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Probabilistic Target Detection by Camera-Equipped UAVs
Andrew Symington, Sonia Waharte, Simon Julier, Niki Trigoni
Abstract— This paper is motivatedby thereal world problem
of search and rescue by unmanned aerial vehicles (UAVs). We
consider the problem oftrackingastatic targetfrom a bird’s-
eye view camera mounted to the underside of a quadrotor UAV.
We begin by proposingatarget detection algorithm, which we
then execute on a collection of video frames acquired from
four different experiments. We show how theefficacyofthe
target detection algorithm changes as a function of altitude.
We summarise this efficacy intoatable which we denote the
observation model. We then run the target detection algorithm
on a sequence of video frames and use parameters from the
observation model to update a recursive Bayesian estimator.
Theestimator keeps track ofthe probability that a target
is currently in view ofthecamera, which werefer to more
simply as target presence. Between each target detection event
the UAV changes position and so the sensing region changes.
Under certain assumptions regarding the movement ofthe UAV,
the proportion of new information may be approximated toa
value, which we thenuse to weightthe prior in each iteration
oftheestimator. Through a series of experiments we show how
the value ofthe prior for unseenregions, the altitude ofthe
UAV and thecamera sampling rate affectthe accuracyofthe
estimator. Ourresults indicate thatthere is no single optimal
sampling rate for all tested scenarios. We also show how the
prior may be used as a mechanism for tuning theestimator
according to whether a high false positive or high false negative
probability is preferable.
Index Terms—UAV, vision, target detection, sensing
I. INTRODUCTION
Unmanned Aerial Vehicles (UAVs) are typically commis-
sioned for tasks that are perceived as too dull or dangerous
for a humanpilottocarryout [13]. In the past, research
involving UAVs was constrainedbylargeand expensive
flight platforms whichofferedgreater payloads. However,
recent advances in embedded computing and sensors have
made small, low-cost autonomoussystems accessible to the
broaderresearch community.
In this paper weconsider a single UAV with a bird’s-
eye view video camera, which it uses to sense the world
beneath it. Computer vision is an active research field that
has already seenvarious applications to UAVs, such as
navigation [12], stabilisation and localisation [11], feature
tracking [7], SLAM [5], collision avoidance [15] and au-
tonomous landing [3]. The work in this paper was inspired
by Mondragon et al [7] who use vision-based targettracking
This work wassupportedbythe SUAAVE project. Further information
aboutthis projectcanbe found at http://www.suaave.org.
Andrew Symington, Niki Trigoni and Sonia Waharteare with the Oxford
University Computing Laboratory, Wolfson Building, Oxford, OX13QD,
UK.niki.trigoni@comlab.ox.ac.uk
Simon Julier is with the Department of Computer Science, Uni-
versity College London, Malet Place, London, WC1E 6BT, UK.
s.julier@cs.ucl.ac.uk
to estimate the velocityof the UAV relative to a global visual
reference frame. In this work weadopt a similar vision-
based algorithm, except we use it to track whether or not a
particular targetis inview of thecamera. We then measure
theeffect of thealtitude of the UAV and the frame rate of
thecamera on theaccuracyof the tracker over time.
We beginbyproposing atarget detection algorithm that
acts as a binary classifier or, put more simply, it determines
whether or not a target object exists in a video frame. One
would expectthattheefficacyof such aclassifier varies
according to the physical appearance of the target, camera
resolution,lighting conditions, etc. However, inour work
we will assume thatthese factors remain constant and the
efficacy issimply a function of the UAV’s altitude:the further
thecamera from the target, the less information is available
to the target detection algorithm, which causes it to miss
targets. To this end, we run the target detection algorithm on
a series of video frames and tabulate its efficacy as a function
of altitude, which we denote the observation model.
The target detection algorithm treats eachframe indepen-
dently and so we therefore introduce a recursive Bayesian
estimator to fuseaseries of noise-affecteddetection events
(observations) over time. Theestimator takes thisseries to
track the probabilityoftarget presence (whether the target
is inview of thecamera), taking into accounttheefficacy
of the target detection algorithm atthecurrent altitude. The
values it uses toquantify this efficacy are drawndirectlyfrom
the observation model. Our estimator also takes into account
the factthatthecamera view changes over time. Under
certain assumptions regarding the movement of the UAV, the
proportion of new information is givenbythe sampling rate
of the detector. We therefore introduce a term that decays
theestimateaccording to the proportion of new information,
which wecall the exploration ratio, thatis addedbetween
successive observations.
