此，我們重復這個過程篩選?次，得到??（T）的等式 2.3??（T）=HJ-1（T）-MJ-1（t） IMF1IMF（2.4）（T）=H?（ （2.4現(xiàn)在，描述的停止標準篩選過程。為了確保IMF分量保留振幅和頻率調(diào)制的足 對于一個典型的價值SD0.20.3進行設(shè)定。也就是說，當SD滿足2<SD03，在篩選過程停止。該標準已實際意思是：當停止條件滿足時，??將滿際金組織的標準，充分。也過篩的時間進行控制，并從原始信號的振幅的篩選過程，或不同于小于1，然后過篩過程停止。這個標準是用來通過HHT工具箱V1.0（Hilbert-Huang變換工具箱，專業(yè)版V1.0，普林斯頓系統(tǒng)，普林斯頓新澤西州，2000年。作為一個改進的SD標準，瑞霖等提出了前進3閾值標準。他們（T）（E（T）E（T）/2和σ（T）=|M（T）/A（T|m（t）EMDσ（T）θ1α的總時間和σ（t）θ2對剩余的部分。閾值的典型值α=005，θ1=00和θ210θ1由于殘基，R1（t）subsequents??（t）其結(jié)果是方程（2.6：?2（T）=R1（T）-IMF2（T），...，R?（T）=RN-1（T）-IMF（T 取。通過總結(jié)篩選過程上面我們最終得到等式（2.7）因此，我們在數(shù)據(jù)導入的分解得出?經(jīng)驗的模式，以及殘基，R?（t）量圖2.3。原始數(shù)據(jù)是合并有許多局部極值，并分解成六個部分。雖然EMD算法已收到顯著重視，近年來，理論基礎(chǔ)還沒有完全建立起來。大多數(shù)基本的數(shù)學問題仍然沒有得到處理。最近，有理論研究，試圖了解為什么了EMD算法的工作。矩陣ASS。這里的平均包絡(luò)是上部和們從點的位置是不變的一步EMD。然后如下的篩選算法可以改寫：（一）S0=S=X給定的閾值τI=1（四）S=SI-1-ASI-1（五）如果∥ASI-1∥小于給定的閾值τ，終止算法;否則，I=I+ 并轉(zhuǎn)（B由于信封矩陣的本征值都在[0,1]，我們得出這樣的結(jié)論矩陣序列是收斂的。因此，序列S是收斂的BEMD弱小目標檢測與在本節(jié)中，基于EMD的弱小目標檢測算法。金組織的希爾伯特譜和殘留分析顯F（XY）mn圖像，并且升EMD讓?K?=F（XY），K=0R=1（一）f?=F（R1N）?行的圖像，這是一個信號。計算第一國際貨幣IMF（?）f?。（二）讓??（R，1：N）=RK（R，1：N）-國際金組（?）?MR=R+1，然后轉(zhuǎn)到（二（一）;否則轉(zhuǎn)到（三C=1（三）f?=RK（1MC）?圖像，這是一個信號列。計算第一國際貨IMF（F?）f?。（四）讓?K（1：M，C）=RK（1：M，C）-國際金織（F?）?NC=C+1，然后轉(zhuǎn)到（三）（c）（四K=K+1，IMF?（XY）=RK-1，[R?=IK-1Rk-1K= K如果?L，去（二）;否則算法結(jié)束。為方程（3.1： IMF?（XY）IMF?（XY）是殘留物中。為了從所示的紅外圖像中提取弱小目標圖3.1，根據(jù)我們的實驗中，背景的良好估計是實現(xiàn)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）的灰度值是相當?shù)?，這意味著它可能包含目標的信息較少。HHT3.（aIMF43.4（a）中，很容易看BEMD織4超過行。傅里葉變換的關(guān)注與沿可變的整個范圍所采取的信號的頻譜。它不能呈現(xiàn)的信號的時間-頻率特性。我們知道國際金組織包含目標的特息。所以包含足夠的背景信息，沒有的分解需要。隨著BEMD圖像被分解成固有模態(tài)函數(shù)和殘留?4（XY。固有模態(tài)函數(shù)表示的目噪聲的去除新形象R4（XY）從原始圖像。通過選擇新的圖像作為閾值的最大灰度感。完整的算法是由兩個獨立的部分：檢測部和部分。（一）背景重建。當前幀分解成固有模態(tài)函數(shù)和殘留?4（XY）它表示一個（二）背景消除。我們通過消除獲得與目標和噪音的新形象?4（XY）（三）III（A）為實驗結(jié)（4.1）其中（X，Y）是像素的坐標，F(xiàn)（X，Y）和代表的灰度值（XY）mnf是圖像的最確的對象被移除的算法將作的更好。據(jù)稱較高PNSR數(shù)字來指示的平方差更好的性能f和較小。結(jié)ContentslistsavailableatSignalProcessing:ImageContentslistsavailableatSignalProcessing:Image Dimtargetdetectionandtrackingbasedonempirical HongLia,ShaohuaXua,LuoqingLiDepartmentofMathematics,HuazhongUniversityofScienceandTechnology,WuhanFacultyofMathematicsandComputerScience,HubeiUniversity,WuhanarticleinfArticleReceived8June2007Receivedinrevisedform8October2008Accepted8October:TargetdetectionandtrackingEmpiricalmode IntrinsicmodefunctionMathematicalmorphologyHilberttransform

