学术会议海报例子

TitleAuthor*a,Authora,Authora,Authorb,aCollegeofElectricalEngineering,ZhejiangUniversity,310027,China;bInstituteofComputerApplicationTechnology,HangzhouDianziUniversity,310018,ChinaIntroductionTheoriginalbarycentriccoordinateapproachinterpretstheendmemberunmixingproblemasasimplexvolumeratioproblem,whichissolvedbycalculatethedeterminantsoftwoaugmentedmatrix.Oneconsistsofallthemembersandtheotherconsistoftheto-be-unmixedpixelandalltheendmembersexceptfortheonecorrespondingtothespecificabundancethatistobeestimated.WefirstmodifiedthealgorithmofBarycentricCoordinateapproachbybringingintheMatrixDeterminantLemmatosimplifytheunmixingprocess,whichmakesthecalculationonlycontainslinearmatrixandvectoroperations.So,thematrixdeterminantcalculationofeverypixel,astheoriginalalgorithmdid,isavoided.Bytheendofthisstep,theestimatedabundancemeettheASC(abundancesum-to-oneconstraint)constraint.Then,theMost-NegativeRemoveProjectionmethodisusedtomaketheabundancefractionssatisfietheANC(abundancenon-negativityconstraint).AlgorithmsExperimentConclusionReferences[1]P.HoneineandC.Richard,GeometricUnmixingofLargeHyperspectralImages:ABarycentricCoordinateApproach,GeoscienceandRemoteSensing,IEEETransactionson,vol.50,pp.2185-2195,2012-01-012012.[2]R.Heylen,D.BurazerovicandP.Scheunders,FullyConstrainedLeastSquaresSpectralUnmixingbySimplexProjection,GeoscienceandRemoteSensing,IEEETransactionson,vol.49,pp.4112-4122,2011-01-012011.[3]C.Chein-IandW.Su,Constrainedbandselectionforhyperspectralimagery,GeoscienceandRemoteSensing,IEEETransactionson,vol.44,pp.1575-1585,2006-01-012006.WehaveintroducedanewfullconstrainedmethodforlinearspectralunmixingofhyperspectraldatabaseduponBarycentriccoordinatesabundanceestimation.Bybringinginthematrixdeterminantlemma,wesimplifiedthewaytoimplementtheBCAEprocess.Thenweusedtheiterativemostnegativeabundanceendmemberremoveprojectionmethodtofindtheprojectionpointinthesimplexasthereconstructionpointoftheoriginalone.ThisprocessjoinedwiththefastBCAEprocessmakingthefinalabundanceestimationsatisfythefullconstraints.WehavetestedtheproposedalgorithminaseriesofsyntheticimagesandtheAVIRISCupriteDataset.BycomparingwiththeFCLSalgorithm,FCBCAEshowssimilaraccuracyperformance,buthasasuperiorcomputationtimeperformance.I.SyntheticImageDataFig2.TimecomparisonofFCBCAEandFCLS3.bothalgorithmshavethesufficientunmixingaccuracyresultinthisexperiment.Theprocessingtimeincreasesexponentiallyasafunctionofpforbothalgorithms.And,theFCBCAEperformedsignificantlybetterthantheFCLSforanynumberofendmembers.DefinetheorientedvolumeofthesimplexwithverticesasLet\denotethesetdifferenceoperator,withasthesetdefinedbyset,wherehasbeenremovedandradded.ThevolumeofthesimplexwithreplacedbyrcanbedefinedasFromCramer’srule,eachcoefficientcanbeobtainedasieII.ModifiedBCAEUsingMatrixDeterminantLemmaThematrixdeterminantlemmaisgivenbyLet、whereuandvaregivenasandvistheunitvectorwheretheelementinithpositionis1andtheotherelementsare0,withoutdeterminantcalculation,thecoefficientcanbeestimatedasIII.OntheNon-negativityConstraintTheBCAEalgorithmandthemodifiedversionwouldmeettheSNCnaturally,whileabundanceestimationresultsofthepixelsoutsidethesimplexwouldstillviolatetheANC.Fromtheviewofconvexgeometry,thereisnoclosesolutionforthepixelsoutsidethesimplexwithanon-negativityconstraint.Tosolvethisproblem,wereplacetheoriginalpointwithitsprojectionontothesimplexforanapproximation.Theprocessoffindingtheprojectionofapointontothesimplex.•LetrdenotethecolumnvectorandEdenotethematrixwhosecolumnarelinearlyindependentin.TheorthogonallyprojectionofontothesubspacespannedbythecolumnsofEisgivenby•Theorthogonalprojectionrontothesimplexplane2•Accordingtotheknowledgeofconvexgeometry,theestimatedabundancewouldnaturallymeettheASCandANCifthegivenpixelisaninteriorpixelofthesimplex.Combiningthiswiththesimplexplaneprojection,wecanbuildaniterativeprojectionalgorithmtofindthenearestprojectionpoint.Afteronetimeofprojectionandabundanceestimation,ifalltheabundanceshavemeettheANC,thentheprocessisended.Oriftherestillexistsnegativeabundance,wethenremovetheendmemberwhosecorrespondingabundanceisthemostnegativefromtheendmembermatrixofandsetitscorrespondingabundancetozero.Asimpleexampleisillustratedasthefollow.Theiterationiscontinueduntilalltheabundancesarenon-negativeoronlyoneendmemberisleft.Basedontheaforementionedintroduction,theiterativeprocessoftheproposedFullConstrainedBarycentricCoordinatesforabundanceestimation(FCBCAE)isdescribedindetailasfollows.1)Dotheabundanceestimationofpixelrbyusing(1).IfalltheabundancesmeetANC,endtheestimationprocess.Orifnot,gotostep2.2)Updatetheendmembersetbyremovingtheendmembercorrespondingtothemostnegativeabundanceandmarktheabundanceaszero.Ifthereisonlyoneendmemberleft,settheabundanceofthisendmemberas1andterminatetheprocess.Orifnot,gotostep3.3)Projectrtotheupdatedendmemberset,thengotostep1.II.AVIRISCupriteImageDataIV.SummarypFCLSFCBCAEBCAE20.031410.032560.0338650.035380.036100.04930100.011960.012010.01782230.022150.021680.02439pFCLS/sFCBCAE/s240.2717.495150.2367.8110288.65127.31231705.79859.6