The remainder of this paper is organised as follows. In
Section II we describe the series of experiments that were
conducted toobtain the videodata used in this paper and
show the post-processing steps that we followed to label
the images with a ground truth. In Section III we beginby
describing the target detection algorithm. We then measure
theefficacyof this algorithm against a set of images in
order to constructthe observation model. In Section IVwe
firstly show the methodology behind thecalculation of the
exploration ratio for ourUAV platform and then introduce the
recursive Bayesian estimator. In Section Vwe first measure
theaccuracyofour estimator by comparing the probability
of target presence againstthe ground truthover time, varying
the UAV altitude, sampling rateand prior. We then comment
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on our findings. Section VI concludes this paper.
II.DATAACQUISITION AND P RE PARATION
In thissection we discuss howour videodata was acquired
and thenprepared for use by the target detection algorithm.
A. Acquisition
Inorder toobtainvideodata used in this paper we fixed a
FlyCamOne2 video camera to the underside of an Ascending
Technologies Hummingbirdquadrotor UAV. A number of
targets were positioned in a 20m×20mgridona flat grass
field. We flew the UAV over the grid at fixed altitudes of
5m, 10m, 15m and 20m. In addition to capturing videodata
at 27 frames per second, the UAV also recorded GPS and
inertial dataat around 10Hz. We found thatthe human target
depicted in Fig. 2 consistentlyyielded a sufficient amount of
information to train an effective target detection algorithm,
so we used it as the targetinour model.
B. Preparation
The first objective of data preparation is to isolateaset
of example video frames that we will use to train the target
detection algorithm. Eachof these video frames must contain
anunoccluded example image of the target. We draw a
rectanglearound the target and only the information within
that rectangle is used to train the target detection algorithm.
For our data set we used ten such frames for each altitude.
These frames constitute the training set, while the remainder
constitute the evaluation set.
The second objective is to label eachframe in theevalua-
tion set with a ground truth. The ground truth is effectively a
binary flag which tell us whether the framecontains either(i)
some or all of the target, or(ii)none of the target at all. The
efficacyof the target detection algorithm will be measured
by comparing the result of the detector againstthe ground
truth, for all frames in theevaluation set.
III. TARGET DETECTION
Thissection begins by describing the target detection
algorithm that we used. Our goalisnottopresent a novel and
provably superior algorithm, but rather to leverageexisting
techniques to createarealistic system, which wecanuse to
generate meaningful results. In essence,onecouldusean
alternate method such as Violaand Jones’s [14]boosting
to achieveexactly the same outcome, perhaps with a greater
accuracy. However, regardless of thealgorithm thatis chosen,
it will act as a binary classifierfor unseen images. Itthe
second part of thissection we showhow to measure the
efficacyof the target detection algorithm and summarise it
in the form of anobservation model, which we will thenuse
in the next section toupdate our belief of target presence.
A. The target detection algorithm
For our application we requireatarget detection algorithm
that determines whether or not a single imagecontains an
instance of the target. Inorder to achieve this we use Bay,
Tuytelaars and Van Gool’s [1] Speeded-up Robust Features
Fig. 1. This diagram provides a high-level summaryof the target detection
algorithm and the method by which it was evaluated. Recall thatthe video
frames are split into a training set and evaluation set. For eachframe
in theevaluation set, the target detection algorithm loops through the
templateexampleand determines whether it contains the target object: the
algorithm uses SURF keypoint matching with FLANN to find the most
likelyhomographic projection of the training image into theevaluation
image. The result of the target detection algorithm is compared to the ground
truth labelto form the observation model.
