Online Adaptive Decision Fusion Framework Based on Entropic Projections onto Convex Sets with Application to Wildfire Detection in Video

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by  Osman Gunay

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Online Adaptive Decision Fusion Framework Based
on Entropic Projections onto Convex Sets with
Application to Wildfire Detection in Video
Osman Gu¨nay∗, Behcet Ug˘ur To¨reyin†, Kıvanc¸ Ko¨se∗ and A. Enis C¸etin∗
∗Department of Electrical and Electronics Engineering
Bilkent University, Ankara, Turkey, 06800
Telephone: [phone] Fax: [phone]
1 Email: {osman,kkivanc,cetin}@ee.bilkent.edu.tr
1 †Texas A&M University at Qatar, Education City, 23874, Doha, Qatar
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2 Telephone:[phone]
Email: [e-mail]
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(EDICS:) ARS-IIU:Image & Video Interpretation and decisionsfromdifferentclassifiersarecombinedusingalinear

] Understanding Object recognition and classification; Fore- combiner[3].Amultipleclassifiersystemcanproveusefulfor
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ground/backgroundsegregation; Scene analysis difficult pattern recognition problems especially when large
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Abstract—In this paper, an Entropy functional based online classsetsandnoisydataareinvolved,becauseitallowstheuse
s. Adaptive Decision Fusion (EADF) framework is developed for of arbitrary feature descriptors and classification procedures
image analysis and computer vision applications. In this frame-
c at the same time [4]. Instead of determining the weights
[ work, it is assumed that the compound algorithm consists of
severalsub-algorithmseachofwhichyieldingitsowndecisionas using orthogonal projections as in [1], [2], we introduce the

1 arealnumbercenteredaroundzero,representingtheconfidence entropice-projectionapproachwhichisbasedonageneralized
v levelofthatparticularsub-algorithm.Decisionvaluesarelinearly projection onto convex set.
9 combinedwithweightswhichareupdatedonlineaccordingtoan Thestudiesinthefieldofcollectiverecognition,whichwere
4 active fusion method based on performing entropic projections
started in the middle of the 1950s, found wide application in
7 onto convex sets describing sub-algorithms. It is assumed that
4 there is an oracle, who is usually a human operator, providing practiceduringthelastdecade,leadingtosolutiontocomplex
. feedback to the decision fusion method. A video based wildfire large-scale applied problems [5]. One of the first examples
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detectionsystem isdeveloped toevaluate theperformance of the of the use multiple classifiers was given by Dasarathy in [3]
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1 algorithm in handling the problems where data arrives sequen- in which he introduced the concept of composite classifier
tially. In this case, the oracle is the security guard of the forest
1 systemsasameansofachievingimprovedrecognitionsystem
lookout tower verifying the decision of the combined algorithm.
v: Simulation results are presented. The EADF framework is also performancecomparedtoemployingtheclassifiercomponents
i tested with a standard dataset. individually.Themethodis illustratedby studyingthe case of
X
the linear/NN(Nearest Neighbor) classifier composite system.
Index Terms—Projection onto convex sets, active learning,
r
a decision fusion, online learning, entropy maximization, wildfire Kumar and Zhang used multiple classifiers for palmprint
detection. recognition by characterizing the user’s identity through the
simultaneoususeofthreemajorpalmprintrepresentationsand
achievebetterperformancethan either oneindividually[6]. A
I. INTRODUCTION
multipleclassifierfusionalgorithmisproposedfordeveloping
AN online learning framework called Entropy functional an effective video-based face recognition method [7]. Garcia
based Adaptive Decision Fusion (EADF) is proposed and Puig present results showing that pixel-based texture
which can be used for various image analysis and computer classification can be significantly improved by integrating
vision applications. In this framework, it is assumed that the texture methods from multiple families, each evaluated over
compound algorithm consists of several sub-algorithms each multisized windows [8]. This technique consists of an initial
of which yielding its own decision. The final decision is training stage that evaluates the behavior of each considered
taken based on a set of real numbers representing confidence texture method when applied to the given texture patterns of
levels of various sub-algorithms. Decision values are linearly interest over various evaluation windows of different size.
combined with weights which are updated online using an Inthisarticle,theEADFframeworkisappliedtoacomputer
activefusionmethodbasedonperformingentropicprojections vision based wildfire detection problem. The system based
(e-projections) onto convex sets describing sub-algorithms. on this method is currently being used in more than 50
Adaptivelearningmethodsbased on orthogonalprojections forest fire lookout towers. The proposed automatic video
are successfully used in some computer vision and pattern based wildfire detection algorithm is based on five sub-
recognitionproblems[1], [2]. In this active learningapproach algorithms:(i)slowmovingvideoobjectdetection,(ii)smoke-
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colored region detection, (iii) wavelet transform based region entire image dependingon the sub-algorithm of the computer
smoothness detection, (iv) shadow detection and elimination, visionproblem.Forexample,inthewildfiredetectionproblem
(v)covariancematrixbasedclassification.Eachsub-algorithm presentedinSectionIII,thenumberofsub-algorithmsisM=5
decides on the existence of smoke in the viewing range and each pixel at the location x of incoming image frame is
of the camera separately. Decisions from sub-algorithms are considered as a sample input for every detection algorithm.