abstracDimtargetdetectionandtrackingalgorithmbasedontheempiricalmode tion(EMD)isproposed.EMDisintroducedto posetheoriginalimageintoade?nitenumberofhighfrequencyandlowfrequencycomponentsbymeansofsifting.WiththeEMDalgorithm,itisvalidtoestimatethebackgroundandgetthedimtargetbyremovingthebackgroundfromtheoriginalimage.Thealgorithmdetectsdimmovingtargeteffectivelyandestimateitstrajectoryaccuray.Thedataysisandexperimentsshowthattheproposedalgorithmisadaptabletorealtimetargetdetectionandtracking.&2008ElsevierB.V.AllrightsDetectionandtrackingofdimtargetofunknownpositionandunknownvelocityatlowsignalnoiseratio(SNR)isanimportantissueininfraredsearchingandtrackingsystem.Whentheinfraredsensorisnotinthedirectcontactwiththetarget,thetargetisimmersedinaheavyclutteredbackground.Duetotheexistenceofatemperature?eld,targetedgesareblurredandcannotbeaccurayde?ned.Wecannotgetfeatureinformationabouttheinteriordetailsofatarget.Furthermore,aeroopticdisturbancesandairturbulencemaketheSNRofasingleinfraredimageverylowonrealworlddata.Thebackgroundininfraredsceneshowsspatialcorrelationbetweeneachpixelanditssurroundings.Becauseoftheeffectsofinherentsensornoiseandthephenomenaofnaturethereexistsomehighgrayregionsintheinfraredimageascomplicatedcloudedgeandirregularsunlitspot.Alloftheabovemakethetargetdif?culttodetectandtrack.However,aninfraredimagedescribesthedistribu*Corresponding .:+86 E-mail (L.

tionofheatradiationfromatargetanditsbackgroundandtheinfraredradianceofdimpointtargetisirrelevanttothesurrounding.Generallywesupposethatthetargetiseitherdarkerorbrighterthanitsimmediateadjacentbackground.Thus,dimtargetscanberegardedassingularpointsintheinfraredimage.Thethermalimagesareobtainedbysensingtheradiationintheinfraredspectrum,whichiseitheremittedorre?ectedbytheobjectinthescene.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]proposedasimplestochasticmodelforimagesofnaturalbackgroundsbasedonthepointwisenonlineartransformationofGaussianrandom?elds,anddemonstrateditseffectivenessandcomputationalef?ciencyinmodelingthetexturesfoundinnaturalterrainimageryacquiredfromairborneinfraredsensors.Geneticalgorithm:Geneticalgorithmiseffectivefor?ndinganoptimalvalueinthecomplexoptimizationproblembysimulatingthebiologicalevolutionaryproprocessor,whichhasstrongcapabilitytosearchtheoptimizationinallpossible?eldsandisaneffectivemethodtosolvetheproblemofoptimalcombination.Ithasbeenintroducedtodetectdimtargetincomplexdetectionandrecognitionability,Xiong[29]proposed?lters.AndLi[13]studiedacombinationofgeneticalgorithmandmultistagehypothesistrackingmethod.Wavelettransformation:Thewavelettransformisakindoftimefrequencyysismethod.Itis?ttedtoextracthighfrequencyfromlowfrequency.Thedirectionadaptivewavelettransformgoesbeyondthelimitationofdirectionsandprovidesaneffectivealgorithmfordimtargetdetection[14].Highordercorrelation:Highordercorrelationmethodproposedin[15]recursivelycomputesthespatiotemporalcrosscorrelationsbetweendataofconsecutivescans.Thismethodnotonlysigni?cantlyimprovestheclutterrejectionrate,butalsoincreasesthefeasibilityofthemodi?edhighordercorrelationmethodforotherareassuchastrackidenti?cation,dataassociation,classi?cationandtracking[16,17].Therearestillmanyotheralgorithmsfortargetdetectionsuchasfeaturematching,rotationandshiftinvariant,adaptive?lterandneuralnetwork[1].Inthepaper,thedimtargetdetectionalgorithmbasedonthe