(SURF)1. The features producedbySURF are, essentially,
keypoints on a 2D image that are robusttoslightchanges
in scale, rotation and perspective. Each SURF keypoint has
an associated multidimensional descriptor2that characterises
the grayscale image gradientin the region surrounding the
keypoint. The similaritybetween twokeypoints is calculated
by measuring the distance between their descriptors with
the n-dimensional Euclidean metric. The Hessiandetermi-
nantthresholdgoverns the sensitivityof the SURF detector
and, hence, the number offeatures that are returned. We
determined empirically that a thresholdof500 culled many
of the weaker(and oftenbackground) keypoints, while
maintaining an acceptable number of keypoints on objects
at high altitudes.
Recall thatin the previoussection we divided all the video
frames inour data setinto a training set and an evaluation
set. For clarity, let us assume that weare working with the
data from onealtitudeonly. Now, assume that weare given
somearbitrary image which might or mightnot contain the
target, or part of a target. We refer to this as the unseen
image. The target detection algorithm simply loopsover all
images in the training set and attempts to locateeachone
of these images within the unseen image. If a location is
1Thealgorithm that we implemented is basedonthe find obj.cpp sample
code in the OpenCV pre-2.0distribution.
2Usually a 64 or128 double vector, depending on the required resolution.
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found for any of the training images thealgorithm returns
apositive detection event, which signals thatthe target was
found. Otherwise, a negative detection eventis returned.
What remains tobeexplained is how the training image is
located in anunseen image. This is where the SURF features
are used. The detection algorithm begins by calculating the
SURF keypoints for both images. Theaim is to find a
correspondence between the keypoints in the training image
and the keypoints in the unseen image. Inorder todo
so the Fast Library for Approximate Nearest Neighbors
(FLANN)[8] algorithm is used. This algorithm provides a
fast approximation to knearest-neighbour classification. The
result being that eachkeypointin the unseen image is paired
withits closest keypointin the training image. Recall that
the similarityof twokeypoints is calculatedbymeasuring
the distance between their two associated SURF descriptors.
In the next stage of the detection phase we removeall
of the weak correspondences. Weak correspondences usually
occur when some keypointlocatedonthe background clutter
in the unseen image is incorrectlypaired with a keypoint
in the training image; FLANN always maps to the nearest
neighbour, regardless of the distance to it. The intuitive way
todothis wouldbe to threshold thecorrespondences based
on the distance betweeneachpair of keypoints. Inpractice,
this heuristic fails. A superior approach involves thresholding
basedonthe distance ratiobetweeneachkepyointin the
unseen imageand its two closest matching neighbours. That
is, if the ratioof the distances between the two closest
matches is greater than some threshold wecull thecorrespon-
dence — the idea being thatifone keypointin the unseen
image maps to twokeypoints in the template image with
equal strength, it isunlikely thatitdescribessome particular
feature uniquely [6]. Rather, it is more likely thatthe feature
is background clutter being arbitrarily mapped to close
neighbours indescriptor space. Ramisa et al [10] discuss the
selection of this threshold for a varietyof keypoint detectors.
Theirresearch shows that good results are typicallyobtained
for SURF using a thresholdbetween0.6 and 0.8. Through
experimentation we found that a value of 0.6 was best for
our application: many background keypoints were discarded,
while meaningful keypoints were preserved.
Finally, thecorrespondence setis passed to the RANdom
SAmple Consensus (RANSAC)[4] algorithm, whichdeter-
mines the mostlikelyprojection of the template image into
the unseen image, given the presence of some statistical
outliers. Figure 2 illustrates this process –it shows the
correspondence set as acollection of whitelines connecting
the template image keypoints to the unseen image keypoints.
The projection isshown as a bounding polygon in the scene.
If the RANSAC algorithm finds a projection and it has
greater than fivecorrespondences weassume thatthe scene
contains the target. Through experimentation we found that
if the threshold isset any lower the target detection algorithm
returnssignificantly more false detections atlower altitudes.
Conversely, if we setthe threshold any higher, the target
detection showssignificantly more false negatives occur at
higher altitudes.
Fig. 2. Atthe top left of this figure is an example training imageand
beneath it is anunseen imagecontaining the target. SURF keypoints for
both the targetimageand scenearecalculated. FLANN is used to find
mappingsfrom keypoints in the unseen image tokeypoints in the template
image (shown as lines in the figure). For clarity, we have not drawn any
weak mappings – those whichhaveadistance ratio above the threshold.
