Application Of Dsm Theory For Sar Image Change Detection

2009·0.48 MB·

by  S. Hachicha

APPLICATIONOFDSM THEORYFORSARIMAGECHANGEDETECTION
S.HachichaandF.Chaabane
URISALaboratory
SUP’COM, RoutedeRaouedKm 3.5,2083Ariana,Tunisie.
ABSTRACT Recent workshaveproventhat thestatistics ofSAR im-
agescanbewellmodelledbytheprobabilitydistributionfam-
SyntheticApertureRadar(SAR)dataenablesdirectobserva-
ilyknownasGammadistribution[1].Otherstudiesintroduce
tionoflandsurfaceatrepetitiveintervalsandthereforeallows
somesigni(cid:383)cantstatisticalmeasuresforthechangedetection
temporal detection and monitoring of land changes. How-
purpose [2]. In the same context, an interesting approach
ever,theproblemofradarautomaticchangedetectionismade
using statistical change measures between two SAR images
more dif(cid:383)cult, mainly with the presence of speckle noise.
havebeenintroducedin[3].Theoriginalityofthisworkisthe
ThispaperpresentsanewmethodforSARimagechangede-
fusionofchangesignaturescomputedontwoSARimagesus-
tectionusingtheDezert-SmarandacheTheory(DSmT).First,
ingDezert-Smarandachetheory.Thispaperextendsthiswork
a Gamma distribution function is used to characterize glob-
and proposes two main contributions. First, SAR texture is
allytheradartexturedataandallowsmassassignmentthrow
modelledbyaGammadistributioninsteadofaGaussianone.
Kullback-Leibler distance. Then, local pixel measurements
Then,inadditiontoclassdistributionsignaturesweintroduce
areintroducedtore(cid:383)nethemassattributionandtakeintoac-
localchangeattributestakingintoaccountthecontextinfor-
countthe contextinformation. Finally, DSmT is carried out
mation.
bycomparingthemodellingresultsbetweentemporalimages.
The paper is organised as follows. Section 2 presents
The originality of the proposed method is on the one hand,
somepre-processingtoolsappliedinordertoestimateGamma
the use of DSmT which achieve a plausible and paradoxi-
distribution parameters for each class of a temporal image.
calreasoningcomparingtoclassicalDempster-ShaferTheory
Section 3 exposes global and local measures introduced to
(DST). On the other hand, the given approach characterizes
characterizechangesignatures. InSection4,abriefdescrip-
the radar texture data with a Gamma distribution which al-
tion of DST and DSmT is presented. The second part of
lowsabetterrepresentationofthespeckle. Theradartexture
this section shows the mass belief assignment used to com-
is being usually modeled by a Gaussian model in previous
pare two images for the change detection purpose. Section
DSTandDSmTfusionworks.
5 presentsexperimentalresults obtainedusing two temporal
IndexTerms— SARimagechangedetection,Kullback- Envisatimages.ConclusionsaregiveninSection6.
Leiblerdistance,DSTandDSmTfusiontheories
2. DISTRIBUTIONPARAMETERSESTIMATION
1. INTRODUCTION
This section provides an investigation to ascertain the most
Changedetection from imagescoveringthe same scene and
appropriatepre-processingtoolswhichcouldbeusedforim-
taken at different times is of widespread interest for a large
ageclassi(cid:383)cationinordertoestimateGammadistributionpa-
numberofapplications,especiallyintheremotesensingdo-
rameters.Thetemporalradarimagesare(cid:383)rst(cid:383)lteredwithout
main. SAR images are very useful tools to surface change
altering SAR texture features and then classi(cid:383)ed. For each
detection especially in regions where optical data are rarely
class ofeach image, the Gammadistribution parametersare
available.Inmanyareas,moreandmoreimagesareacquired
estimated.Wecannoticeherethatthe(cid:383)lteringprocesswhich
onrepeatedorbitsthankstotherepetitivityofradarsatellites
isadelicatepre-processingstepisusedonlyfortheclassi(cid:383)-
suchasERS1,ERS2andEnvisat.However,somedif(cid:383)culties
cation purpose. Parameter estimation is applied on original
areassociatedwithSARimageschangeanalysis:thespeckle
images.