empiricalmode position(EMD)isproposed.Theoriginalimageis posedintoIMFs(intrinsicmodefunctions).Itisfoundthattheresidueitemisusefultoestimatethebackground,whichisextractedbyEMDalgorithm.Wecoulddetectthedimtargetbyremovingthebackgroundfromtheoriginalimage.Furthermore,thestudyofthebehaviorofthe positionontensorproductEMDshowsitsef?ciencyintermsofcomputationalcost.Thepaperisorganizedasfollows.InSection2,onedimensionEMDisdescribed.Thebidimensionalempiricalmode position(BEMD)anddimtargetdetectionandtrackingarediscussedinSection3.Section4illustratesouralgorithmbysimulationexperiments.AconclusionisgiveninSection5.Empirical EMDTheEMDmethodwasproposedbyHuangetal.in1998[12].Itcan intrinsicmodefunctionsadaptively.IMFisafunctionthatsatis?estwoconditions:(a)inthewholedataset,thenumberofextremeandthenumberofzerocrossingsthemeanvalueoftheenvelopede?nedbythelocalaandtheenvelopede?nedbythelocalminimaiszero.The?rstconditionissimilartothetraditionalnarrowbandrequirementsforastationaryGaussianprocess.Thesecondconditionmodi?estheclassicalglobalrequirementtoalocalone.AnIMFaftertheHilberttransformgivesthebestinstantaneousfrequencywithphysicalmeaning.Withthisde?nition,anIMFisnotrestrictedtoanarrowbandsignalanditcanbebothoramplitudemodulatedfunctionscanbeIMFsfortheyhave?nitebandwidthaccordingtothetraditionalde?nition.Unfortunay,mostofthedataarenotIMFs.The posedintosuccessiveIMFsbyusingEMD.ByvirtueoftheIMFs,the positionmethodcansimplyusetheenvelopesde?nedbythelocal aandminimaseparay.Oncetheextremeareidenti?ed,allthelocal aareconnectedbyacubicsplinelineastheupperenvelopeemaxetT.RepeatthelocalminimatoproducethelowerenvelopeeminetT.Theupperandlowerenvelopesshouldcoverallthedatabetweenthem.SupposethesignalisxetT.Themeanisdesignatedasm0etT,andthedifferencebetweenthesignalxetTandm0etTisthe?rstcomponent,h1etT,i.e.,h0etT? h1etT? 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.,h1etT.Ideally,h1etTdescribedaboveseemstosatisfyalltherequirementsofIMF.Inreality,however,overshootsundershootsmayexist,andtheygeneratenewextremaIllustrativeexamplesthatexhibitundershootsandovershootscanbefoundatthe25,120and160pointsinmeanandnottheenvelopes,thatwillenterthesifting

Asdescribedabove,thesiftingprocessistoseparatethe?nestlocalmodefromthedata?rstbasedonlyonthecharacteristictimescale.Thesiftingprocess,however,hastwoeffects:(a)toeliminateridingwaves;and(b)tosmoothunevenamplitudes.Now,weshalldescribethestopcriterionforsiftingprocess.TomakesuretheIMFcomponentsretainenoughphysicalsenseofbothamplitudeandfrequencymodulations,acriterionforthesiftingprocesstostopshouldbetoCauchyconvergencecriterion:process.Anexamplecanbefoundforthehump160inthedatainFig.1(b).Afterthe?rstitionofsiftingprocess,

SD

1ZTjhJetThJ

thehump esalocal umatthesametimelocationasinFig.1(c).Newextremageneratedinthisway