The RANSAC algorithm uses the mappings to calculate the mostlikely
projection of the training image into the unseen image (shown as a polygon).
B. Observation model
The performance of a machine learning algorithm is
measuredbycounting the number of true positives (TP), true
negatives (TN), false positives (FP) and false negatives (FN).
For a binary classifier these values are typically expressed in
the form of a 2x2 confusion matrix [9].
To evaluate the performance of the target detection al-
gorithm weexecuted it on every frame in theevaluation
set and compared the detection result to the ground truth.
If the target detection algorithm agreed with the ground
truth, we incremented the TP and TN count for positiveand
negative detection events respectively. If the target detection
algorithm detected a targetincorrectly, the false positive
count was incremented. On the other hand, if the target
detection algorithm failed todetect a targetthat was there,
the false negativecount was incremented. We repeated this
process for all four altitudes and the resultant confusion
matrix is listed in Table I.
The observation modelis deriveddirectlyfrom theconfu-
sion matrix. In essence, the observation modelissimply the
false positive probabilityαhand false negative probabilityβh
as a function of the UAV’s altitudeh. Wecalculate values
for αhand βhusing Eqn. 1 and Eqn. 2 respectively. The
H"GA
values for our data set arealso listed in Table I .
αh=F P
(F P +T N )(1)
βh=F N
(F N +T P )(2)
IV. RE CU RS IV E BAY ESIAN ESTIMATOR
In thissection we firstlydescribe how to measure the
amount of new information thatis introducedbetween two
observations, which wecall theexploration ratio. We then
presentthe recursive Bayesian estimator, whichuses both
theexploration ratio and the observation model for a given
altitude to maintain a best estimate of target presence.
TABLE I
CONFU SION M ATRI CES AND OB SE RVATION MODEL
Altitude Truth Detected Not Detected αhβh
5m Present 88 24 0.24569 0.21428
Absent 685 2103
10mPresent 100 25 0.06286 0.20000
Absent 87 1296
15mPresent 516 258 0.03107 0.33333
Absent 38 1185
20mPresent 571 302 0.00130 0.34593
Absent 2 1526
A. Calculating theexploration ratio
The role of theexploration ratio is to measure the
proportion of new information thatis introduced at each
observation, resulting from the movement of the UAV, as
a function of the UAV’s altitudeand the sampling rate of the
sensor. To simplify thecalculation of theexploration ratio we
will make the following assumption regarding the movement
of the UAV:italways moves at aconstant speed in a single
direction. Although onecoulduseamoreaccurate method
thattakes into accounttheattitudeand velocityof the UAV,
for this initial study we useasimpler approximation.
Let xhand yhbe the length and widthof thecamera
sensing region at somealtitudeh, all of which are given
in meters. Both xhand yhare related tooneanother
according to theaspect ratioof thecamera. In Fig. 3 we show
thecamera sensor coverageafter the UAV displacessome
distance das a result of moving in the specifieddirection.
The new, shared and lost areas areclearly marked in the
figure. Theexploration ratioeissimply the ratioof new
area to entire observation area. Inorder to calculate this ratio
we’ll first need a value for d. The value for dis calculated
by dividing theconstant velocityvof the UAV (in meters
per second)by the sampling rate r(in frames per second).
Eqn. 3 shows the full equation for calculating e.
e=dxh
yhxh
(3)
=v
ryh
(4)
Fig. 3. Thecoverage or observation region of the video camera sensor is
givenbya rectangle of length xand width y. Betweeneachobservation
the UAV movessome small distance dand the observation region changes
accordingly. The ratioof new area (d×xh)over the total sensing area
(xh×yh) is referred to as theexploration ratio and it varies as a function
of altitudeand sampling rate.
We determined the xhand yhvalue for each altitude in
our videodata set using the one meter intervalticks on the
star-shaped calibration pattern that we laidonthe ground.
