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Research ArticleMultifeature Fusion Vehicle Detection Algorithm
Based onChoquet Integral
Wenhui Li,1,2,3 Peixun Liu,1 Ying Wang,1,2 and Hongyin Ni1
1 College of Computer Science and Technology, Jilin University,
Changchun 130012, China2 State Key Laboratory of Automotive
Simulation and Control, Jilin University, Changchun 130022, China3
Key Laboratory of Symbolic Computation and Knowledge Engineering of
Ministry of Education, Jilin University,Changchun 130012, China
Correspondence should be addressed to Ying Wang; wangying
[email protected]
Received 13 May 2014; Accepted 25 June 2014; Published 24 July
2014
Academic Editor: Weichao Sun
Copyright © 2014 Wenhui Li et al. This is an open access article
distributed under the Creative Commons Attribution License,which
permits unrestricted use, distribution, and reproduction in any
medium, provided the original work is properly cited.
Vision-based multivehicle detection plays an important role in
Forward Collision Warning Systems (FCWS) and Blind SpotDetection
Systems (BSDS). The performance of these systems depends on the
real-time capability, accuracy, and robustness ofvehicle detection
methods. To improve the accuracy of vehicle detection algorithm, we
propose a multifeature fusion vehicledetection algorithm based on
Choquet integral. This algorithm divides the vehicle detection
problem into two phases: featuresimilarity measure and multifeature
fusion. In the feature similarity measure phase, we first propose a
taillight-based vehicledetectionmethod, and then vehicle taillight
feature similaritymeasure is defined. Second, combiningwith the
definition of Choquetintegral, the vehicle symmetry similarity
measure and the HOG + AdaBoost feature similarity measure are
defined. Finally, thesethree features are fused together by Choquet
integral. Being evaluated on public test collections and our own
test images, theexperimental results show that our method has
achieved effective and robust multivehicle detection in complicated
environments.Ourmethod can not only improve the detection rate but
also reduce the false alarm rate, whichmeets the engineering
requirementsof Advanced Driving Assistance Systems (ADAS).
1. Introduction
As an important part of the intelligent transportation
system(ITS), the Advanced Driving Assistance Systems (ADAS)can
significantly improve the driving safety. Forward Col-lision
Warning Systems (FCWS) and Blind Spot DetectionSystems (BSDS) are
principal portions of ADAS, and theirperformance depends on the
real-time capability, accuracy,and robustness of the vehicle
detection method. Recently,with the increasing maturity of visual
sensors, vision-basedvehicle detection has become a hot topic in
the field ofintelligent vehicle. There are plenty of approaches
proposedfor the day time vehicle detection. These methods can
bedivided into the following categories: methods based on
priorknowledge, such as shadow-based [1, 2], taillight-based [1,2],
horizontal (vertical) edge-based [2–4], and symmetry-based vehicle
detection method [2]; methods based onstereo vision; this type of
method detects vehicles by using
the three-dimensional information. The most widely usedmethods
are inverse perspective transformation (IPM) basedmethod and
disparity map based method [1]; template-basedmethods use
predefined patterns of vehicle class and performcorrelation between
the image and the template [1]; the maindetection steps of
appearance-based methods are as follows:the appropriate descriptors
are first used for representingvehicles in the image; then the
machine learning methodsare used to train these descriptors. Much
processes havebeen made in appearance-based vehicle detection, such
asalgorithm based on HOG + AdaBoost [5], Haar + HMM[6], Haar +
AdaBoost [7–9], HOG + SVM [10], PCA – ICA+ GMM [11], and minimum
Mahalanobis distance classifier[12]. The method based on the motion
information detectsvehicles by using the motion information between
vehiclesand scenes, such as finding out vehicles by calculating
thechange of optical flow information which is caused by
therelative motion of vehicles or scenes [13].
Hindawi Publishing CorporationJournal of Applied
MathematicsVolume 2014, Article ID 701058, 11
pageshttp://dx.doi.org/10.1155/2014/701058
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2 Journal of Applied Mathematics
To improve the accuracy of vehicle detection methods,several of
above methods are combined together to detectvehicles. Lin et al.