T jhJ—1actuallyrecoverthepropermodeslostintheinitialexamination.Infact,thesiftingprocesscanrecoverlowamplituderidingwaveswithrepeatedsiftings.Thesiftingprocessservestwopurposes:toeliminateridingwavesandtomakethewavepro?lesmoresymmetric.Towardthisend,thesiftingprocesshastoberepeatedmoretimes.Inthesecondsiftingprocess,h1etTistreatedasthesignalandthemeanisdesignatedasm1etT,thenh2etT?h1etTm1etT.Thesignalh2etTshowninFig.2hasstilllocal aandminima.Therefore,werepeatthissiftingprocedureJtimesandgethJetT:hJetT?hJ mJ Then,itisdesignatedasimf1,the?rstIMFfromtheimf1etT?hJ

AtypicalvalueforSDcanbesetbetween0.2and0.3.Thatis,whenSDsatis?es02SD03thesiftingprocessstops.Thecriterionhasphysicallymeaning:whenthestopcriterionissatis?ed,hJwillsatisfythecriterionofIMFsuf?ciently.Alsothetimesofsiftingiscontrolledandtheamplitude?uctuationsfromtheoriginalsignalcanbeIn1999,Huangproposedanewstopcriterion[10].Iftheextremumnumberequalsthenumberofzerocrosspointsinthreecontinuoussiftingprocess,ordifferslessthanone,thensiftingprocessstop.ThiscriterionwasusedbyHHTtoolboxv1:0(HilbertHuangTransformToolbox,ProfessionalEditionv1:0,PrincetonSaliteSystems,Princeton,NJ,2000).AsanimprovementtoSDcriterion,Rilling,etal.[23]proposedforward3criterion.Theyde?neaetT?eemaxetTeminetTT=2and?jmetT=aetTj,wheremetTismeanenvelope.EMDperformsthesiftingprocessuntileTforfractionH.Lietal./SignalProcessing:ImageCommunication23(2008) 1aofthetotaltimeandsTyfortheremainingfraction.Thetypicalvalueofthethresholdsarea?0:05,y1?0:05andy2?10y1.Overall,the?rstIMF,imf1etT,ispresentedbyEq.(2.4)accordingtothestopcriterion.Wecanseparatefromtherestofthedatar1etT?xetT Sincetheresidue,r1etT,stillcontainsinformationoflongerperiodcomponents,itistreatedasthenewdataandsubjectedtothesamesiftingprocessasdescribedabove.ThisprocedurecanberepeatedonallthesubsequentsrjetT,andtheresultisr2etT?r1etTimf2etT;...;rNetT?rN1etTimfNetT.Thesiftingprocesscanbestoppedbyanyofthefollowingpredeterminedcriteria:(i)whentheIMFcomponent,imfNetT,ortheresidue,rNetT, essosmallthatitislessthanthepredeterminedvalueofsubstantialconsequence;(ii)whentheresidue,rNetT, functionfromwhichnoIMFcanbeextracted.Bysummingupthesiftingprocessabovewe?nallyobtainxetT?imfketTt k

Thuswearriveata positionofthedataintoNempiricalmodes,andaresidue,rNetT,whichcanbeeitherthemeantrendoraconstant.Toillustratethe positionprocess,wepresentalltheIMFsobtainedfromtherepeatedsiftingprocessesinFig.3.Theoriginaldataarecomplicatedwithmanylocalextremaandare posedintosixcomponents.ConvergentpropertyofAlthoughEMDalgorithmhasreceivedsigni?cantattentioninrecentyears,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)Theyobtainasigni?cantconclusion:eigenvaluesofenvelopematrixareinInordertodiscusstheconvergentproperty,weassumethatthepositionofextremepointisinvariantwhensiftingprocessitessuf?ciently.WeinvestigateEMDfromthestepthatthepositionofextremepointisinvariant.Thenthesiftingalgorithmcouldberewrittenasfollows[28]:SetS0?S?x,givenathresholdtandi?FindthelocalextremalConstructamatrixAthatcomputesthemeanvalueoftheupperandlowerenvelops.ComputeSi?i ASIfki1kislessthanthegiventhresholdt,terminatethealgorithm;otherwise,i?it1andgotoStep(b).ItiseasytoseeiS0Si?AeIATkS0ifkPkconcludethatthematrixsequencei-1AeIATkS0kconvergent.ThereforethesequenceSiisDimtargetdetectionandtrackingbasedonInthissection,dimtargetdetectionalgorithmbasedonEMDisproposed.TheHilbertspectraoftheIMFsandresidueareyzedtoshowthevalidityofthestopcriterion.Theresidueisusedtoestimatethebackgroundortolocatethetarget.Themathematicalmorphology?lterisalsousedtoremovethenoisesoftheBidimensionalempirical Toextract2DIMFsofanimageduringthesiftingprocess,Nunesetal.[20]andSinclairetal.[26]usedtheFig.4.Aframeinimage