combined together by the adaptive decision fusion method. Let D(x,n)=[D (x,n),...,D (x,n)]T, be the vector of
1 M
Initial weights of the sub-algorithms are determined from decision values of the sub-algorithmsfor the pixel at location
actual forest fire videos and test fires. They are updated by x of input image frame at time step n, and w(x,n) =
using entropic e-projections onto hyperplanes defined by the [w (x,n),...,w (x,n)]T be the current weight vector. For
1 M
fusionweights.Itisassumedthatthereisanoraclemonitoring simplicity we will dropx in w(x,n) for the rest of the paper.
the decisions of the combined algorithm. In the wildfire We define
detection case, the oracle is the security guard. Whenever a
fire is detected the decision should be acknowledged by the yˆ(x,n)=DT(x,n)w(n)= wi(n)Di(x,n) (1)
securityguard.Thedecision algorithmwill also producefalse i
X
alarmsin practice.Wheneveranalarmoccursthesystem asks
asanestimateofthecorrectclassificationresulty(x,n)ofthe
the security guard to verify its decision. If it is incorrect the oraclefor the pixelat locationx of inputimage frameattime
weights are updated according to the decision of the security
stepn,andtheerrore(x,n)ase(x,n)=y(x,n)−yˆ(x,n).As
guard. The goal of the system is not to replace the security
itcanbeseeninthenextsubsection,themainadvantageofthe
guardbutto providea supportingtooltohelp himor her.The proposedalgorithmcomparedtootherrelatedmethodsin[10]-
attention span of a typical security guard is only 20 minutes
[13], is thecontrolledfeedbackmechanismbased onthe error
in monitoring stations. It is also possible to use feedback at term. Weights of the algorithms producing incorrect (correct)
specifiedintervalsandrunthealgorithmautonomouslyatother decision is reduced (increased) iteratively at each time step.
times. For example,the weightscan be updatedwhen there is
Another advantage of the proposed algorithm is that it does
nofireintheviewingrangeofthecameraandthenthesystem notassumeanyspecificprobabilitydistributionaboutthedata.
can be run without feedback.
Thepaperisorganizedasfollows:Entropyfunctionalbased
Adaptive Decision Fusion (EADF) framework is described A. Set Theoretic Weight Update Algorithm based on Orthog-
in Section II. The first part of the section describes our onal Projections
previous weight update algorithm which is obtained by or-
Inthis subsection,we firstreviewthe orthogonalprojection
thogonal projections onto convex sets [1], the second part
based weight update scheme [1]. Ideally, weighted decision
proposesentropybasede-projectionmethodforweightupdate
valuesofsub-algorithmsshouldbeequaltothedecisionvalue
of the sub-algorithms. Section III introduces the video based
of y(x,n) the oracle:
wildfire detection problem. The proposed framework is not
restricted to the wildfire detection problem. It can be also y(x,n)=DT(x,n)w (2)
used in other real-time intelligent video analysis applications
which represents a hyperplane in the M-dimensional space,
in which a security guard is available. In Section IV each
RM. Hyperplanes are closed and convex in RM. At time
one of the five sub-algorithms which make up the compound
instant n, DT(x,n)w(n) may not be equal to y(x,n). In
(main)wildfiredetectionalgorithmisdescribed.InSectionV,
our approach, the next set of weights are determined by
experimental results are presented and the proposed online
active fusion method is compared with the universal linear projectingthecurrentweightvectorw(n)ontothehyperplane
predictorandtheweightedmajorityalgorithms.Theproposed represented by Eq. 2. The orthogonal projection w(n + 1)
EADF method is also evaluated on a dataset from the UCI of the vector of weights w(n) ∈ RM onto the hyperplane
machinelearningrepository[9].Well-knownclassifiers(SVM, y(x,n)=DT(x,n)w is the closest vector on the hyperplane
K-NN) are combined using EADF. During the training stage to the vector w(n).