[3] applied the SURF and edge featuresto represent the vehicle and,
combining with probabilisticmethods, their methods have achieved
vehicle detection inthe blind spot area. Chen et al. [6] first used
a road modellingmethod to confine detection regions, and then
Haar-likefeatures and eigencolours were used for detecting
vehicles.Finally, a tackling method was used. Tehrani Niknejad et
al.[10] proposed a deformable vehiclemodel based onHOG fea-ture;
the method can achieve the adaptive threshold vehicledetection
under urban roads. Wang and Lien [11] proposed avehicle
detectionmethod based on a statistical model of localfeature. They
applied the public dataset Caltech Cars (Rear)[16] to test their
method. Alonso et al. [12] proposed a vehicledetection method based
on multidimensional classification.They represented vehicles in
form of rectangular subregionsbased on the robust classification of
features vectors resultof a combination of multiple morphological
vehicle features.Their method can detect vehicles with very
different aspect-ratio, color, and size. Chang and Cho [8]
presented a vehicledetection algorithm based on combination of Haar
featureand online boosting. Their algorithm has realized
vehicledetection in various environments. Sivaraman and Trivedi[9]
proposed an active-learning framework based on Haarfeature and
AdaBoost for vehicle detection on the highway.Jazayeri et al. [13]
proposed an optical flow and hiddenMarkov model-based vehicle
detection method which modethe locations andmotion information of
vehicles in the imagelevel. Their method can deal with the vehicle
identificationproblem under the scene of changing illumination
andenvironment well.
Vehicle detection method based on a single feature canquickly
detect vehicles in images. However, using singlefeature methodmay
cause a lot of false alarms, because singlefeature only describes
one certain characteristic of vehicles.Most of the appearance-based
vehicle detection methods’performance excessively depends on the
number and scaleof training samples. Various samples in different
situationsare needed to generate more powerful classifiers. In
addition,detecting vehicles in images using appearance-based
meth-ods which has to scan the whole image requires
excessivecalculation and cannot meet the real-time requirement
ofFCW. To solve the above-mentioned problem, a widely usedmethod is
multifeature fusion which combines several singlefeature-based
algorithms together by using voting method.This can significantly
reduce the false alarm rate, but thedetection rate is reduced
either. In recent years, mathematicaltheory has been widely used
for improving the performanceof complex vehicle systems. Much
process has been made inthe field of mathematical modeling and
control methods [17–23], such as adaptive back stepping control for
active suspen-sion systems with hard constraints [17], saturated
adaptiverobust control for active suspension systems [18], and
adap-tive robust vibration control of full-car active
suspensionswith electrohydraulic actuators [19]. Choquet integral
is awidely used method in data fusion [24–26]; it can seek
themaximum consistency of decision from the consistency andconflict
detection results of multiple features. To improve
the performance of vehicle detection algorithm and to
solveproblems above, we propose a multifeature fusion
vehicledetection algorithm based on Choquet integral.
Experimentresults show that our multifeature fusion method will
notonly improve the detection rate but also reduce the false
alarmrate.
Figure 1 illustrates the workflow of our approach. Therest of
the paper is organized as follows. Section 2 brieflyintroduces the
shadow-based vehicle region of interest (ROI)detection method. In
Section 3, vehicle taillight feature sim-ilarity measure, vehicle
symmetry feature similarity mea-sure, and HOG + AdaBoost feature
similarity measure arepresented, respectively. Then our
multifeature fusion vehicledetection algorithm based on Choquet
integral is introducedin Section 4. Experiment results for the
proposedmethod areshown in Section 5; finally Section 6 draws
conclusions.
2. Shadow-Based Vehicle ROI Detection
The shadow-based vehicle detection algorithm is usuallyapplied
to extract the vehicle ROIs in the whole images forreducing
computation complexity [1]. We have developeda shadow-based vehicle
detection method, and the basicprinciple of the method is that
regions underneath vehiclesare distinctly darker than any other
regions on an asphaltroad. The grayscale of pixels in shadow
regions is muchlower than that in any other regions in the same
image.Grayscale histogram (GH) can reflect the whole imagegrayscale
distribution well. The grayscale of vehicle shadowpixels belongs to
the lower parts of GH. So we can detectthe shadow regions
underneath vehicles by segmenting GHwith a threshold th BW. Figure
2(a) is a vehicle image fromCaltech Cars (Rear) [27]. Black regions
in Figure 2(b) areshadow regions segmented by setting th BW to
0.1.The greenlines in Figure 2(c) are vehicle shadow lines detected
byshadow-based vehicle detection method.
3. Feature Similarity Measure
To make full use of the Choquet integral in our mul-tifeature
fusion vehicle detection framework, each singlefeature should be
first represented in form of fuzzificationbefore calculating the
Choquet integral. After this phase, thealgorithm can fuzz the
output of each single feature; then theresult can be determined by
using the fuzzy judgment insteadof direct judgment. Therefore, in
this section, we detailedlyintroduce three feature-based vehicle
detection methods andtheir feature similarity measure
functions.
