Change Detection from Remote Sensing ImagesBased on Evidential ReasoningZhun-ga Liu1,3, Jean Dezert2, Gr egoire Mercier3, Quan Pan1,Yong-mei Cheng11. School of Automation, Northwestern Polytechnical University, Xian, China, Email: liuzhunga@gmail.com2. Onera - The French Aerospace Lab, F-91761 Palaiseau, France, Email: jean.dezert@onera.fr3. T el ecom Bretagne, Technop ole Brest-Iroise, 29238, France, Email: Gregoire.Mercier@telecom-bretagne.euAbstractTheories of evidence have already been applied moreor less successfully in the fusion of remote sensing images. In theclassical evidential reasoning, all the sources of evidence andtheir fusion results are related with the same invariable (static)frameof discernment. Nevertheless, therearepossiblechangeoccurrences through multi-temporal remote sensing images, andthese changes need to be detected efciently in some appli-cations. Theinvariableframeof classical evidential reasoningcant efcientlyrepresent nor detect the changes occurrencesfromheterogenous remote sensing images. To overcome thislimitation, Dynamical Evidential Reasoning(DER) isproposedfor the sequential fusion of multi-temporal images. A new statetransition frame is dened in DER and the change occurrencescanbepreciselyrepresentedbyintroducingastatetransitionoperator. The belief functions used in DER are dened similarlyto those denedinthe Dempster-Shafer Theory (DST). Twokinds of dynamical combinationrules workinginfree modeland constrained model are proposed in this new framework fordealing with the different cases. In the nal, an experiment usingthreepieces of real satelliteimages acquiredbeforeandafteranearthquake are providedtoshowthe interest of the newapproach.Keywords: Evidence Theory, Change Detection, DynamicalEvidential Reasoning, DST, DSmT, Remote Sensing.I. INTRODUCTIONInformation fusion resulting from multi-temporal and multi-sources remote sensing images remains an open and importantproblem [1]. The remote sensing images can be quite differentin their modality [2]: orbits may be ascending and descending,parameters of acquisitions may differ fromone image toanotherevenwhenthetwoacquisitionsareissuedfromthesamesensor. That iswhy, forchangedetectionpurpose, theuse of the difference image is not an appropriate point of viewdue to the number of false alarms it induces. The situation iseven worse on high resolution images over urban areas sincemanybuildingappears differentlyinthetwoimages tobecompared due to the geometry of sensors, the perspective, thelight conditionandshadows... Hencethecomparisonoftheclassiedimages seems tobemoreappropriated. But, thisyields todeal withuncertain, imprecise andevenconict-ing information. Evidence theories including Dempster-ShaferTheory(DST)[3]andDezert-SmarandacheTheory(DSmT)[4] are good for dealing with such information, and theyhavebeenappliedforremotesensingapplications[1, 5, 6].Inpastworks, aparticularattentionwaspaidtoobtainveryspecicresultsfordecision-makingsupportthroughefcientfusion of sources of evidence. Thus many works focusedmainlyontheredistributionoftheconictingbeliefs[7, 8].These combination approaches can be called static approaches,since they work under the assumption that the frame, onwhichis basedthe decision-makingsupport, is temporallyinvariableinthefusionprocess. However, inthefusionofthe multi-temporal remote sensing images, unexpected changeoccurrencescanariseinsomepartsoftheimages. Soboththe image classication and change detection will be involvedtogether. The classical combination rules in evidence theoriesprovide specic classication results in the invariable parts ofimages, but it cannot precisely detect the change