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: [email protected].
Onera - The French Aerospace Lab, F-91761 Palaiseau, France, Email:
[email protected]. T el ecom Bretagne, Technop ole
Brest-Iroise, 29238, France, Email:
[email protected] 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