noise,whichdisturbsautomaticchangedetection.Indeed,the
speckle imposing a granular texture to radar images makes
2.1. GammaDistribution
verydif(cid:383)culttheuseoftheseimagesevenwithslightlydiffer-
ent acquisition angles. Nevertheless, despite the complexity In thecase ofradarimages, previousworksshowed thatthe
ofdataprocessing,SARsensorshaveimportantpropertiesat Gammadistribution is moreaccuratethan the Gaussian dis-
anoperationallevel,sincetheyareabletoacquiredatainall tribution to model the real SAR intensity [4]. The Gamma
weatherconditions. distributionPGammaisgivenby:
978-1-4244-5654-3/09/$26.00 ©2009 IEEE 3733 ICIP 2009
pixel. A pixel will be considered as having changed if its
1
PGamma(x;α;β)= βαΓ(α)xα−1e−x/β (1) sIntatoisrdtiecraltodiqsutraibnutitfiyonthcihsacnhgaensgfer,owmeonneeedimaagmeetaosutrheewothhiecrh.
where α is the(cid:2)shape parameter and β is the scale parame- mapstheestimatedstatisticaldistributionsforeachpixeltoa
terandΓ(z)= ∞e−ttz−1dt,z >0istheGammafunction. scalarindexofchange.
0
Then,eachclasswillbecharacterizedbythetwoGammadis- Inthiswork,wechoosetheGammaKullback-Leiblerdi-
tributionparametersαandβ. vergenceintroduced in [6]. The proposed texture similarity
measurebetween two Gammadistributionsoftwo imageI1
2.2. Parameterestimation
andI2 canthenbegivenby:
2.2.1. Pre-processing
Speckle, a form of multiplicative, locally correlated noise, DKLGamma(I1,I2)=logΓ(α(I1))+α(I1)logβ(I1)
plagues imaging applications. For images that contain
speckle, a goal of enhancement is to remove the speckle −α(I1)(Ψ(α(I2))+logβ(I2))+ α(I2)β(I2). (2)
without destroying important image features. The reducing β(I1)
(cid:383)lters have originated mainly from the synthetic aperture
Forsimplicity,thedistributionvalueIk(i,j)forthepixel
radar(SAR)community. Themostwidelycitedandapplied
(i,j)oftheimageIk,k =1,2,isnotedIk intheaboveequa-
(cid:383)lters in this category include the Lee, Frost, Kuan, and
tion. Thefactorsα(Ik) andβ(Ik),aretheshapeandthescale
GammaMAP(cid:383)lters.
parametersassociatedwithdistributionIk,k =1,2.
Morerecently,anewPartialDifferentialEquation(PDE)
approach to speckle removal was introduced and called
Speckle Reducing Anisotropic Diffusion (SRAD) [5]. The 3.2. Localpixelmeasures
PDE-based speckle removalapproach allows the generation
Thecontrastmeasuretakescareofthepixelrealizationsfrom
of an image scale space (a set of (cid:383)ltered images that vary
astochasticpointofview. Tohighlightcontrastinformation,
from (cid:383)ne to coarse) without bias due to (cid:383)lter window size
the conventionalPixel by Pixel Ratio Measure (PPRM) be-
andshape.SRADnotonlypreservesedgesbutalsoenhances
tween two SAR images is exploited. This detector is well-
thembyinhibitingdiffusionacrossedgesandallowingdiffu-
knownandwidelyusedinSARimagerydueto itsabilityto
siononeithersideoftheedge.
greatlyreducethespecklein(cid:384)uenceonthechangemap. The
TheaimofSRAD(cid:383)lteringistoameliorateimageclassi(cid:383)-
cationresultsinordertoperformabetterGammadistribution PPRM ofa pixelbetween two imageI1 and I2 is computed
and normalized on a small window through a contrast mea-
parametersestimation.AfterSARimage(cid:383)ltering,aK-means
clustering technique is applied to classify the pixels into k surer(i,j)de(cid:383)nedby:
and k(cid:3) classes for both temporal images. The combination (cid:3) (cid:3)
betweentheSRAD(cid:383)lterandtheK-meansalgorithmprovides I1(k,l) I2(k,l)
averysuf(cid:383)cientclassi(cid:383)cation. (k,l)∈v (k,l)∈v
r(i,j)=log(max( (cid:3) , (cid:3) )) (3)
2.2.2. ML-estimation I2(k,l) I1(k,l)
(k,l)∈v (k,l)∈v
After applying pre-processing steps in order to carry out an
appropriateclassi(cid:383)cation imagemask for both temporalim- where v is the pixel (i,j) neighborhoodde(cid:383)ned by a given
ages, we estimate statistical Gamma distribution parameters window.