3.1. Vehicle Taillight Feature Similarity Measure. The
redtaillights and braking lights are important features for
detect-ing the rear-view vehicle. Taillight-based feature
providesan important criterion for our multifeature fusion
vehicledetection framework. The RGB components of pixels
intaillight regions are obviously different from the other partsof
vehicle ROI (except red cars). Therefore, by followingthis rule, we
present a similarity measure method based oncolor feature of
vehicle taillights. First, taillight regions in
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Journal of Applied Mathematics 3
Vehicle taillightfeature similarity
measure
Vehicle symmetryfeature similarity
measure
classifier similaritymeasure
ROI detection byusing shadow-based vehicle
detection method
fusion based onChoquet integral
Vehicle
Y
N
If the value ofChoquet integral is greater
than threshold
Notvehicle
Inputimages
HOG + AdaBoost
Multifeature
Figure 1: Framework of our approach.
(a) (b)
(c)
Figure 2: Result of shadow-based vehicle ROI detection
method.
the vehicle ROI are detected by threshold value
segmentationmethod. The key threshold of method can be acquired
byanalyzing RGB components from images of taillights and theother
parts of vehicle. The collection of images for settingthe threshold
should be large enough and includes differentvehicles and various
scenes. We acquire the 𝑅, 𝐺, and 𝐵components distributions by
analyzing the public collection[27] and images captured by our
camera. As shown inFigure 3(b), differences between the 𝑅 component
and the𝐺 component of the other regions of vehicle are
mainlydistributed on the range of [1, 31]. It is different from
thevalues of |𝑅 − 𝐺| in taillight regions illustrated in Figure
3(a);therefore, the taillight regions of vehicle ROI can be
detectedby setting a certain thresholdTh Taillight:
𝐼Taillight (𝑥, 𝑦)
= {255, if 𝑅 (𝑥, 𝑦) − 𝐺 (𝑥, 𝑦)
≥ Th Taillight0, otherwise.
(1)
Figure 4(a) is the vehicle ROI detected by the shadow-based
vehicle detection method. Figure 4(b) is the binaryimage of
taillights detected by employing (1) on the vehicleROI. Canny-based
edge detection method is used to detectthe edges of taillights in
Figure 4(b), and Figure 4(c) is theedge image of Figure 4(b). Then
the connected domains inFigure 4(c) are extracted. The input images
of connecteddomain extraction method are binary and edge imagewhich
are illustrated as Figures 4(b) and 4(c), respectively.
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4 Journal of Applied Mathematics
02468101214161820
0–15 16–31 32–47 48–63 64–79 80–95 96–111 112–127
Num
ber o
f pix
els
Statistical interval
|R − G|
|G − B|
|R − B|
×104
>128
(a)
02468101214161820
0–15 16–31 32–47 48–63 64–79 80–95 96–111 112–127
Num
ber o
f pix
els
Statistical interval
|R − G|
|G − B|
|R − B|
×104
>128
(b)
Figure 3: Comparison of RGB components between taillights and
the other parts of vehicles.
(a) (b)
(c) (d)
Figure 4: Extraction of taillight areas.
Finally, the minimum circumscribed rectangles (MCR) ofconnection
domains are calculated. The detected MCRs areillustrated as the red
rectangles in Figure 4(d).
Each MCR of connected domain is represented bythe left top point
MinPoint
𝑖(𝑥, 𝑦) and the right top point
MaxPoint𝑖(𝑥, 𝑦) of MCR. Two left top points in vehicle ROI
can form a straight line; the slope of straight line is defined
as
𝐾𝑖
condomains =𝑦𝑖
minpoint − 𝑦𝑖−1
minpoint
𝑥𝑖
minpoint − 𝑥𝑖−1
minpoint. (2)
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Journal of Applied Mathematics 5
The distance between each MCR is represented as (3). Thetwo
taillights of vehicle are usually on a horizontal line, andthe
thresholds th 𝐿 and th 𝐻 can get rid of the straight linesthat are
not horizontal or almost horizontal:
width taillights
=
{{
{{
{
Max (𝑥𝑖maxpoint − 𝑥𝑖−1
minpoint) ,
if th 𝐿 ≤ 𝐾𝑖condomains ≤ th 𝐻,0, otherwise.