occurrencesin the variable parts.Therefore, a dynamical evidential reasoning (DER) workingunder the condition that the frame does not necessarily remaininvariable in the fusion is proposed. In this paper, a new framecalled State-transition power-set is dened, and the changeoccurrences among different hypotheses can be precisely rep-resentedbythestatetransitionoperator inthis frame. Thedynamical belief functions Bel(.), plausibility functions Pl(.)and pignistic probability BetP(.) [9, 10] are dened similarlyas in DST. Dynamical combination rules are then proposed towork either in the free model, or in the constrained model. Thefree model is well adapted when no prior knowledge is knownon elements of the frame. The constrained model can be usedif some integrity constraints about the change occurrences areknown. Thedynamical approachimproves theperformanceof theclassicationof areasandestimationof thechangesthrough the fusion of multi-temporal sources of evidence. Ourproposedapproachisnallyappliedfor thefusionof threesequential pieces of satellite images acquired before and afteran earthquake.II. DYNAMICAL EVIDENTIAL REASONING APPROACHA. A brief review of DSmTWe needtointroduce brieyDSmTframeworkbecausetheDynamical Evidential Reasoningapproachshares somecommon ideas with DSmT, in particular the necessity to dealwithhybridmodels of theframes insomeapplications forchanges detection. The purpose of DSmT is to overcome thelimitationsofDST[3]mainlybyproposingnewunderlyingmodels for theframes of discernment inorder tot betterwith the nature of real problems, and proposing new efcientcombination and conditioning rules. In DSmT framework, the14th International Conference on Information FusionChicago, Illinois, USA, July 5-8, 2011978-0-9824438-3-5 2011 ISIF 977elements i, i =1, 2, . . . , nof a given frame are notnecessarily exclusive, and there is no restriction on i but theirexhaustivity. The hyper-power setDin DSmT is dened astheset ofall compositepropositionsbuilt fromelementsofwithoperators and . For instance, if = {1, 2},thenD= {, 1, 2, 1 2, 1 2}. A (generalized) basicbelief assignment (bbafor short) isdenedasthemappingm: D[0, 1]. The generalizedbelief andplausibilityfunctions are dened in almost the same manner as in DST.Two models1(the free model and hybrid model) in DSmTcan be used to dene the bbas to combine. In the free DSmmodel, thesourcesofevidencearecombinedwithouttakinginto account integrity constraints. When the free DSm modeldoesnotholdbecausethetruenatureofthefusionproblemunder consideration, wecantakeintoaccount someknownintegrityconstraints anddenebbas tocombineusingtheproperhybridDSmmodel. All detailsofDSmTwithmanyexamples can be easily found in [4].B. The space of state transitions in DERDSmThas beenalreadyappliedfor thefusionof multi-temporal satellite images in [1]. However, the classical frameused is not well adapted for measuring the changes among itselements. Theconjunctiveelements(intersections)inhyper-power set Drepresent either the overlap between hypothesesin free DSm model, or the conict produced by the conjunctivecombinationinHybridDSmmodelwhenthisisanintegrityconstraint. Actually, the conjunction A Bis unable tocharacterize the transition A changing to B (denoted A B),or Bchangingto A(denoted BA). Therefore, if weneed to distinguish two possible state transitions for changesdetection, we needtodene newoperator andcannot usetheclassical conjunctive/intersectionoperator asinclassicalapproaches. We propose the state transition operator changingto, denoted , satisfying the following reasonable conditions:(C1) Impossible (forward) state-transitionA (C2) Impossible (backward) state-transition