for each class. Maximum likelihood estimators are used to Moreover,we de(cid:383)nea signi(cid:383)cancemeasureas a criteria
extractradartextureparameters. dedicatedtoreducetheambiguityofthepixelbehaviour.The
signi(cid:383)cance measure of a pixel (i,j) for images I1 and I2
3. CHANGEMEASURES
maybede(cid:383)nedby:
Mostoftherelevantchangedetectiontechniquesarebasedon (cid:3) (cid:3)
thedifferenceorratiooperatorswhenusingradarimages. In s(i,j)= I1(k,l)∗ I2(k,l) (4)
ourcase, we introducetwo measuresto characterizechange
(k,l)∈v (k,l)∈v
signatures. The(cid:383)rstonehasaglobalbehavioursinceitoper-
atesonclassesandthesecondoneiscalculatedlocallyfora Wecannoticethatthecontrastandthesigni(cid:383)cancemeasures
pixelneighbourhood. are calculated for a pixel neighbourhoodand not for a class
distribution. Besides, those measures characterize the evo-
3.1. GammaKullback-Leiberdistance lution of each pixel and are not necessary linked to ground
change but give potential candidates to ground evolution.
Thechangedetectionalgorithmisbasedonthemodi(cid:383)cation
That is why those indicators are to be considered into an
of the statistics between the two acquisition dates of each
evidentialandparadoxicalreasoning.
3734
4. THEDEZERT-SMARANDACHETHEORY 4.2.1. De(cid:383)nition
The Dezert-Smarandache Theory (DSmT) [7] is a general- Let Θ = {θ1,θ2,...,θN} be a set of N elements which
ization of the classical Dempster-Shafer Theory (DST) [8], can potentially overlap. We consider in our example Θ =
which allows formal combining of rational, uncertain and {θch,θnoch} involving only two elementary hypotheses
paradoxicalsources. TheDSmTisabletosolvecomplexfu- ’change’and ’no change’. The hyper-power set DΘ is de-
sionproblemswherethe DST usuallyfails, especiallywhen (cid:383)nedasthesetofallcompositehypothesesobtainedfromΘ
con(cid:384)ictsbetween sources becomelarge. In this section, we with∩and∪operatorssuchthat:
will (cid:383)rst review the principle of the DST before discussing
thefundamentalaspectsoftheDSmT. i. ∅,θ ,θ ,...,θ ∈DΘ
1 2 N
4.1. Dempster-ShaferTheoryprinciple ii. IfA,B ∈DΘthen(A∩B)∈DΘand(A∪B)∈DΘ.
The DST makes inferences from incomplete and uncertain
iii. Noother elementsbelongtoDΘexceptthosede(cid:383)nedin
knowledge by combining sources of con(cid:383)dence, even in
i.andii.
the process of partially contradictory sensors. In the DST,
there is a (cid:383)xed set of mutually exclusive and exhaustive
elements, called the frame of discernment, which is sym-
bolized by the set of N elements potentially overlapped Wede(cid:383)neDΘinourexamplebyDΘ ={∅,θch,θnoch,θch∩
Θ = {θ1,θ2,...,θN}. The frame of discernment Θ de(cid:383)nes θnoch,θch∪θnoch}.
thepropositionsnotedAi forwhichthesourcescanprovide AsintheDST,theDSmTde(cid:383)nesamapm(.):DΘ →[0,1].
con(cid:383)dence. Information sources can distribute mass values Thismapde(cid:383)nesthecon(cid:383)dencelevelthateachsensorasso-
on subsets of the frame of discernment, Ai ∈ 2Θ. If an ciateswiththeelementofDΘ.Thismapsupportsparadoxical
informationsourcecannotdistinguishbetweentwoproposi- informationandwehavethiscondition:
tionsAi andAj, itassignsamassvaluetothesetincluding (cid:3)
both hypotheses (Ai ∪ Aj). The mass distribution for all m(A)=1. (6)
hypotheseshastoful(cid:383)llthefollowingconditions A∈DΘ
i. 0≤m(Ai)≤1. Thebeliefandplausibilityfunctionsarede(cid:383)nedinthesame
ii. m(∅)=0. wayasfortheDST.TheDSmTruleofcombinationofcon-
(cid:4) (cid:384)ictinganduncertainsourcesisgivenbytheaboveequation:
iii. Ai∈2Θm(Ai)=1.