(3)
Definition 1. The taillight feature similarity measure
function𝐶tailCoeff is defined as
𝐶tailCoeff =width taillightswidth ROI
. (4)
3.2. Vehicle Symmetry Feature Similarity Measure. The sym-metry
measure is a statistic to describe the symmetry oftarget. Vehicles
are obviously symmetrical objects; therefore,we use the symmetry
feature as a similarity measure inour algorithm. According to the
symmetry-based methoddescribed in [28], we use the symmetry measure
methodbased on normalized entropy to calculate the symmetry valueof
each vehicle ROI. The symmetry measure is describedas (5), where
𝑆(𝑥
𝑠) is the symmetry measure of target. 𝐸(𝑙)
is the information entropy, which is also the
mathematicalexpectation of information content. 𝐸
𝑚is the max value of
information entropy. Consider
𝑠𝑔
=[(𝑆 (𝑥
𝑠) + 1) /2 + 𝐸 (𝑙) /𝐸𝑚]
2
=𝑆 (𝑥𝑠) × 𝐸𝑚
+ 2 × 𝐸 (𝑙) + 𝐸𝑚
4 × 𝐸𝑚
.
(5)
Definition 2. The symmetry feature similarity measure func-tion
𝐶symCoeff is defined as
𝐶symCoeff = {𝑠𝑔, 0 ≤ 𝑠
𝑔≤ 1,
1, 𝑠𝑔
> 1.(6)
3.3. HOG and AdaBoost Classifier Feature Similarity Measure.The
histogram of oriented gradient (HOG) is a descriptor offeaturewhich
has beenwidely used in object detection. Zhu etal. [29] introduced
an efficient pedestrian detection methodbased on HOG and AdaBoost.
In our previous work, we useHOG feature to detect pedestrian [14].
The HOG feature isrepresented by calculating the histogram of
oriented gradientof local region in the image. First, the image is
divided into aplurality of grids according to a certain size; these
grids arecalled BLOCK which are illustrated as in Figure 5(a).
Theneach BLOCK is divided into four regions which are calledCELL.
Each CELL projects an orientation-based histogramwhich includes
nine bins. In this histogram, the horizontalordinate is a range of
direction angles which divide 180∘into nine equal parts, and the
vertical coordinates are anaccumulation of each angle range.
Finally, a 36D featurevector named BLOCK is formed. Due to the
strong edge
feature of vehicles, we employ the HOG feature to
representvehicles; then the AdaBoost-based algorithm [30] is
appliedto generate weak classifiers.
In this paper, the training samples of generating HOG +AdaBoost
classifiers are images captured from actual drivingenvironments.
Vehicle regions of these images are positivesamples, and other
regions of images are negative samples.The amount of positive
samples andnegative samples are both10000. These samples are
normalized to the same size (30 ×30). Screenshots of samples are
shown in Figures 5(b) and5(c). There are two phases to employ the
HOG + AdaBoostclassifier and the training and the detection phase.
In thetraining phase, we extract HOG features by applying CELLsize
of 5 × 5, 10 × 10, and 15 × 15, respectively; the scanningstep size
is three pixels, and the weak classifiers are selectedby AdaBoost
algorithm. After training, we use the samples(positive 10000 and
negative 10000) which are different fromthat of the training phase
to test the weak classifiers.TheROCcurves of HOG + AdaBoost
algorithm under three differentCELL sizes are illustrated as in
Figure 6; the performance ofHOG + AdaBoost classifiers whose CELL
size is 15 × 15 is thebest among these three types; therefore, we
set the CELL sizeto 15 × 15 in our further experiments.
To enhance the performance of HOG + AdaBoost clas-sifiers,
inspired by method in [9], the active-learning basedHOG + AdaBoost
framework is used by following the stepsin the Active-Learning
Framework. The advantage of thisframework is that you are only
adding negative samples thatwould otherwise be causing false
positives. There is no pointin adding more negative samples that
are handled by theoriginal training anyways.
Active-Learning Framework.
Step 1. Train HOG + AdaBoost classifiers using the10000 positive
samples and 30000 negative samples.Step 2. Run the algorithm by
using well-trainedHOG + AdaBoost classifiers on a large video set
(notthe training set from Step 1).Step 3. Any false positives from
the run in Step 2 canbe put in the negative set.Step 4. Retrain the
algorithm using the original truepositive set and the updated
negative set (negativesfrom both Step 1 and Step 3).Step 5. This
can be repeated as many times as appro-priate, using new video on
each iteration.