imageextrematocomputethesurfaceinterpolation.Liuetal.[18,19]studiedtextureclassi?cationandsynthesisthroughEMD.Flandrinetal.reportedinthepaper[8]thatthebuiltinadaptivityofEMDmakesitbehavespontaneouslyasa‘‘waveletlike’’?lterbank.WeextendonedimensionalEMDtoBEMDbasedontensorproductmethod.We poserowsandcolumnsoftheimageandextractthelocalinformation.Thealgorithmisdescribedindetailfollowedbytheexampleofaninfraredimage.Supposefex;yTisthemxnimage,andlistheempiricalvaluewhichcontrolshowtostopEMDalgorithm.LetRk?Ik?fex;yT,k?Letr?fr?fer;1:nTistherrowoftheimage,whichisasignal.Calculatethe?rstIMFimfefrTofthesignalfr.LetRker;1:nT?Rker;1:nTimfefrT,ifrr?rt1,andgoto(II)(a);otherwisegotoLetc?fc?Rke1:m;cTistheccolumnoftheimage,whichisasignal.Calculatethe?rstIMFimfefcTofthesignalfc.LetRke1:m;cT?Rke1:m;cTimfefcT,ifcnc?ct1,andgoto(III)(c);otherwisegotoLetk?kt1,imfkex;yT?R1,Rk?Ik1R1,Ik?Rk.Ifkgoto(II);otherwise?nishtheThealgorithmgivesapossibleconstructionforIMFs.Thus,everyimagefex;yTcanbe posedasfex;yT?imfkex;yTtRlex; kwhereimfkex;yTareIMFsandRlex;yTistheInordertoextractthedimtargetfromtheinfraredimageshowninFig.4,accordingtoourexperiment,agoodestimationofbackgroundisachievedwhenl?4.Fig.5(a)(d)showthefourintrinsicmodefunctions,andFig.6depictsthe residue.Amongthem,Fig.5(a)isimf1ex;yT,whichcontainsthe?nestscaleandhighestfrequency,thefeatureinformationofthetargetandnoise.Fig.6isR4ex;yT,theresidue,whichcontainsinformationofbackground.Naturally,R4ex;yTcanbeusedastheestimationofthebackground.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,andthefrequencyisde?nedthroughtheHilberttransform[5].BasedontheHilberttransform,wecouldobtainthelocalpropertyofthesignal,whichisnotobtainedbyFouriertransform.Fig.7(a)showsonedimensionaltimeamplitudeofintrinsicmodefunctionimf4overrows.Itisknownthatthetargetandnoiseisinhighfrequency.FromFig.7(a),itiseasytoseethatthehighfrequencyislocatedaccurayafterHilberttransform.Itnotonlyilluminatestheef?ciencyoftheBEMDmethod,butalsoshowsthelocal ysischaracteristicsoftheHilberttransform.Forcomparison,Fig.7(b)showsonedimensionalFouriertransformofintrinsicmodefunctionofthesignaltakenalongthewholerangeofvariable.Itcannotpresenttimefrequencycharacteristicsofthesignal.Weknowthatimf4containsfeatureinformationoftarget.Sotheresiduewillcontainenoughinformationofbackground,nomore positionisneed.ThesuperiorityofHilberttransformisshowninFig.BackgroundWithBEMDtheimageis posedintointrinsicmodefunctionsandresidueR4ex;yT.Intrinsicmodefunctionsrepresenttargetandnoiseinhighfrequency,whileR4ex;yTrepresentsthebackgroundwithalittlenoise.ThereforeweobtainanewimagewithtargetandnoisebyremovingR4ex;yTfromtheoriginalimage.Bychoosinganappropriaterateofthe umgrayvalueofthenewimageasthreshold,noisecanbeeffectivelyremoved.Ifthenoisestillexistsinsomeimages,itiseasytoremovebymathematicalmorphologybecausemorphologicalsizedistributioncouldbeusedtoisolatefeaturesfromnoiseonthecorrespondingscale.[21]proposedanewalgorithmforimagenoisereductionusingmathematicalmorphology.Fig.9showsthedetectedresultofFig.4.Itshowsthatthetargetisintherightpositionandhasareasonablesize.