A(C3) Distributivity of w.r.t. (A B) C= (A C) (B C)(C4) Distributivity of w.r.t. A (B C) = (A B) (A C)(C5) Associativity of state-transition(A B) C= A (B C) = A B C.For notation convenience, a (state) transitionA Bwill bedenotedtA,B. It is important to note that the order of indexesdoesmatterbecausetA,B =tB,Aingeneral, but if A=B1Actually, Shafersmodel, consideringall elementsoftheframeastrulyexclusive, can be viewed as a special case of hybrid model.obviously. tA,A=A Arepresentsaparticularinvariabletransition. Achainoftransitions1 2 nwill bedenotedt1,2,...,n. A transitioni (j k) will be denotedti,jk, etc.Inthetheoriesofbelieffunctions(DST, DSmTorTrans-ferableBeliefModel[9]),theresultofthefusionofsourcesof evidencedenedonasameframeof discernment , isobtained by a given rule of combination relatively to a fusionspaceG, whereGcanbeeither theclassical power set2, a hyperpower-setD, or a superpower set (the power setof therenedframe) dependingonthetheoryused. Inthispaper, weproposetouseanotherfusionspace(thespaceoftransitions), denotedT, inordertodeal explicitlywithallpossible state transitions we want to detect.Firstly, the transition frame is given by:1n= 1 2 . . . n= {tX1,X2,...,Xn|Xi i, i = 1, 2, . . . , n}whereiis the frame associated with thei-th source and is the Cartesian product operator.Inthispaper, weassumetoworkinamoresimplecasewhereallframesi, i=1, 2, . . . , narethesameandequalto , and where G= 2. In other words, we will work withthe simpler space denotedTnand dened byTn= 21n= 2ntimes

. . . Tncan be called state transition power-set, which is composedbyalltheelementsin1nwiththeunionoperator . Wedene as componentwise operator in the following way:tX, tY Tn , tX tY= tXY. (1)Following conditions C1-C5, we note that generallyt(X1,X2,...,Xn) t(Y1,Y2,...,Yn)= t(X1,X2,...,Xn)(Y1,Y2,...,Yn)= tX1Y1,X2Y2,...,XnYnIf Xi = Yi; Xi, Yi are singletons, t(X1,X2,...,Xn)(Y1,Y2,...,Yn)indicates only two kinds of possible transitions:tX=(X1,X2,...,Xn)or tY =(Y1,Y 2,...,Yn), whereas the elementtX1Y1,X2Y 2,...,XnYnrepresents 2 2 2 = 2nkinds of possible transitions. It is obvious that they are quitedifferent, andtX1Y1,X2Y2,...,XnYnis much more imprecisethant(X1,X2,...,Xn)(Y1,Y2,...,Yn).As we see, the important and major difference between theclassical approaches (DST, TBM, DSmT) and DER approachisthechoiceofthefusionspaceweareworkingwith.WithDST, TBMor DSmT, the fusion space we work with isalwaysthesame(independent ofthenumberofsources)assoonasthesourcesaredenedwithrespect tosameframe, whereaswithDERapproachthefusionspaceisalwaysincreasing with the number of sources, even if the sources areall referringtothesameframe. Thisof courseincreasesthecomplexityof DERapproach, but this is thepricetopay to identify and estimate the possible change occurrences978in remote sensing images sequence as it will be shown in lastsectionofthispaper. Clearly, DSTandDSmTarenot welladaptedfor detectingchangeoccurrences. For example, thetransition tA,B,A from state A in source 1, to state B in source2, andbacktostateAinsource3cannot berepresentedinthe fusion space proposed with TBM, DST, nor in DSmT.Example 1: Lets consider = {1, 2} with Shafers model,then2= {, 1, 2, 12}. We rst consider at time1 theinitial set of invariable transitions dened as follows:11= ;T1 2={t , t1 1, t2 2, t12 1 2}Ifwewanttoconsiderallthepossibletransitionsfromtimestamp1 to stamp2, one starts with the cross product frame12= = {t1,1, t1,2, t2,1, t2,2}whichhas || ||=2 2=4distinctelements, andwebuild its power setT2= 212including its 16 elements asin the classical way. The element can be interpreted as thefollowing set of impossible state transitions