In detection phase, each vehicle ROI detected by shadow-based
vehicle detection method is resized to the same size ofthe training
sample; the HOG feature is extracted in the sameway of training
phase. Then use the well-trained classifiersto identify the vehicle
ROI; the classification value of eachvehicle ROI is calculated
by
hogadbCoeff =𝑇
∑
𝑖=1
𝛼𝑖
⋅ ℎbase𝑖
⋅ th strong. (7)
Most ofAdaBoost-based object detectionmethods decidewhether the
ROI is object or interference by judging whether
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6 Journal of Applied Mathematics
Block
Cell
(a) (b) (c)
Figure 5: Some samples of training dataset.
−0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7−0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
5 × 5
10 × 10
15 × 15
Det
ectio
n ra
ter+
False alarm rate r−
Figure 6: ROC curves of HOG + AdaBoost algorithm under
threedifferent HOG CELL sizes.
00.10.20.30.40.5
Prop
ortio
n
hogadbCoff
VehicleOthers
1∼1.5
0.5∼1
0∼0.5
−0.5∼0
−1∼−0.5
−1.5∼−1 2
−−2.5∼
<−2.5
−2∼−1.5
Figure 7: Statistic distribution of hogadbCoeff belonging to
vehiclesand interferences.
the symbol of the hogadbCoeff is positive or negative. Thisway
is not suitable to employ the HOG and AdaBoost-basedclassifiers in
our Choquet integral-based multifeature fusionvehicle detection
framework. To represent the hogadbCoeffin form of probability, we
first test the well-trained classifiers
Table 1: Mapping table between 𝐶𝑠𝑦𝑚𝐶𝑜𝑒𝑓𝑓
and hogadbCoeff.
hogadCoff 1.5ChogadbCoff 0.85 0.9 0.95 0.99 1
by using the testing sample set which is different from
thetraining sample set. And then the statistic distribution
ofhogadbCoeff is calculated. Finally themapping table betweenthe
HOG and AdaBoost classifier feature similarity measurevalue
𝐶hogadbCoeff and the hogadbCoeff is formed. The statis-tic
distributions of hogadbCoeff belonging to vehicles andinterferences
are illustrated in Figure 7; we use the algorithmprecision 𝑝+
corresponding to interval of hogadbCoeff to bethe 𝐶hogadbCoeff; the
precision is defined as (16) in this paper;the mapping table is
created as Table 1.
Definition 3. TheHOG + AdaBoost classifier feature similar-ity
measure function 𝐶hogadbCoeff is defined as Table 1.
4. Multifeature Fusion Vehicle DetectionAlgorithm Based on
Choquet Integral
In this paper, fuzzy integral theory is applied to
vehicledetection in complex scenarios. First, the basic theory
ofChoquet integral is introduced here. And then the fuzzymeasure of
each feature is defined. Finally, the features oftaillight,
symmetry, andHOG+AdaBoost classifier are fusedby Choquet integral
of fuzzy theory. The brief conceptsof Choquet integral and the
fuzzy measure used in ouralgorithm are followed from the concepts
in [24–26].
Definition 4. Let 𝑋 be a finite set, and 𝑌 is a power set
whichis composed of subsets of 𝑋, 𝑔 : 𝑌 → [0, ∞] is the
mappingfunction from the power set 𝑌 to the range of [0, ∞]. If
𝑔satisfies the following three conditions, 𝑔 is a fuzzy measureon
𝑌.
(1) Boundedness: 𝑔(𝜑) = 0.
(2) Monotonicity: ∀𝐴, 𝐵 ∈ 𝑌, if𝐴 ⊆ 𝐵, then 𝑔(𝐴) ≤ 𝑔(𝐵).
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Journal of Applied Mathematics 7
(3) Continuity: if ∀𝐴𝑛
∈ 𝑌, and {𝐴𝑖
| 𝑖 ∈ [1, +∞]} ismonotonous. This is also represented in the
form of𝐴1
⊆ 𝐴2
⊆ ⋅ ⋅ ⋅ ⊆ 𝐴𝑛
⋅ ⋅ ⋅ or 𝐴1
⊇ 𝐴2
⊇ ⋅ ⋅ ⋅ ⊇ 𝐴𝑛
⋅ ⋅ ⋅ ,then lim
𝑖→∞𝑔(𝐴𝑖) = 𝑔(lim
𝑖→∞𝐴𝑖).
The fuzzymeasurewhich is widely applied inmultifeaturefusion is
the regular fuzzy measure: if 𝑋 ∈ 𝑌 and 𝑔(𝑋) = 1,the fuzzy measure
𝑔 is regular.