DetectionandtrackingThoughagreatdealofefforthasbeenexpendedondetectingandtrackingobjectsinvisualimages,therehasbeenonlylimitedamountofworkoninfraredimagesinthecomputervisioncommunity.Currentlytherearetwobasictargettrackingapproaches:DBTandTBDmethods.DBTcanhaveareasonableperformanceforhighsignaltonoise/clutterratiowhileTBDtechniquesareespeciallyusefulforverylowSNRscenarios[2].Muchoftherecentworkontargettrackinghasfocusedonimprovingtheseapproaches.HereweprovideanalgorithmbasedonBEMDwhichcandetectthetargetfromthesingleframeprecisely.ThealgorithmhasbetterperformanceforlowSNRandisalsoinsensitivetonoise.Thecompletealgorithmiscomposedoftwoseparateparts:thedetectionpartandthetrackingpart.BackgroundThecurrentframeis posedintointrinsicmodefunctionsandresidueR4ex;yTwhichrepresentsthebackgroundwithalittlenoise.BackgroundWeobtainanewimagewithtargetandnoisebyremovingR4ex;yTfromtheoriginalimage.Bychoosinganappropriaterateoftheumgrayvalueofthenewimageasthreshold,targetcanbeeffectivelydetected.Ifthenoisestillexistsinsomeimages,itiseasytoremovebymathematicalIfthetargethasbeendetected,markitandgotostepII.Otherwise,gotostepI(a)forthenextOncethetargetisdetected,thealgorithmexecutesthefollowingstepstoperformtracking.Loadinganewframe,we?ndapatchwhichcentersonthedetectedtargetinthepreceding 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.PSNRisde?nedas 1PmPn?fex; andbackgroundchangesintensity.Grayleveloftargetissimilartothelowergraylevelofthebackground.

PSNR?10log10

x1yff

itishardto?xoneortwothresholdtopicktargetouteventhoughcertaintransformationisused.WecandetectthetargetaccuraybytheproposedalgorithmasshowninFig.11.Forcomparison,wegiveanotherthedetectionresultsbyusingtwokindofwavelettransformmethodsas

whereex;yTisthepixel’scoordinate,fex;yTandf?ex;yTrepresentthegrayvalueofex;yTintheoriginalimageandtheimageafterremovedtheobject,respectively.mxnisthesizeoftheimages,maxfisthe umpixelvalueoftheimage.ThePSNRisbasedonthedifferencebetweenFig.10.Theoriginalserial4Fig.11.ThetargetdetectionresultsbyFig.12.ThetargetdetectionresultsbywaveletbackgroundFig.13.ThetargetdetectionresultsbywavelettargetH.Lietal./SignalProcessing:ImageCommunication23(2008) theoriginalimageandtheoriginalwithobjectremoved.Itwouldseemthatthemoreaccuraytheobjectisremovedthebetterthealgorithmwouldbeoperating.ThehigherPNSRnumbersareclaimedtoindicatebetterperformanceforthesquareddifferenceoffandf?isAccordingtothede?nitionofPSNR,thesuperiorityoftheBEMDmethodiseasytoobtainbycomparingtheresultsinTable1.ComparedtowavelettransformbasedontargetextractionalgorithmshowninFig.12,theBEMDmethodismoreaccurate,sincethetargetdetectedbywavelettransformislargerthantheoriginaltarget,andhasinterstice.thetargetwhosegraylevelissimilartothebackground,suchasFig.14.Thecharacteristicsofthepicturearethatthetargetistoosmalltobedistinguishedandmovesfast,whilethegraylevelofthetargetissimilartotheTableThePSNRvaluesoftwokindsofmethods:BEMDandwaveletbackgroundsuppression(unit:dB)123456789Fig.14.(a)Imagewithdimtarget.(b)Detected

ineveryframe.The?nalresultisshowninFig.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