(cid:3) (cid:5)d
Massdistributionsfromddifferentsourcesarecombinedwith
m(A)= mi(Ai). (7)
Dempster’sorthogonalrule.
A1,A2,...,Ad∈DΘi=1
A1∩...∩Ad=A
(cid:3) (cid:5)d
m(A)=(1−K)−1 mi(Ai) (5)
4.2.2. Massbeliefassignment
A1∩...∩Ad=Ai=1
(cid:4) (cid:6)
twiohnerefaKctor=measAu1r∩in..g.∩Athde=∅condi(cid:384)=i1ctmbi(eAtwi)eeins athneorsmouarlcizeas-. KChuallnbgaecsk-mLaeyibbeeredxipsteacntceedfDorKaLpGiaxmelm(ai,(Ij1),wI2h)e,ntthheecGoanmtrmasat
Two functions can be evaluated to characterize the uncer- measurer(i,j) and thesigni(cid:383)cance measures(i,j)become
t(cid:4)ainty about the hypotheses. The belief functionBel(A) = signi(cid:383)cant. Furthermore, the decision may be taken when
rweh(cid:384)Aeeirc⊆etasAst,mhteh(emApail)xaiummseiubamisluituryensfcuetnhrtceatiimnotniynPivmal(luuAme).u=nc(cid:4)ertAaii∩nAty(cid:8)=a∅bmou(tAAi), twbhyeerapenriosappaopscreoonpintrriaaTdtaeibclcteioom1nbtbhienetawtmieoaensnsotfhasecshitghanrnemgeeeinnstidgwinchaatitocuhrrse.sis.TdhToehnnee,
decision is taken through the maximum of credibility with
4.2. TheDezert-SmarandacheTheory(DSmT) BeliefonchangeBel(θch).
WhiletheDSTconsidersΘasasetofexclusiveelements,the
DSmTrelaxesthisconditionandallowsforoverlappingand
Hypothesis Massbeliefassignment
intersectinghypotheses. Thisallowsforquantifyingthecon-
∅ 0
(cid:384)ictthatmightarisebetweenthedifferentsourcesthroughout
θch r(i,j)∗DKLGamma(I1,I2)∗s(i,j)
theassignmentofnon-nullcon(cid:383)dencevaluestotheintersec-
θnoch (1−r(i,j))∗(1−DKLGamma(I1,I2))∗(1−s(i,j))
tionofdistincthypotheses.
θch∪θnoch r(i,j)∗(1−DKLGamma(I1,I2))∗s(i,j)
θch∩θnoch 1−(m(∅)+m(θch)+m(θnoch)+m(θch∪θnoch))
Table1.MassBeliefAssignementforimagefusion.
3735
Distance Kullback Leiber Image Contrast Image Significance Image
50 50 50 50 50
100 100 100 100 100
150 150 150 150 150
200 200 200 200 200
250 250 250 250 250
300 50 100 150 200 250 300 300 50 100 150 200 250 300 300 50 100 150 200 250 300 300 50 100 150 200 250 300 300 50 100 150 200 250 300
Fig.1.OriginalEnvisatSARimages. Fig.2. Changemeasuresresultsgivenrespectively(fromleft
to right) by Kullback-Leiber distance, contrast and signi(cid:383)-
cancemeasure.
5. RESULTS
Change detection by DST Change detection by DSmT 1 ROC plots(red:DST blue:DSmT yellow:KLGamma green:r black:s)
0.9
The proposedmethodhas beenappliedon two temporal 50 50 0.8
100 100 0.7
ENnovrtihsaAtSfrAicRai(mseaegFesigc.ov1e).rinTgheth(cid:383)erssatmoneereigsiaocnqoufirTeduniins2C0i0ty5, 125000 125000 sensitivity0000....3456
whereasthesecondoneisacquiredin2007. Aconsiderable 250 250 00..12
amountofurbanchangesoccurredbetweenthesetwo dates. 300 50 100 150 200 250 300 300 50 100 150 200 250 300 00 0.2 0.41 (cid:358) specificity0.6 0.8 1
Thesetwoimagesarealreadyregistered.