Definition 5. If the fuzzy measure satisfies the
followingconditions: ∀𝐴, 𝐵 ∈ 𝑌, 𝐴 ∩ 𝐵 = 𝜑, if there exists a
constantvalue𝜆,𝜆 > −1 satisfying𝑔(𝐴∪𝐵) =
𝑔(𝐴)+𝑔(𝐵)+𝜆𝑔(𝐴)𝑔(𝐵),then 𝑔 is a 𝜆-fuzzy measure. 𝜆 can be
calculated by (8), where𝑔𝑖
= 𝑔({𝑥𝑖}); it is used to indicate the importance of a single
feature classifier for the final evaluation, where 𝑥𝑖
∈ 𝑋 =
{𝑥1, 𝑥2, . . . , 𝑥
𝑛}. Consider
1 + 𝜆 =
𝑛
∏
𝑖=1
(1 + 𝜆 × 𝑔𝑖) . (8)
Definition 6. 𝑓 : 𝑋 → [0, 1] is a nonnegative functiondefined on
𝑋, 𝑔 is a fuzzy measure defined on power set 𝑌,and then Choquet
integral of function 𝑓 on 𝑋 with respect tofuzzy measure is defined
by
∫ 𝑓𝑑𝑔 = ∫
∞
0
𝑔 (𝑌𝜇) 𝑑𝜇, (9)
where 𝑌𝜇
= {𝑥 | 𝑓(𝑥) ≥ 𝜇, 𝑥 ∈ 𝑋}, 𝜇 ∈ [0, ∞); the mainidea of (9) is
determining the value of Choquet integral usingRiemann integral by
an infinite approximation method. Thedefinition of Choquet integral
is as follows when 𝑋 is a finiteset:
∫ 𝑓𝑑𝑔 =
𝑛
∑
𝑖=1
[𝑓 (𝑥𝜃(𝑖)
) − 𝑓 (𝑥𝜃( 𝑖−1)
)] 𝑔 (𝐾𝜃(𝑖)
) , (10)
where 𝜃 is a permutation of the indices such that
0 = 𝑓 (𝑥𝜃(0)
) ≤ 𝑓 (𝑥𝜃(1)
) ≤ ⋅ ⋅ ⋅ 𝑓 (𝑥𝜃(𝑛)
) ≤ 1,
𝐾𝜃(𝑖)
= {𝑥𝜃(𝑖)
, 𝑥𝜃(𝑖+1)
, 𝑥𝜃(𝑖+2)
, . . . , 𝑥𝜃(𝑖+𝑛)
} , 𝑖 = 1, 2, . . . , 𝑛.
(11)
When fuzzy measure 𝑔 is a 𝜆-fuzzy measure, any subsetis defined
by
𝑔 (𝐾𝜃(1)
) = 𝑔 ({𝑥𝜃(1)
}) = 𝑔𝜃(1)
,
𝑔 ({𝑥𝜃(𝑖)
}) = 𝑔𝜃(𝑖)
,
𝑔 (𝐾𝜃(𝑖)
) = 𝑔𝜃(𝑖)
+ 𝑔 (𝐾𝜃(𝑖−1)
)
+ 𝜆𝑔𝜃(𝑖)
𝑔 (𝐾𝜃(𝑖−1)
) , 𝑖 = 2, . . . , 𝑛.
(12)
To apply the Choquet integral to detect vehicles incomplex
environments, 𝑂 is first initialized as the vehicleROI detected by
shadow-based vehicle detection algorithm.𝐹 = {vechile, interfernce}
is a classification framework. 𝑋 ={𝑥1, 𝑥2, 𝑥3} is the feature set
for detecting vehicle, where 𝑥
1,
𝑥2, and 𝑥
3represent the vehicle symmetry feature, the vehicle
00.20.40.60.81
1.2
tempchoquet
Region of interest
VehicleInterference
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85
89 93
Figure 8: Comparison of temp choquet between the vehicle and
theinterference.