Thecalibration pattern is clearlyvisible in the sample frame
shown in Fig. 2. We then measured theaverage velocityof
the UAV by integrating theacceleration readingsfrom the
inertial data todetermineareasonable value for v, which
turnedouttobe slightlyover one meter per second. Finally,
wecalculated the evalue for all combinations of the four
altitudes (5m, 10m, 15m and 20m) and sampling rates (1 ,5
and 10 frames per second) that wechose to test. The result
of ourcalculations are listed in Table II.
TABLE II
EXP LOR ATION R ATIO FO R VA RI OUS ALT ITUDE S AND SA MPL ING R ATES
Altitudeh yhr= 1 FPS r= 5 FPS r=10 FPS
5m 4m 0.250000 0.050000 0.025000
10m 7m 0.142857 0.028571 0.014286
15m10m 0.100000 0.020000 0.010000
20m13m 0.076923 0.015385 0.007692
B. The recursive Bayesian estimator
The role of the recursive Bayesian estimator is to take
a series of observations and maintain the the probabilityof
target presence. Moreover, theestimator takes into account
the factthatthecamera view changes over timeand also that
there issomeerror associated with the observation,bothof
whichvary with altitude.
The observation model parameters are the probabilityof
false positiveand the probabilityoffalse negative, we defined
earlier as αhand βhrespectively for somealtitudeh. Let us
assume thatthecamera sensor has an observation region
O(kt)which is visible from thecamera when the UAV is
located at position ktattime t. Let xTrepresentthe target.
H"GF
We use Chung’s [2] error model, where dt= 0 and dt= 1
denote negativeand positive target detection events:
P rh(dt= 1|xT∈O!kt") = 1 −βh
P rh(dt= 0|xT∈O!kt") = βh
P rh(dt= 0|xT$∈ O!kt") = 1 −αh
P rh(dt= 1|xT$∈ O!kt") = αh
Let dtbe the tth observation,Dtbe the set of tobserva-
tions and let xT= 1 be theeventthat a target exists in a
particularframe. The probability thatthe targetis presentin
the frameattime tis computedusing Bayes rule:
P r(xT= 1|Dt) =
P r(dt|xT= 1)P r(xT= 1|Dt−1)
P r(dt|Dt−1)(5)
The updateequation for the recursive Bayesian estimator
is conditional on whether a positive or negative detection
eventis encountered. Eqn. 6 shows this updateequation.
Pt=#(1−βh)Pt−1
(1−βh)Pt−1+αh(1−Pt−1),if dt= 1
βhPt−1
βhPt−1+(1−αh)(1−Pt−1),if dt= 0 (6)
So far theestimator has implicitly assumed thatthecamera
view does not change betweenobservations. However, since
the UAV is moving this is notthecase. We therefore
introduce a state transition term to theestimator thattakes
into accountthat a portion of thecurrent framecontains
new information. The probabilityP0represents our prior
belief of target presence for some unexplored region. In each
iteration the refactoredprior, given in Eqn. 7, is a weighted
combination of the previousstep’s posterior and P0.
Pt−1←eP0+ (1 −e)Pt−1(7)
This weightedupdateequation causes theestimate to
convergeexponentially to P0over time. This is useful for two
reasons. Firstly, it takes into accountthe factthatthecamera
changes position over timeand, hence,objects may appear
and disappearfrom view. Secondly, it provides a method of
ensuring thattheestimate never converges to zeroorone
after a series of positive or negative detection events, which
happens as a result of the limited storagecapacityof floating
point data types.
V. EXPERIMENTS AND RESULTS
Weconducted a series of experiments inorder to mea-
sure theeffect of altitude, sampling rateand prior on the
performance of theestimator. We used real streams of
video frames, taken from four different altitudes (5m, 10m,
15m and 20m)3. For example, Fig. 4 shows the result of
running the Bayesian estimator on a video stream taken
from an altitude of 5m. If after anobservation the posterior
probabilityof theestimator exceeds 0.5 (see the dashed line
in the bottom three graphs in Fig. 4) weconsider this tobea
positive detection event. By comparing the ground truth with
3Recall thattheaccuracyof the target detection algorithm dependson
thealtitude, asshown in Table I.
theestimator’s predictions, wecan measure the probability
of the detector making a false positive prediction and that of
making a false negative prediction. We use these two metrics
to assess theestimator’saccuracy4.