corresponding tot,,t,1,t,2,t,12,t1,,t2,andt12,. We recall that theimprecise elements are derived from application of conditionsC3 and C4 and not from the componentwise union of n-uplesinvolved in transition indexes. The cardinality of Tnincreaseswith the value ofn as |Tn | = 2||n.The power set of transitions we want to work with for suchvery simple example will be given by:T2=212={, t1,1, t1,2, t2,1, t2,2,t1,1 t1,2= t1,12, t1,1 t2,1= t12,1,t1,1 t2,2= t(1,1)(2,2), t1,2 t2,1= t(1,2)(2,1),t1,2 t2,2= t12,2, t2,1 t2,2= t2,12,t1,1 t1,2 t2,1= t(1,1)(1,2)(2,1),t1,1 t1,2 t2,2= t(1,1)(1,2)(2,2),t1,1 t2,1 t2,2= t(1,1)(2,1)(2,2),t1,2 t2,1 t2,2= t(1,2)(2,1)(2,2),t1,1 t1,2 t2,1 t2,2= t12,12}.C. Basic denitions in DERBelief functionBel(.), plausibility functionPl(.) and pig-nisticprobabilityBetP(.)[9, 10]2arebasicandimportantfunctionsforthedecisionmaking. TheycanbealsousedinDER approach as well. Indeed, all the elements in 1ncom-posedbythestatetransitionsthroughthesingletonelementshavespecicanduniquemeaning, andtheyareconsideredthesingletonelements. AllthefocalelementsinTncanbedecomposed in the disjunctive canonical form using these sin-gleton elements with the operator , and we call that canonical2DSmP(.) transformation proposed in [4] which provides of betterprobabilistic informational content thanBetP(.) can also be chosen instead.But DSmP(.)ismorecomplicatedtoimplementthanBetP(.)andithasnot been tested in our application for now.focal element. For example, m(t(12),3) = m(t1,3t2,3)becauseofthecondition(C3). Thebelief, plausibilityfunc-tions and the pignistic transformation are dened in DERsimilarly as in DST; that is:Bel(A) =

A,BTn;BAm(B) (2)Pl(A) =

A,BTn;AB=m(B) (3)The interval[Bel(A), Pl(A)] is then interpreted as the lowerand upper bounds of imprecise probability for decision-makingsupport [3] andthe pignistic probability BetP(A)commonly used to approximate the unknown probability P(A)in[Bel(A), Pl(A)] is calculated by:BetP(A) =

A,BTn,AB|A B||B|m(B) (4)where |X| is thecardinal of theelement X. InDER, thecardinalofA Tnisthenumberofthesingletonelementsit contains in its canonical form. For example, |t(12),3| =|t1,3 t2,3| = 2.D. Combination rules in DERThe classical combination rules usually work under theassumptionthat all thesources of informationrefer tothesame common frame. The results of existing combinationrules do not deal with unexpected changes in the frameandtheymanagetheconictingbeliefswithout takingintoaccount these possible changes in the frame. Nevertheless, theconicting information is more important than the informationfrom the agreement for changes detections.The fundamental difference between the classical approachand this new Dynamical Evidence Reasoning (DER) approachis that the frame of the fusion process is considered possiblyvariableovertime, andthefusionprocessisadaptedforthechanges detectionandidentication. Whentheelements oftheframeareinvariable,theycanbeconsideredasaspecialcaseof changes correspondingtoinvariabletransition. Thedynamical combination rules will be dened by using the statetransitionoperator totakebenet of theuseful informationincludedinthe conict betweensources. The combinationrules work in free model and constrained model as well.1) Combination rule in the free model of transitions: In thefreemodel, thereisnopriorknowledgeonstatetransitions,andallkindsofchangesamongtheelementsareconsideredpossible to happen. We start with the combination of the twotemporal sources of evidences at rst. Let m1andm2betwo bbas provided by two temporal sources of evidence overthe frame of discernment satisfyingShafers model. Itscorrespondingpower-set is2= {, 1, 2, 1 2, . . . , }.m1(A), A 2is the mass of belief committed to thehypothesis Abythesourceno. 