individual decisions of classifiers are used to find the weight Let us formulate the problem as a minimization problem:
of each classifier in the composite EADF classifier. Finally, min||w∗−w(n)||
conclusions are drawn in Section VI. w∗ (3)
subject to DT(x,n)w∗ =y(x,n)
II. ADAPTIVEDECISION FUSION (ADF) FRAMEWORK The solution can be obtained by using Lagrange multipliers.
If we define the nextset of weights as w(n+1)=w∗ it can
Let the compound algorithm be composed of M-many de-
be obtained by the following iteration:
tection sub-algorithms: D ,...,D . Upon receiving a sample
1 M
input x at time step n, each sub-algorithm yields a decision w(n+1)=w(n)+ λD(x,n) (4)
value D (x,n) ∈ R centered around zero. If D (x,n) > 0, 2
i i
it means that the event is detected by the i-th sub-algorithm. where the Lagrange multiplier, λ, can be obtained from the
Otherwise, it is assumed that the event did not happen. The
hyperplane equation:
type of the sample input x may vary depending on the algo-
rithm.Itmaybeanindividualpixel,oranimageregion,orthe DT(x,n)w∗−y(x,n)=0 (5)
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as follows: B. Entropic Projection (E-Projection) Based Weight Update
Algorithm
y(x,n)−yˆ(x,n) e(x,n)
λ=2 =2 (6) The l norm based minimization approaches provide suc-
||D(x,n)||2 ||D(x,n)||2 1
cessful signal reconstruction results in compressive sensing
problems [22], [23], [24], [25]. However the l and l norm
where the error, e(x,n), is defined as e(x,n) = y(x,n) − 0 1
basedcostfunctionsusedincompressivesensingproblemsare
yˆ(x,n)andyˆ(x,n)=DT(x,n)w(n).PluggingthisintoEq.4
notdifferentiableeverywhere.The entropyfunctionalapprox-
imates the l norm |w (n)| for w (n)>0 [26]. Therefore
e(x,n) 1 i i i
w(n+1)=w(n)+ D(x,n) (7) it can be used to find approximate solutions to the inverse
||D(x,n)||2 P
problemsdefined in [22], [23] and other application requiring
l norm minimization. Bregman developed convex optimiza-
isobtained.Hencetheprojectionvectoriscalculatedaccording 1
tion algorithms in 1960’s and his algorithms are widely used
to Eq. 7.
inmanysignalreconstructionandinverseproblems[16],[27],
Wheneveranewinputarrives,anotherhyperplanebasedon
the new decisionvaluesD(x,n) of sub-algorithms,is defined [28], [29], [30], [15], [31], [31], [32], [2]. Bregman’s method
in RM providesgloballyconvergentiterativealgorithmsforproblems
with convex, continuous and differentiable cost functionals
y(x,n+1)=DT(x,n+1)w∗ (8) g(.):
min g(w) (10)
This hyperplane will not be the same as y(x,n) = w∈C
DT(x,n)w(n)hyperplane.Thenextsetofweights,w(n+2), such that
are determinedby projectingw(n+1)ontothe hyperplanein DT(x,n)w(n)=y for each time index n (11)
Eq. 8. Iterated weights converge to the intersection of hyper-
planes [14], [15]. The rate of convergencecan be adjusted by In the EADF framework the cost function is g(w) =
introducing a relaxation parameter µ to Eq. 7 as follows Mw (n)log(w (n)) and each equation in (11) represents
i i i
a hyperplane H ∈ RM which are closed and convex sets.
n
w(n+1)=w(n)+µ e(x,n) D(x,n) (9) PIn Bregman’s method the iterative algorithm starts with an
||D(x,n)||2 arbitrary initial estimate and successive e-projections are per-
formed onto the hyperplanesH , n=1,2,...,N in each step
n
where 0<µ<2 should be satisfied to guarantee the conver- of the iterative algorithm.
gence according to the projections onto convex sets (POCS) The e-projection onto a closed and convex set is a gen-
theory [16]-[19]. eralized version of the orthogonal projection onto a convex
If the intersection of hyperplanes is an empty set, then set[26].Letw(n)denotetheweightvectorforthen sample.
th
the updated weight vector simply satisfies the last hyper- Its e-Projection w∗ onto a closed convex set C with respect
plane equation. In other words, it tracks decisions of the to a cost functional g(w) is defined as follows
oracle by assigning proper weights to the individual sub-
w∗ =argmin L(w,w(n)) (12)
algorithms [17], [18]. w∈C
The relation between support vector machines and orthog-
where
onal projections onto halfplanes was established in [18], [20]
and [21]. As pointed out in [20] SVM is very successful L(w,w(n))=g(w)−g(w(n))−<▽g(w),w−w(n)>
in batch settings but it cannot handle online problems with (13)
drifting concepts in which the data arrive sequentially. In the adaptivelearningproblem,we have the hyperplaneH :
DT(x,n).w(n+1)=y(x,n) for each sample x. For each
hyperplane H, the e-projection (12) is equivalent to
Algorithm 1 The pseudo-codefor the POCS based algorithm
Adaptive Decision Fusion(x,n) ▽g(w(n+1))=▽g(w(n))+λD(x,n) (14)
for i = 1 to M do DT(x,n).w(n+1)=y(x,n) (15)
w (0) = 1 ,Initialization
i M
end for where λ is the Lagrange multiplier. As pointed above the e-
e(x,n)=y(x,n)−yˆ(x,n) projection is a generalization of the orthogonal projection.