Fig.3. Changedetectionresults. (Left)DSTChanges(Mid-
Fig. 2showsacomparisonbetweenthechangemeasures
dle)DSmTChanges(Right)ROCplotscomparisonbetween
results obtained respectively with the KL distance, the con-
Contrast,signi(cid:383)ance,KLGamma,DSTandDSmTchangede-
trast and the signi(cid:383)cance measures. As we can see, some
tectionmeasures.
changeregionsarehighlightedbythethreesignatures. How-
ever,othersareenhancedonlybyoneortwomeasureswhich 7. REFERENCES
underlinethecomplementaritiesoftheseattributes.
[1] F. Chatelain, J.-Y. Tourneret, and J. Inglada, “Change
Fig. 3 shows decision results obtained by maximizing
detection in multisensor SAR images using bivariate
the belief change function exposed previously. Even if this
Gammadistributions,”IEEETGRS,vol.17,pp.249–258,
method takes a strong decision, it is possible to analyse the
March2008.
beliefresponseortheinterval[credibility,plausibility]toin-
troduceacon(cid:383)dentintervalintothedecision.Thisdecisionis
[2] J. Inglada and G. Mercier, “A New Statistical Similar-
madeunderDSTandDSmT.
ityMeasureforChangeDetectioninMultitemporalSAR
ChangesdetectedbyDSmTprocessing(seeFig. 3(Mid- Images and Its Extension to Multiscale-Change Analy-
dle) shows that this approach provides better performances sis,” IEEETGRS,vol.45,pp.1432–1446,May2007.
than the classical DST one (see Fig. 3 (Left)). Comparing
these results to original images presented in Fig. 1, we can [3] G. MercierandS. Derrode, “SAR imagechangedetec-
noticethatthe proposedmethoddetects themost signi(cid:383)cant tionusing distancebetweendistributionsof classes,” in
changeswithaveryfewfalsealarms.So,takingintoaccount IGARSS.IEEE,2004,pp.3872–3875.
con(cid:384)ictbetweenthedifferentsourcesenhancesconsiderably
[4] B. Dong, Y.and Forster and A. Milne, “Evaluation of
the change detection results. Fig. 3 (Right) gives a quanti-
radarimagesegmentationbyMarkovrandom(cid:383)eldmodel
tativeevaluation(ROCplots)oftheresultsusingtheground
with GaussiandistributionandGammadistribution,” in
truth. It shows the performances of all used measures and
IGARSS.IEEE,1998,pp.1617–1619.
itcon(cid:383)rmsthatDSmT(blue)is moreaccuratecomparingto
DST(red)andalltheotherindicators. [5] Y. Yu and S. T. Acton, “Speckle ReducingAnisotropic
Diffusion,”IEEETransactionsonImageProcessing,vol.
6. CONCLUSION
11,pp.1260–1270,November2002.
Changedetectioninmulti-temporalSARimagesrequiresthe
[6] J. Inglada, “Change detection on SAR images by us-
computation of speci(cid:383)c measures which have to be sensi-
ing a parametric estimation of the Kullback-Leibler di-
tivetovariouskindsofchangesandrobusttospeckleeffects.
vergence,” inIGARSS.IEEE,2003,pp.4104–4106.
ThosemeasuresarecombinedandusedbyDSmTtotakeinto
accountcon(cid:384)ictsbetweensourceswhichenhancechangede-
[7] F.SmarandacheandJ.J.Dezert, “ApplicationsandAd-
tection results. The performanceof the proposed technique
vances of DSmT for InformationFusion,” in American
is very suffcient comparingto DST results and original im-
ResearchPress,vol1andvol2,2006.
ages.Infutureworks,wecantakethebene(cid:383)tfromtheDSmT
hybridmodelandintroducethemultiscaleinformationinthe [8] G. Shafer, “A mathematical theory of evidence,” in
proposedchangedetectionapproach. This will allow detec- PrincetonUniversityPress,1976.
tionofchangeswithvarioussizes.
3736
VViieeww ppuubblliiccaattiioonn ssttaattss