1, andm2(B), B2isthemasscommittedtoBbythesourceno. 2. Thesourcesno. 1 and no. 2 are considered as independent.979In this work, we propose to compute the mass of belief of aforward transitiontAk,Bl= Ak Bl, l kasm(tAk,Bl) =mk(A)ml(B) where k and l are temporal stamps/indexes.Notethat becausemk(A)ml(B)=ml(B)mk(A), thismassof belief alsocanbeassociatedtothebackwardtransitiontBlAk= Bl Ak. We assume always working with orderedproducts correspondingtoforwardtemporal transitions. Byconvention, the bba mi provided by the source no. i is assumedtobe available at time i andbefore the bba mjprovidedbythesourceno. j. Indexesofsourcescorrespondactuallyto temporal stamps. Following this very simple principle, theconjunctive combination rule in the free model of transitions,denoted DERf, is dened by:tX1,X2 T2, m12(tX1,X2) = m1(X1)m2(X2) (5)whereX1 21andX2 22.For simplicity and in our application, we consider that theframesareall thesame; that is 1=2=. . . =n=. Thissimpleconjunctiverulecanbeextendedeasilyforcombiningn sequential sources of evidence as follows: Direct joint fusion ofn sources: tX1,X2,...,Xn Tnm1n(tX1,X2,...,Xn) = m1(X1)m2(X2) mn(Xn)(6)whereXi 2i, i = 1, . . . , n.In this free model, the result of the combination is very specicsince all kinds of change occurrences are distinguished in theresults, but thecomputationburdenisverylargebecauseofthe large increase of the cardinality ofTnwithn.Thefollowingexamplewill showthedifferencebetweenDER and DSmT in free model.Example 2: Lets consider three bbas on = {1, 2} as121 2m10.6 0 0.4m20 1 0m30 0.5 0.5 With DSm free model:1) DSmC:m(1 2) = 0.6, m(2) = 0.42) DERf:m(t1,2,2) = 0.3, m(t1,2,12) = 0.3m(t12,2,12) = 0.2, m(t12,2,2) = 0.2For the singleton elements, based on DERf, one gets:Bel(.) BetP(.) Pl(.)t1,2,20.3 0.60 1t1,2,10 0.20 0.5t2,2,10 0.05 0.2t2,2,20 0.15 0.4Theresults of DERf preciselyrepresents thebelief ofchange occurrences, whereas the elements in DSmCcannot reect the process of state transition because of itsinvariable frame. In the decision making, it indicates thatthe hypothesis t1,2,2 is most possible to happen accordingtoBel(.), Pl(.)or BetP(.), whichmeans 1insource1changes to 2 in source 2 and to 2 in source 3. It impliesDSmT is not adapted for the change detection because ofits invariable frame.2) Combinationruleintheconstrainedmodel of transi-tions: In the constrained model of transitions, one knows thatsomekinds of changes amongthedifferent elements cantoccur according to our prior knowledge. The set {M, }canbedenedinintroducingsomeintegrityconstraints asdone in the hybrid model of DSmT.Mincludes all thetransitionsinTi, i =1, 2, . . . , n, whichhavebeenforcedtobeemptybecauseof thechosenintegrityconstraints inthe model M, and is classical empty set. If the sources ofevidencesharethesamereliabilityinthecombination, theconict amongthe evidences will be regardedas possiblechanges or as emptysets dependingontheconstraints wehave. The mass of empty sets arising from integrity constraintscanbedistributedtotheotherfocal elements. ThenotationtA,BM=t, means that the transitiontA,Bis equivalent to thetransitiont intheunderlyingmodel Mgiventheintegrityconstraints. DERDSruleof combination:Themassofemptysetsisproportionallydistributedtotheotherfocal elementssimilarlytoDempster-ShafersrulehereandwedenotethisrulebyDERDSforshort.Ofcourse,theconictingmass can also be redistributed by some other ways. Thecombinationrule DERDSis mathematicallydenedasfollows:tn1 Tn1, Xn 2n 2, tn Tn , n 2m1n(tn) =

ttn1,XnM=tnm1n1(tn1)mn(Xn)1 K(7)whereKrepresents the mass of belief committed to theempty sets (i.e. the degree of conict) which is given byK=