for i = 1 to M do When the cost functional is the Euclidean cost functional
endwif(onr+1)←wi(n)+µ||De((xx,,nn))||2Di(x,n) gl2(wn)orm= squiawrei(onf)2thtehedidffisetraennccee Lve(cwto1r,w(w2)1b−ecwom2)e,s atnhde
P
yˆ(x,n)= w (n)D (x,n) the e-projection simply becomes the well-known orthogonal
i i i
if yˆ(x,n)≥0 then projection onto a hyperplane.
return 1P When the cost functional is the entropy functional g(w)=
else iwi(n)log(wi(n)), the e-projectiononto the hyperplaneH
return -1 leads to the following update equations:
P
end if wi(n+1)=wi(n)eλDi(x,n), i=1,2,...,M (16)
4
where the Lagrange multiplier λ is obtained by inserting (16) III. AN APPLICATION:COMPUTERVISION BASED
into the hyperplane equation: WILDFIRE DETECTION
DT(x,n)w(n+1)=y(x,n) (17) The Entropy function based Adaptive Decision Fusion
because the e-projectionw(n+1) must be on the hyperplane (EADF) frameworkdescribedin detailin the previoussection
with tracking capability is especially useful when the online
H in Eq. 15. This globally convergent iterative process is
active learning problem is of dynamic nature with drifting
depicted in Fig. 1.
concepts [33]-[35]. In video based wildfire detection problem
introducedinthissection,thenatureofforestalrecordingsvary
over time due to weather conditionsand changes in illumina-
tion which makes it necessary to deploy an adaptive wildfire
detectionsystem.Itisnotfeasibletodeveloponestrongfusion
model with fixed weights in this setting with drifting nature.
An ideal online active learning mechanism should keep track
ofdriftsin videoand adaptitself accordingly.Theprojections
in Eq. 16 and Eq. 7 adjust the importance of individual sub-
algorithmsbyupdatingthe weightsaccordingtothe decisions
of the oracle.
Fig. 1. Geometric interpretation oftheentropic projection method: Weight Manned lookout posts are widely available in forests all
vectors corresponding to decision functions at each frame are updated as to
around the world to detect wild fires. Surveillance cameras
satisfythehyperplaneequationsdefinedbytheoracle’sdecisiony(x,n)and
thedecisionvectorD(x,n).LinesinthefigurerepresenthyperplanesinRM. can be placed in these surveillance towers to monitor the
Weightupdatevectorsconvergetotheintersectionofthehyperplanes.Notice surroundingforestal area for possible wild fires. Furthermore,
thate-projections arenotorthogonal projections.
they can be used to monitor the progress of the fire from
remote centers.
The above set of equations are used in signal reconstruc- AsanapplicationofEADF,acomputervisionbasedmethod
tion from Fourier Transform samples and the tomographic for wildfire detection is presented in this article. Security
reconstruction problem [27], [17]. The entropy functional is guards have to work 24 hours in remote locations under
defined only for positive real numbers which coincides with difficultcircumstances.Theymaysimplygettiredorleavethe
our positive weight assumption. lookouttower forvariousreasons.Therefore,computervision
The pseudo-code for the e-projection based adaptive deci- based video analysis systems capable of producing automatic
sion fusion based algorithm is given in Algorithm 2. To find fire alarmsare necessary to help the securityguardsto reduce
the λ value that minimizes the squared error at each iteration the average forest fire detection time.
a simple search between possible λ values can be performed Cameras, once installed, operate at forest watch towers
or a nonlinear equation should be solved (Eqs. 16 and 17). throughout the fire season for about six months which is
mostly dry and sunny in Mediterranean region. There is
Algorithm 2 The pseudo-code for the EADF algorithm
usually a guard in charge of the cameras, as well. The
E-Projection Based Adaptive Decision Fusion(x,n) guard can supply feed-back to the detection algorithm after
for i = 1 to M do the installation of the system. Whenever an alarm is issued,
wi(0) = M1 ,Initialization she/he can verify it or reject it. In this way, she/he can
end for participate to the learning process of the adaptive algorithm.
for λ = λmin to λmax do Theproposedactivefusionalgorithmcanbealsousedinother
for i = 1 to M do supervised learning problems where classifiers combinations
vi(n)=wi(n) through feedback is required.
vi(n+1)←vi(n)eλDi(x,n) As described in the following section, the main wildfire
end for
detection algorithm is composed of five sub-algorithms. Each
if ||y(x,n) − ivi(n + 1)Di(x,n)|| < ||y(x,n) − algorithm has its own decision function yielding a zero-mean
wivTi((nn)+Di1()x,←nP)v||(nth+en1) roefalanvuimdeboersfeoqruesnlocwe. mDoevciinsigonregviaolunessatfreovmerysuibm-aalggeorfirtahmmes
P
end if
are linearly combined and weights of sub-algorithms are
end for
adaptively updated in our approach.