taillight feature, and vehicle HOG + AdaBoost
classifiersfeature, respectively. Let 𝑔 : 𝑋 → [0, 1] be the fuzzy
densityof vehicle ROI 𝑂 belonging to the class 𝐹
𝑖; define 𝑔(𝑥
𝑖) to be
the degree of importance of the feature𝑥𝑖in decidingwhether
vehicle ROI is vehicle or interference. Define 𝑔(𝑥1) = 𝑔({𝑥
1}),
𝑔(𝑥2) = 𝑔({𝑥
2}), and 𝑔(𝑥
3) = 𝑔({𝑥
3}); the higher the 𝑔(𝑥
𝑖) is,
the more important the feature 𝑥𝑖is. The fuzzy function 𝑓 is
defined in [0, 1] so that 𝑓(𝑥1) = 𝐶tailCoeff, 𝑓(𝑥2) =
𝐶symCoeff,
and 𝑓(𝑥3) = 𝐶hogadbCoeff. To calculate the value of Choquet
integral for each vehicle ROI, the features 𝑥𝑖in the set 𝑋
are
needed to be rearranged with respect to the order 𝑓(𝑥1) ≤
𝑓(𝑥2) ≤ 𝑓(𝑥
3).
Main steps of our multifeature fusion vehicle detectionalgorithm
based on Choquet integral are as follows.
Multifeature Fusion Vehicle Detection Algorithm Based onChoquet
Integral.
Step 1. Calculate the fuzzy measure of each feature.We test each
feature-based vehicle detection methodon the same vehicle sample
set, and, according to (16),the precision of each vehicle detection
method can beacquired. Let the precision 𝑝+ be the fuzzy measure
𝑔corresponding to each feature-based method.Step 2. Calculate 𝜆 by
(8).Step 3. Estimate the 𝜆-fuzzy measure by (12).Step 4. The
Choquet integral value of each ROItemp choquet can be calculated by
(10) combiningwith three feature similarity measures.Step 5. Decide
whether the vehicle ROI is vehicleaccording to (13). As it is
illustrated in Figure 8,the temp choquet belonging to the vehicle
and thatbelonging to the interference are much more differ-ent; the
threshold Th vehicle can be set according toFigure 8:
isVehicle = {1, if temp choquet > Th vechicle,0,
otherwise.
(13)
5. Experiment Results
To verify the performance of the algorithm, experimentalplatform
has been built in c using OpenCV 1.0 library
-
8 Journal of Applied Mathematics
0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.000.3
0.4
0.5
0.6
0.7
0.8
Threshold
TaillightSymmetry
Prec
ision
p+
HOG + AdaBoost
Figure 9: Algorithm precision under various thresholds.
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.500.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Choquet fusionTaillightSymmetry
Det
ectio
n ra
ter+
False alarm rate r−
HOG + AdaBoost
Figure 10: Algorithm ROC curves.
and Visual Studio 2010. The vehicle detection algorithm
isperformed on an Intel Core i7-3770GHZPC. A part of vehicleimages
for testing are from the public test library CaltechCars (Rear)
[27]. The rest of vehicle images are captured inthe real
environments (parking lot and urban road) by usingDEWETRON DEWE2-M4
(camera: DEWE-CAM-01, lens:computar M3Z1228C) and SAMSUNG GT-S7562
camera(5,000,000 pixels). There are 5 video sequences in our
testdatasets; the frames of our datasets are 1500, and the numberof
vehicles in datasets is 3219. The test images include
singlevehicle, multivehicle, and illumination changing in the
scene.We use three indicators to measure the performance
ofalgorithms: the detection rate 𝑟+, the false alarm rate 𝑟−,and
the algorithm precision 𝑝+. The criterion to determine
a “good” detection in this paper is the overlap of the
detectedbounding box versus the annotated bounding box. If
theoverlap is larger than a certain threshold, the detection is
a“good” detection. Consider
𝑟+ =Number of detected vehicles
Total number of vehicles in testing data set, (14)
𝑟− =Number of false alarms
Total number of vehicle ROI, (15)
𝑝+ = Number of detected vehicles
× (Number of detected vehicles
+ Number of false alarms)−1.
(16)
Experiment 1 (calculate the fuzzymeasure of each algorithm).In
our multifeature fusion vehicle detection algorithm, fuzzymeasure
of each feature-based algorithm is set accordingto the performance
of its own. We test each feature-basedvehicle detection method on
the same vehicle sample setnamed JVTL. The images in JVTV are
vehicle ROIs detectedby shadow-based method which is introduced in
Section 2.The positive samples of JVTL are vehicles, and the
negativesamples are interferences in JVTL. The numbers of
positiveand negative samples are 3219 and 6000. According to(16),
the precision of each vehicle detection method canbe acquired. Let
the precision 𝑝+ be the fuzzy measure 𝑔corresponding to eachmethod.
According to Figure 9, we canset the fuzzy measure of every
algorithm.