ttn1,Xnm1n1(tn1)mn(Xn). (8)When considering the direct combination of n sequentialsources altogether, one has tn Tn , andXi 2, i =1, 2, . . . , nm1n(tn) =

tX1,X2,...,XnM=tnm1(X1) mn(Xn)1 K(9)whereK=

tX1,X2,...,Xnm1(X1) mn(Xn). (10)Remark: Thesummationintroducedin(7) and(9) allowstotakeintoaccounttheintegrityconstraintsofthemodelofthespaceoftransitionsasshowninthenextexample. Ifallkinds of transitions among different elements are constrainedto be empty sets, the frame will become Shafers model, andDERDSwill reduce to Dempsters rule. Example 3: Lets consider the frame ={1, 2}withfollowing two integrity constraints representing the impossiblestatetransitions M {t1,2, t2,2}. Therefore, duetothese980integrity constraints, the fusion spaceT2, as given in detailsin the Example 1, reduces to the simple following setT2= {, t1,1, t2,1, t12,1}We also consider the following bbas inputs:12m10.4 0.6 0m20.5 0.2 0.3Accordingtothe underlyinghybridmodelM, onlytheproducts m1(1)m2(2)andm1(2)m2(2)takepart intheconict as:K= m1(1)m2(2) +m1(2)m2(2) = 0.2.Theconjunctivemassofbeliefofpossibletransitionsaregiven bym(t1,1) = m1(1)m2(1) = 0.20m(t1,12) = m1(1)m2(1 2) = 0.12m(t2,1) = m1(2)m2(1) = 0.30m(t2,12) = m1(2)m2(1 2) = 0.18Due to the integrity constraintst1,2M= , t2,2M= , one has

t1,12= t1,1 t1,2M=t1,1 = t1,1t2,12= t2,1 t2,2M=t2,1 = t2,1Therefore, themass m(t1,12)must betransferredtot1,1,whereasm(t2,12) must be transferred tot2,1only. Finally,the result given by DERDSrule ism(t1,1) =m(t1,1) +m(t1,12 t1,1)1 K= 0.40m(t2,1) =m(t2,1) +m(t2,12 t2,1)1 K= 0.60It shows that the combination rule in constrained model canprovide more specic results than in the free model when theassociated constrained information is known.III. APPLICATION ON REAL REMOTE SENSING IMAGESThree pieces of multi-temporal satellite images are analyzedbyusingDERinthisexperiment. ThreeQuickBirdimageshave been acquired before and after the may 21st2003earthquakeintheregionof Boumerdes, Algeria. TheyhavebeencorrectedgeometricallybyusingSRTMelevationdataand resample by a P+Xs pan-sharpening technique to yield a60cm resolution color images (see Fig. 1) [11].It has been analyzed in theory and shown by the numericalexample that DSmT does not work well for the changedetection, especiallywhenthe number of sources is largerthan 2. So only DER will be applied in this experiment. TheunsupervisedclusteringmethodECM(Evidential C-Means),detailedin[12], isappliedfortheimageclassicationonlyby using the radiometric point of view. ECM is adapted to theclassication of uncertain data, and the imprecise classes canbe acquired by ECM. The membership about the classicationof each pixel acquired by ECM are directly used as bbas here.Thethreesequential imagesareclusteredinC=5groups,and the classications are dened as (colors refer to Fig. 1):1={Dark area: green plant(w1)or shadow(w2)}2={Maroon area: bared soil(w3)}3={Dark gray area: gray building(w4)}4={Gray area: road(w5)or incomplete building(w6)}5={White area: white building(w7)or ruin(w8)} ={Ignorance}The other tuning parameters are dened by: Maximum num-berofiterationsT=20, weightingexponentforcardinality =2, weightingexponent =2, terminationthreshold = 1. This classication technique has been used herebecause it is unsupervised and the results can be directlyusedas themass functions (bbas). Nevertheless, anykindof classiers (including supervised ones) may be used at thislevel. Forthedecisionmaking, wetakethecriteriathattruehypothesis gets the maximum of pignistic probability.The time analysis of the three images is mainly takenfor detectingthe important change occurrences toevaluatethe