w(n+1)←wT(n+1) There are several approaches on automatic forest fire de-
yˆ(x,n)= w (n)D (x,n)
i i i tection in the literature. Some of the approaches are directed
if yˆ(x,n)≥0 then
towardsdetectionof the flames using infra-redand/orvisible-
P
return 1
rangecamerasandsomeothersaimatdetectingthesmokedue
else
to wildfire [36]-[40]. There are recent papers on sensor based
return -1
fire detection [41]-[43]. Infrared cameras and sensor based
end if
systems have the ability to capture the rise in temperature
however they are much more expensive compared to regular
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pan-tilt-zoom(PTZ) cameras. An intelligent space framework IV. BUILDING BLOCKS OF WILDFIRE DETECTION
is described for indoor fire detection in [44]. However, in ALGORITHM
this paper, an outdoor (forest) wildfire detection method is
Wildfire detection algorithm is developed to recognize the
proposed.
existence of wildfire smoke within the viewing range of the
It is almost impossible to view flames of a wildfire from a cameramonitoringforestalareas.Theproposedwildfiresmoke
cameramountedonaforestwatchtowerunlessthefireisvery detection algorithm consists of five main sub-algorithms:
near to the tower. However, smoke rising up in the forest due (i) slow moving object detection in video, (ii) smoke-colored
to a fire is usually visible from long distances. A snapshot of regiondetection,(iii) wavelet transformbased regionsmooth-
a typical wildfire smoke captured by a lookout tower camera ness detection, (iv) shadow detection and elimination, (v) co-
from a distance of 5 km is shown in Fig. 2. variance matrix based classification, with decision functions,
D (x,n), D (x,n), D (x,n), D (x,n) and D (x,n), re-
1 2 3 4 5
Guillemant and Vicente [40] based their method on the spectively, for each pixel at location x of every incoming
observationthatthemovementsofvariouspatternslikesmoke image frame at time step n. Computationally efficient sub-
plumes produce correlated temporal segments of gray-level algorithmsare selected in order to realize a real-time wildfire
pixels. They utilized fractal indexing using a space-filling detection system working in a standard PC. The decision
Z-curve concept along with instantaneous and cumulative functions are combined in a linear manner and the weights
velocity histograms for possible smoke regions. They made are determined according to the weight update mechanism
smoke decisions about the existence of smoke according to described in Section II.
the standard deviation, minimum average energy, and shape Decision functions D , i = 1,...,M of sub-algorithms
i
and smoothness of these histograms. It is possible to include do not produce binary values 1 (correct) or −1 (false), but
most of the currently available methods as sub-algorithms in they produce real numbers centered around zero for each
theproposedframeworkandcombinetheirdecisionsusingthe incoming sample x. If the number is positive (negative), then
proposed EADF method. the individualalgorithm decides that there is (not) smoke due
toforestfireintheviewingrangeofthecamera.Outputvalues
ofdecisionfunctionsexpresstheconfidencelevelofeachsub-
algorithm.Higherthevalue,themoreconfidentthealgorithm.
First four sub-algorithms are described in detail in [52]
which is available online at EURASIP webpage. We recently
added the fifth sub-algorithm to our system. It is briefly
reviewed below.
A. Covariance Matrix Based Region Classification
The fifth sub-algorithm deals with the classification of
the smoke colored moving regions. A region covariance ma-
trix [53] consisting of discriminativefeaturesis calculated for
each region. For each pixel in the region, a 9-dimensional
feature vector z is calculated as follows:
k
z = x x Y(x ,x )U(x ,x )V(x ,x )
k 1 2 1 2 1 2 1 2
"
(18)
Fig.2. Snapshotofatypicalwildfiresmokecapturedbyaforestwatchtower T
whichis5kmawayfromthefire(risingsmokeismarkedwithanarrow). dY(x1,x2) dY(x1,x2) d2Y(x1,x2) d2Y(x1,x2)
dx dx dx2 dx2
(cid:12) 1 (cid:12) (cid:12) 2 (cid:12) (cid:12) 1 (cid:12) (cid:12) 2 (cid:12)#
(cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12)
(cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12)
(cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12)
Smoke at far distances (> 100 m to the camera) exhibits
different spatio-temporal characteristics than nearby smoke where k is the label of a pixel, (x1,x2) is the location of
and fire [45]-[47]. This demands specific methods explicitly the pixel, Y,U,V are the componentsof the representationof
developed for smoke detection at far distances rather than thepixelinYUVcolorspace, dY(dxx11,x2) and dY(dxx12,x2) arethe
using nearby smoke detection methods described in [48]. horizontal and vertical derivatives of the region respectively,
The proposed approach is in accordance with the ‘weak’ calculated using the filter [-1 0 1], d2Yd(xx121,x2) and d2Yd(xx122,x2)
Artificial Intelligence (AI) framework [49] introduced by Hu- arethehorizontalandverticalsecondderivativesoftheregion
bert L. Dreyfus as opposed to ‘generalized’ AI. According calculated using the filter [-1 2 -1], respectively.