Experiment 2 (performance of ourmultifeature fusion
vehicledetection algorithm). After setting fuzzy measure of
eachfeature-based algorithm, we apply the sample set JVTL to
testour method and every feature-based algorithm. As shown inFigure
10, the single feature cannot meet the requirement ofhigh detection
rate and low false alarm rate. Our algorithmfuzzes the output of
each single feature, and the result isdetermined by using the fuzzy
judgment instead of directjudgment. At the same time, the use of
fuzzy integral can givefull consideration to the cooperation of
multifeatures and theimportance degree of each feature in the
recognition phase.Therefore, our method outperforms each single
feature. Inour experiment, the average processing time (AVT) of
ourmethod can achieve 50ms per frame when processing onthe Caltech
Rear public test images whose resolutions are896 × 592, which
basically achieve real-time processing. Andthe processing time is
36ms per frame on images whoseresolutions are 640 × 480. Part of
results of our algorithmare shown in Figures 11 and 12. Figure 11
is the result ofalgorithm on Caltech Rear public vehicle images; we
set themain thresholds as follows: th BW = 0.1 and Th vehicle =0.9.
Experimental results show that our method can detectwell vehicles
in different distances.The distances are differentin Figures 12(a)
and 12(b); the distances between vehiclesand camera are from 3m to
50m. Figure 12(c) shows thatour method can not only detect the
single vehicle, but alsohandle themultivehicle detection problem.
Figure 12(d) is thedetection result on urban road.
-
Journal of Applied Mathematics 9
(a) (b) (c)
(d) (e)
Figure 11: Detection results on Caltech Rear public vehicle
images.
(a)
(b) (c)
(d)
Figure 12: Detection results on our data set.
Experiment 3 (algorithm comparison). To verify the perfor-mance
of our method, we compare our method to threefeature-based methods,
the voting method of these threefeature-based methods, and vehicle
detection methods in[11, 15, 16]. Algorithms used for comparison
are all testedon the same collection (the public test library
Caltech Cars(Rear) [27]).There are two ways to get the algorithms’
results.On one hand, we download the source code from
thewebsites
which have been provided in their articles to get the
testingresults. On the other hand, we directly use the testing
resultsillustrated in the articles. Comparison result is shown
inTable 2; it shows that the single feature-based methods candetect
vehicle better, but the false alarm rate is also thehighest.
Although the voting method can reduce the falsealarm rate, the
detection rate is reduced either. Processingtime is another
indicator to measure the performance of
-
10 Journal of Applied Mathematics
Table 2: Algorithm comparison.
Methods Accuracy AVT (ms/frame)(DR/FAR) (896 × 592)
Wang and Lien [11] 98%/0% 510Li et al. [14] 98%/1% 500Ali and
Shah [15] 90.2%/0.6% 500Taillight-based method 95.3%/23.4%
16Symmetry-based method 86.1%/48% 15HOG + AdaBoost 95.1%/44.8%
16Voting method 83.3%/0% 45Our method 95.5%/8.2% 50
algorithms; Ali andWang’s methods outperform our methodin terms
of accuracy, but the processing time of theirmethodsis above 500ms.
Considering both the accuracy and theprocessing time of algorithms,
our method outperforms theother methods.
6. Conclusions
In this paper, we propose a multifeature fusion vehicledetection
algorithm based on Choquet integral. There aretwo major
contributions in this paper. First, we proposea taillight-based
vehicle detection method, and a vehicletaillight feature similarity
measure is defined. In addition, thevehicle symmetry and HOG +
AdaBoost feature similaritymeasures are introduced combining with
the definitionof Choquet integral. Second, these three feature
similaritymeasures are fused by Choquet integral to detect
vehiclesin both static test images and videos. In experiment
part,our algorithm has been evaluated by using public
collectionsand our own test images, and the experiment results
areencouraging. But, to generalize our algorithm, there are
stillseveral problems to solve, such as improving accuracy ofHOG +
AdaBoost feature. To improve the performance ofvehicle detection
methods, we will address these issues andimprove the multivehicle
detection to an upper level.
Conflict of Interests
The authors declare that there is no conflict of
interestsregarding the publication of this paper.
Acknowledgments
The authors would like to thank the reviewers and editors
fortheir comments regarding enhancing the quality of the paper.This
work is supported by Grants from Jilin Planned Projectsfor Science
Technology Development (Grant no. 20120305and no. 20130522119JH)
and Ph.D. Programs Foundation ofMinistry of Education of China
(Grant no. 20130061110054).
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