damage, and we just pay attention to some particulartransitions rather than all the possible transitions. So theconstrained model of DER is applied here. The statetransitions considered from the image Fig. 1-(a) to Fig. 1-(b)includes thechangeoccurrences fromthegraybuildingtoruin as t3,5(ti,j= ti,j) and fromincomplete buildingto white building as t4,5, and all invariable transitions ast1,1, t2,2, t3,3, t4,4, t5,5. The change occurrences fromgraybuildingtoruinast3,5andfromgraybuildingtobaredsoilas t3,2whichmeanstheruinhasbeencleaned, andall theinvariable transitions as t1,1, t2,2, t3,3, t4,4, t5,5are involvedfromthe image Fig. 1-(b) to Fig. 1-(c). Therefore, theconstrained available transitions in the three images are givenby t1,1,1, t2,2,2, t3,3,3, t4,4,4, t5,5,5, t3,5,5, t4,5,5, t3,3,5, t3,3,2.Alltheotherpossibletransitionsconsidereduselessherearedened as empty sets through constrained model in DER.Remark:Thetransitionst3,5andt4,5mayinvolvesmanykinds of possible change occurrences, but some of the changeoccurrences are unavailable according to our prior knowl-edge. Theconstrainedtransitionscanbedenedbyt3,5M=tw4,w8, t4,5M=tw6,w7. The combination results are shown as Fig. 2. Some changeoccurrences are considered more important than the invariabletransitions for the evaluation of the disaster, and they areextracted in Fig. 3.The notations of transitions from 1st to 2nd image are:t1,1: {Green area}, t2,2: {Blue area}, t3,3: {Gray area},t4,4: {White area}, t5,5: {Dark red area},t3,5M=tw4,w8: {Red area}, t4,5M=tw6,w7: {Dark yellow area}.t3,5 andt4,5 correspond to actual changes and they are linkedtodamagemapping(seeFig.3).Fig.3-(a)focusonthose2981classes. The notations of transitions from 2nd to 3rd image:t1,1:{Green area}, t2,2: {Blue area}, t3,3: {Gray area},t4,4:{White area}, t5,5: {Red area}, t3,2: {Cyan area},t3,5: M=tw4,w8: {Purple area}.t3,5, t3,2 corresponds to changes induced after the earthquake.The notations of transitions through the 1st, 2nd and 3rdimages:t1,1,1: {Green area}, t2,2,2: {Blue area},t3,3,3: {Gray area}, t4,4,4: {White area},t5,5,5: {Dark red area}, t3,3,2: {Cyan area},t3,3,5M=tw4,w4,w8: {Purple area},t3,5,5M=tw4,w8,w8: {Red area},t4,5,5M=tw6,w7,w7: {Dark yellow area}.We showmore interest in the variable transitions thanthe invariable transitions, since the variable transitions reectimportant changeoccurrenceswhichisveryvaluableintheevaluationof disaster. Aswecansee, somebuildingswereentirelydestroyedbytheearthquakeas representedbyredcolor mainly on the left side of the image and some incompletebuildings has been completed represented by the yellow colorin Fig. 3-(a), which reects the disaster mainly happenedon the left side. In Fig. 3-(b), the purple area indicatesthat another normal building also collapsed, and the cyanareameanstherunhasbeencleaned. Fig. 3-(c) showsthesequential transitions of the three images, and it represents alltheparticular changeoccurrencesthroughthethreeimages.These fusion results can be helpful for the disaster evaluationinthereal application. Therearesomefewfalsealarmsofchangedetectionswhicharemainlyduetothedifferenceinthe geometry of the acquisitions. If some ancillary informationare available, these noisy changes can be reduced.IV. CONCLUSIONSA Dynamic Evidential Reasoning (DER) approach has beenproposed for the change detection in the multi-temporal remotesensing images. DERapproach starts with the sequentialconstructionof thepower set of admissiblestatetransitionstakingintoaccount, if necessary, someintegrityconstraintsrepresentingsome knownunacceptable (impossible) transi-tions. Based on a particular rule-based algebra, the massof belief of