to this framework each specific problem in AI should be The feature vector for each pixel can be represented as
addressed as an individual engineering problem with its own follows:
characteristics [50], [51]. z =[z (i)]T (19)
k k
6
where,z (i)isthei hentryofthefeaturevector.Thisfeature
k t
vector is used to calculate the 9 by 9 covariance matrix
of the regions using the fast covariance matrix computation
formula [54]:
n
1
C =[c (i,j)]= z (i)z (j)−Z (20)
R R k k kk
n−1" #! (a) Negative trainingimages.
k=1
X
where
n n
1
Z = z (i) z (j)
kk k k
n
k=1 k=1
X X
and n is the total number of pixels in the region and c (i,j)
R
is the (i,j) the component of the covariance matrix.
The region covariance matrices are symmetric therefore
we only need half of the elements of the matrix for
classification. We also do not need the first 3 elements (b) Positive trainingimages
c (1,1),c (2,1),c (2,2)whenusingthelowerdiagonalele-
R R R
Fig.3. Positiveandnegative imagesfromthetraining set.
mentsofthematrix,becausethesearethesameforallregions.
Then, we need a feature vector f with 9×10/2−3 = 42
R
elements for each region. For a given region the final feature
region or not. Morphological operations are applied to the
vectordoesnotdependon the numberof pixels in the region,
detected pixels to mark the smoke regions. The number of
it only depends on the number of features in z .
k connected smoke pixels should be larger than a threshold to
issue an alarm for the region.If a false alarm is issued during
TABLEI
CONFUSIONMATRIXOFTHETRAININGSET training phase, the oracle gives feedback to the algorithm by
declaring a no-smoke decision value (y = −1) for the false
alarm region. Initially, equal weights are assigned to each
Predicted Labels sub-algorithm.Theremaybelargevariationsbetweenforestal
NotSmoke Smoke
areas and substantial temporal changes may occur within the
Actual NotSmoke 11342/(97.2)% 327/(3.8%)
Labels Smoke 49/(0.7%) 6962/(99.3%) same forestal region. As a result weights of individual sub-
algorithms will evolve in a dynamic manner over time.
A Support Vector Machine (SVM) with RBF kernel is In real-time operating mode the PTZ cameras are in con-
trained with the region covariance feature vectors of smoke tinuousscan modevisiting predefinedpresetlocations. In this
regions in the training database. 18680 images are used to mode constant monitoring from the oracle can be relaxed by
train the SVM. 7011 of the images are positive images which adjusting the weights for each preset once and then using the
haveactualsmokeandtherestarenegativeimagesthatdonot same weights for successive classifications. Since the main
have smoke. Sample positive and negative images are shown issue is to reduce false alarms, the weights can be updated
in Fig. 3. The confusion matrix for the training set is given when there is no smoke in the viewing range of each preset
in Table I. The success rate is 99.3% for the positive images and after that the system becomes autonomous. The cameras
and 97.2% for the negative images. stop at each preset and run the detection algorithm for some
The LIBSVM [55] software library is used to obtain the timebeforemovingtothenextpreset.Bycalculatingseparate
posterior class probabilities, p = Pr(label = 1|f ), where weights for each preset we are able to reduce false alarms.
R R
label = 1 corresponds to a smoke region. In this software
library, posterior class probabilities are estimated by approxi- V. EXPERIMENTAL RESULTS
matingtheposteriorswithasigmoidfunctionasin[56].Ifthe
A. Experiments on wildfire detection
posterior probability is larger than 0.5 the label is 1 and the
The proposedwildfire detection scheme with entropy func-
region contains smoke according to the covariance descriptor.
tional based active learning method is implemented on a PC
The decision function for this sub-algorithm is defined as
with an Intel Core Duo CPU 2.6GHz processor and tested
follows:
with forest surveillance recordings captured from cameras
D (x,n)=2p −1 (21)
5 R mountedontopofforestwatchtowersnearAntalyaandMugla
where 0 < p < 1 is the estimated posterior probability provinces in Mediterranean region in Turkey. The weather is
R
that the region contains smoke. In [53], a distance measure stable with sunny days throughoutentire summer in Mediter-
basedoneigenvaluesareusedtocomparecovariancematrices ranean.Ifithappenstorainthereisnopossibilityofforestfire.