The graphs in Fig. 5 show theaccuracyof theestimator
when thealtitude is 5m and 20m, and for different prior(P0)
values and sampling rates. Our first observation is that as the
prior increases, so the false positive probability increases,
whereas the false negative probabilitydecreases. Our second
observation is thatthe lower the sampling rate, the higher
theexploration ratio, and thus the higher the impact of prior
on the false positiveand false negative probabilities. These
twoobservations held for all four altitudes tested, although
not all graphs are included for space reasons.
Our thirdobservation relates to theeffect of altitudeon
the two estimator metrics. When thealtitudechanges the
estimator uses a new set of parameters from the observation
model and a different exploration ratio. Theeffect of the
exploration ratio is relatively straightforward and we dis-
cussed it in the previous paragraph. However, theeffect of
the observation model parameters is less obvious, despite
there being a generaltrend in the parameters themselves —
in Table I we see that αhand and βhdecreaseand increase
respectively with altitude. Moreover, any trend that might
exist maybe further obfuscatedbythe factthat different
video sequences were used to evaluate the four different
altitudes. Therefore, wecannot draw any conclusiveevidence
from ourresults that suggest a trend basedonaltitude.
Finally, our experimental resultsshow thatthatthere is no
best sampling rate for all scenarios. The optimal sampling
rate dependson thealtitude, on the prior, as well as on
whether theapplication is more interested in reducing false
positives orfalse negatives.
VI. CONCLUSION AND FUTURE WORK
In this paper we use videodata to train a target detection
algorithm and measure parameters for anobservation model
that describes its efficacy. We then implemented a recursive
Bayesian estimator to fuseaseries of detectionsover time,
taking into accountthe observation model and exploration
ratio associated with thealtitudeat which the observations
occur. Finally, weconducted a series of experiments to test
the impact of the prior, altitudeand sampling rate on the
performance of theestimator, compared to the ground truth.
Whileourresultsshow that sampling rate has a significant
effecton theestimator’s performance,it is clear thatthere
is no optimal sampling rate that fits all scenarios. The
prior shouldbechosen in conjunction with theapplication
requirements — in thecase of search and rescue one would
seek to minimize the false negative probability, while for
situations where thereareenergy orresource constraints one
would seek to minimize the false positive probability.
In future work we plan to run the full estimator online. We
alsoplan to conduct a detailed study ofhow altitudeaffects
the performance of theestimator.
4These probabilities must not beconfused withαhand βh, which
measure theaccuracyof the target detection algorithm.
H"A"
No
Yes
0 50 100 150 200 250 300 350
Presence
Time (seconds)
Ground truth for 5m altitude
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200 250 300 350
Detection probability
Time (seconds)
5m altitude, 1 frame per second (prior=0.05)
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200 250 300 350
Detection probability
Time (seconds)
5m altitude, 5 frames per second (prior=0.05)
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200 250 300 350
Detection probability
Time (seconds)
5m altitude, 10 frames per second (prior=0.05)
Fig. 4. The top graph shows the ground truth for the videodatacaptured at
5m. The three graphs below show theevolution of the probabilityof target
presence for the same altitudeand period for 1 FPS, 5 FPS and 10 FPS.
The dashed lineat 0.5 is the threshold for a positive detection.
VII. ACKNOWLEDGMENT S
This research wassupportedbythe Sensing Unmanned
Autonomous Aerial Vehicles (SUAAVE) projectunder grants
EP/F064217/1, EP/F064179/1 and EP/F06358X/1. Specifi-
cally, we’d like to thank Stephen Hailes, Renzode Nardi,
Graeme McPhillips, Mohib Wallizadaand Dietmar Backes
for assisting with theacquisition of the videodata.
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Probability of FP
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Probability of FN
Prior
False negative probability as a function of prior (altitude=20m)
1 FPS
5 FPS
10 FPS
Fig. 5. The four graphs above showhow the value of the prior affects
the performance of theestimator, in terms of the false positiveand false
negative probabilities for varioussampling rates. The top and bottom two
graphs were generated from 5m and 20m data respectively.
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