thechangeoccurrencescanbecomputedusingtwo different combination rules theDERforDERDSrule.DERfrule in the free model works under the condition thatnopriorknowledgeabout thechangeoccurrencesisknownwith a great computation burden. DERDSrule in constrainedmodelispreferredwhensomeconstraintsontheimpossiblechangeoccurrences is availabletoget better fusionresultswith less computational complexity. Several simple numericalexamplesweregiventoshowhowtouseDERandtoshowits difference with classical fusion approaches. Finally, anexperiment about the fusion of multi temporal satellite imagesillustrates the interest and the efciency of DER for changesdetection and estimation. The DER fusion of images can welldetect the change occurrences and classify the invariable areas.Our further research works will concern the extension of DERfor working with other DSm fusion rules, etc.AcknowledgementsThis work is supported by China Natural Science Founda-tion(No.61075029) andPhDThesis InnovationFundfromNorthwestern Polytechnical University (No.cx201015).REFERENCES[1] A. Bouakache, A. Belhadj-Aissa, and G. Mercier, Satel-liteimagefusionusingDezert-Smarandachetheory,inAdvances and Applications of DSmT for InformationFusion, F. Smarandache and J. Dezert, Eds. ARP, 2009,vol. 3, ch. 22.[2] G. Mercier, G. Moser, and S. Serpico, ConditionalCopula for Change DetectiononHeterogeneous SARData, IEEETrans. Geosci. Remote Sensing, vol. 46,no. 5, May 2008.[3] G. Shafer, A Mathematical Theory of Evidence. Prince-ton Univ. Press, 1976.[4] F. SmarandacheandJ. Dezert, AdvancesandApplica-tions of DSmT for Information Fusion V1-3. Rehoboth,USA: American Research Press, 2004-2009.[5] S. Corgne, L. Hubert-Moy, and J. D. et al, Land coverchangepredictionwithanewtheoryof plausibleandapradoxical reasoning,inAdvancesandApplicationsof DSmTforInformationFusion, F. SmarandacheandJ. Dezert, Eds. Am. Res. Press, Rehoboth, Jun. 2004.[6] S. Hachicha and F. Chaabane, Application of DSMtheory for SAR image change detection, in Proceedingsof 200916thIEEEInternational ConferenceonImageProcessing (ICIP), Nov. 2009, pp. 37333736.[7] W.Liu,Analyzingthedegreeofconictamongbelieffunctions,Articial Intelligence, vol. 170, no. 11, pp.909924, 2006.[8] A. Martin, A. L. Jousselme, andC. Osswald, Conictmeasurefor thediscountingoperationonbelief func-tions, in Proceeding of Fusion, Germany, 2008.[9] P. Smets, DecisionmakingintheTBM: thenecessityofthepignistictransformation,Int.Jour.Approx.Rea-soning, vol. 38, pp. 133147, 2005.[10] , Thecombinationofevidenceinthetransferablebelief model, IEEE Trans. Pattern Anal. Machine Intell.,vol. 12, no. 5, pp. 447458, 1990.[11] R. Andr eoli, H. Y esou, andN. T. et al, Exploitationen crise et post crise de donn ees satellites haute ettr` eshauter esolutionpourlacartographieded eg atsdes eismes. cas de Bam, Boumerd` es et Al Hoceima, inSirnat, Montpellier, Mar., 1011, 2005, (in french).[12] M. H. MassonandT. Denoeux, ECM: Anevidentialversion of the fuzzy C-means algorithm, Pattern Recog-nition, vol. 41, pp. 13841397, 2008.982(a)(b)(c)Figure1. Multi-temporal QuickBirdsatelliteimagesacquiredbeforeandafter an earthquake. (a) before image: 04/22/2002, (b) after image: 05/13/2003,(c)latteracquisition:06/13/2003.DatasetBoumerdes c CopyrightSERTIT,2009, distribution CNES.(a)(b)(c)Figure 2. Fusion results of classied images by DERDS. (a) Fusion of the1stand2ndimage, (b)Fusionofthe2ndand3rdimage, (c)Fusionofthe1st, 2nd and 3rd image.983(a)(b)(c)Figure 3. Signicant damage map extracted from DER decision of Fig. 2).(a) Changes from the 1st to 2nd classied image, (b) Changes from the 2ndto3rdclassiedimage, (c)Changesthroughthe1st, 2ndand3rdclassiedimages. 984