but we found that individual covariance values also provide The installed system successfully detected three forest fires in
satisfactory results in this problem. the summer of 2008. The system is also independently tested
As pointed above decision results of five sub-algorithms, by the Regional Technology Clearing House of San Diego
D , D , D , D and D are linearly combined to reach a State University in California in April 2009 and it detected
1 2 3 4 5
finaldecisiononagivenpixelwhetheritisapixelofasmoke the test fire and did not produceany false alarms. A snapshot
7
from this test is presented in Fig. 4. It also detected another Algorithm 3 The pseudo-code for the universal predictor
forest fire in Cyprus in 2010. The proposed EADF strategy is Universal Predictor(x,n)
for i = 1 to M do
ℓ(y(x,n),D (x,n))=[y(x,n)−D (x,n)]2
i i
vi(n+1)= Pejxepx(p−(−21c2ℓ1c(ℓy((yx(,xn,)n,D),Di(xj(,nx,)n)))))
end for
yˆ (x,n)= v (n)D (x,n)
u i i i
if yˆ (x,n)≥0 then
u
P
return 1
else
return -1
end if
The POCS based scheme, the ULP based scheme, the
EADF based scheme, and the non-adaptive approach with
fixed weights are compared in the following experiments. In
Tables II and III, 6-hour-long forest surveillance recordings
containing actual forest fires and test fires as well as video
sequences with no fires are used.
Fig.4. Asnapshotfromanindependent testofthesystembytheRegional We have 7 test fire videos ranging from 1 km to 4 km
Technology Clearing House of San Diego State University in California in captured in Antalya and Mugla provinces in Mediterranean
April2009.Thesystemsuccessfullydetectedthetestfireanddidnotproduce
region in Turkey, in the summers of 2007 and 2008. To the
any false alarms. The detected smoke regions are marked with bounding
rectangles. best of our knowledge this is the largest database of forest
fire clips having the initial stages of wildfires. The database
is also used by the European Commission funded project
comparedwith the,projectionontoconvexsets(POCS) based
FIRESENSE[58].Alloftheabovementioneddecisionfusion
algorithm and the universal linear predictor (ULP) scheme
methods detect forest fires within 20 seconds, as shown in
proposedbySingerandFeder[57].TheULPadaptivefiltering
Table II. The detection rates of the methods are comparable
method is modified to the wildfire detection problem in an
toeachother.Ontheotherhand,theproposedadaptivefusion
online learning framework. In the ULP scheme, decisions of
strategysignificantlyreducesthefalsealarmrateofthesystem
individual algorithms are linearly combined similar to Eq. 1
by integrating the feedback from the guard (oracle) into the
as follows:
decision mechanism within the active learning framework
described in Section II. In Fig. 5 a typical false alarm issued
yˆu(x,n)= vi(n)Di(x,n) (22) for moving tree leaves (which cause the white background
i to appear as moving smoke), by an untrained algorithm with
X
decision weights equal to 1 is shown from the clip V12. The
5
proposed algorithm does not produce a false alarm in this
where the weights, v (n), are updated according to the ULP
i
video.
algorithm, which assumes that the data (or decision values
The proposed method produces the lowest average error
D (x,n), in our case) are governed by some unknown prob-
i
in our data set. A set of video clips containing moving
abilistic model P [57]. The objective of a universal predictor
cloud shadows and other moving regions that usually cause
is to minimize the expected cumulative loss. An explicit
false alarms is used to generate Table III. These video clips
description of the weights, v (n), of the ULP algorithm is
i
are especially selected. The table shows the average pixel
given as follows:
classification error for each method. The average pixel error
for a video sequence v is calculated as follows:
exp(− 1ℓ(y(x,n),D (x,n)))
vi(n+1)= exp(−2c1ℓ(y(x,n),Di (x,n))) (23) E¯(v)= 1 FI (en) (25)
j 2c j F N
I I
n=1
P X
where N is the total number of pixels in the image frame,
where c is a normalization constant and the loss function for I
F is the number of frames in the video sequence, e is the
the i-th decision function is: I n
sum of the squared errors for each classified pixel in image
frame n. Exceptfor one video sequenceEADF based method
ℓ(y(x,n),D (x,n))=[y(x,n)−D (x,n)]2 (24) has the lowest pixel classification error.
i i
In Fig. 6, the squared pixels errors of POCS and EADF
based schemes are compared for the video clip V12. The
Theconstantcistakenas4asindicatedin[57].Theuniversal weights are updated until 125th frame for both algorithms.
predictor based algorithm is summarized in Algorithm 3. ThePOCSbasedalgorithmhasaninitialstageuntil30thframe
8
Fig.6. AveragesquaredpixelerrorsforPOCSandEADFbasedalgorithms forthevideoseuqence V12.
TABLEII
FRAMENUMBERSATWHICHANALARMISISSUEDWITHDIFFERENT
METHODSFORWILDFIRESMOKECAPTUREDATVARIOUSRANGESAND
FPS.ITISASSUMEDTHATTHESMOKESTARTSATFRAME0.
Video Range Capture Frame number of first alarm
Sequence (km) Frame Rate POCS Universal Fixed EADF
(fps) Based Weights Based
V1 1 7 47 48 47 42
V2 3 7 135 142 141 125
V3 3 7 130 101 37 134
V4 4 25 160 154 70 150
V5 3 9 65 55 57 56
V6 2 5 70 74 76 75
V7 2 5 93 74 41 83
Fig. 5. False alarm from clip V12. Moving tree leaves in a forestal area Average - - 112.85 92.57 67 97.85
causeafalsealarminanuntrained algorithm withdecisionweights equalto
1(depicted asabounding box).Theproposedalgorithm does notproduce a
5
falsealarminthis video.
in real-time. On the other hand the UCI data sets are fixed.
where the error graduallydropsto zero, whereas EADF algo-
Therefore the dataset is divided into two parts. The first part
rithmconvergesafteronly2frames.Thetrackingperformance
is used for training.
of the EADF algorithm is also better than the POCS based
Duringthetrainingphase,weightsofdifferentclassifiersare
algorithm which can be observed after the frame number 180
determined using the EADF update method. In testing stage
at which some of the sub-algorithms issue false alarms.
the fixed weights obtained from the training stage are used
The software is currently being used in 59 forest watch
to combine the classifier decisions which process the data
towers in Turkey.
in a sequential manner because both the POCS and EADF
frameworks assume that the new data arrive in a sequential
B. Experiments on a UCI Dataset manner.
TheproposedmethodisalsotestedwithadatasetfromUCI The test is performed on the ionosphere data from UCI
(University of California, Irvine) machine learning repository machine learning repository that consists of radar measure-
to evaluate the performance of the algorithm in combining ments to detect the existence of free electrons that form a
different classifiers. In the wildfire detection case the image structureintheatmosphere.Theelectronsthatshowsomekind
data arrivessequentially and the decision weights are updated of structure in the ionosphere return “Good” responses, the
9
TABLEIII
AVERAGESQUAREDPIXELERRORSISSUEDBYDIFFERENTMETHODSTO VI. CONCLUSION
VIDEOSEQUENCESWITHOUTANYWILDFIRESMOKE. Anentropyfunctionalbasedonlineadaptivedecisionfusion
(EADF) is proposed for image analysis and computer vision
Frame Video applications with drifting concepts. In this framework, it
Average Errors (×10−3)
is assumed that the main algorithm for a specific applica-
Video Rate Duration
tion is composed of several sub-algorithms each of which
Sequence (fps) (sec.) POCS Universal Fixed EADF
yielding its own decision as a real number centered around
Based Weights Based zero representing its confidence level. Decision values are
V8 7 480 7.0076 94.6995 138.2102 9.3712 linearly combined with weights which are updated online
by performing non-orthogonale-projections onto convex sets
V9 25 300 8.3375 38.2390 54.9168 5.5494
describing sub-algorithms. This general framework is applied
V10 25 600 8.9892 77.5699 101.7512 3.2637 to a real computer vision problem of wildfire detection. The
V11 10 900 5.2054 23.6602 30.0455 2.4314 proposed adaptive decision fusion strategy takes into account
thefeedbackfromguardsofforestwatchtowers.Experimental
V12 7 60 15.5350 98.0371 136.8163 12.1520
results show that the learning duration is decreased with the
Average - - 9.0149 66.4411 92.3480 6.5535
proposed online adaptive fusion scheme. It is also observed
that error rate of the proposed method is the lowest in our
dataset, comparedtouniversallinear predictor(ULP) andthe
projection onto convex sets (POCS) based schemes.
othersreturn“Bad”responses.Thereare351sampleswith34- The proposed framework for decision fusion is suitable for
element feature vectorsthat are obtained by passing the radar problems with concept drift. At each stage of the algorithm,
signals through an autocorrelation function. In [59], the first themethodtracksthechangesin thenatureoftheproblemby
200 samples are used as training set to classify the remaining performing an non-orthogonale-projection onto a hyperplane
151testsamples.Theyobtained%90.7accuracywithalinear describing the decision of the oracle.
perceptron, % 92 accuracy with a non-linear perceptron, and
% 96 accuracy with a back propagation neural network. ACKNOWLEDGMENT
For this test SVM, k-nn (k-Nearest Neighbor) and NCC
This work was supported in part by the Scientific and
(normalizedcross-correlation)classifiersareused.Also,inthis
TechnicalResearch Council of Turkey,TUBITAK, with grant
classificationthedecisionfunctionsoftheseclassifiersproduce
no. 106G126 and 105E191, in part by European Commis-
binary values with 1 corresponding to “Good” classification
sion 6th Framework Program with grant number FP6-507752
and-1correspondingto“Bad”classificationratherthanscaled
(MUSCLE Network of Excellence Project) and in part by
posterior probabilities in the range [−1,1]. FIRESENSE (Fire Detection and Management through a
The accuraciesof the sub-algorithmsand EADF are shown Multi-Sensor Network for the Protection of Cultural Heritage
in Table IV. The success rates of the proposed EADF and AreasfromtheRisk ofFireandExtremeWeatherConditions,
POCS methods are both % 98.01 which is higher than all the FP7-ENV-2009-1244088-FIRESENSE).
sub-algorithms. Both the entropic projection and orthogonal
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