1College of Civil Aviation Nanjing University of Aeronautics and Astronautics Nanjing 211106 China2Aviation Information Technology R amp D Center Binzhou University Binzhou 256603 China
Correspondence should be addressed to Haijun Wang whjlym163com
Received 10 March 2016 Accepted 13 July 2016
Academic Editor Jiri Jan
Copyright copy 2016 Haijun Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
We present a fast and robust object tracking algorithm by using 2DPCA and ℓ2-regularization in a Bayesian inference framework
Firstly we model the challenging appearance of the tracked object using 2DPCA bases which exploit the strength of subspacerepresentation Secondly we adopt the ℓ
2-regularization to solve the proposed presentation model and remove the trivial templates
from the sparse tracking method which can provide a more fast tracking performance Finally we present a novel likelihoodfunction that considers the reconstruction error which is concluded from the orthogonal left-projectionmatrix and the orthogonalright-projection matrix Experimental results on several challenging image sequences demonstrate that the proposed method canachieve more favorable performance against state-of-the-art tracking algorithms
1 Introduction
Visual tracking is one of the fundamental topics in computervision and plays an important role in numerous researchesand practical applications such as surveillance human com-puter interaction robotics and traffic control Existing objecttracking algorithms can be divided into two categories thatis discriminative or generative Discriminativemethods treattracking as a binary classification problem with local searchwhich estimates the decision boundary between an objectimage patch and the background Babenko et al [1] proposedan online multiple instance learning (MIL) which treatsambiguous positive and negative samples as bags to learn adiscriminative classifier Zhang et al [2] propose a fastingcompressive tracking algorithm which employs nonadaptiverandom projections that preserve the structure of the imagefeature
Generative methods typically learn a model to representthe target object and incrementally update the appearancemodel to search for the image region with minimal recon-struction error Inspired by the success of sparse representa-tion in face recognition [3] supersolution [4] and inpainting[5] recently sparse representation based visual tracking [6ndash9] has also attracted increasing interests Mei and Ling [10]first extend sparse representation to object tracking and cast
the tracking problem as determining the likeliest patch witha sparse representation of templates The method can handlepartial occlusion by treating the error term as sparse noiseHowever it requires solving a series of complicated ℓ
1norm
related minimization problems many times and the timecomplexity is quite significant Although some modified ℓ
1
norm methods have been proposed to speed up tracker theyare still far away from being real time
Recently many object tracking algorithms have been pro-posed to exploit the power of subspace representation fromdifferent points Ross et al [11] present a tracking methodthat incrementally learns a PCA low-dimensional subspacerepresentation efficiently adapting online to changes in theappearance of the target However this method is sensitiveto partial occlusion Zhong et al [8] proposed a robust objecttracking algorithm via sparse collaborative appearancemodelthat exploits both holistic templates and local representationsto account for appearance changes Zhuang et al [12] castthe tracking problem as finding the candidate that scores thehighest in the evaluation model based upon a matrix calleddiscriminative sparse similarity map Qian et al [13] exploitan appearance model based on extended incremental non-negative matrix factorization for visual tracking Wang andLu [14] present a novel online object tracking algorithm byusing 2DPCAand ℓ
1-regularizationThismethod can achieve
Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2016 Article ID 7975951 7 pageshttpdxdoiorg10115520167975951
2 Journal of Electrical and Computer Engineering
good performance among many scenes However the coeffi-cients and the sparse error matrix used in this method needan iterative algorithm to compute and the space and timecomplexity are too large to meet the real-time tracking
Motivated by the aforementioned work this paperpresents a robust and fast ℓ
2norm tracking algorithm with
adaptive appearance model The contributions of this workare threefold (1) we exploit the strength of 2DPCA sub-space representation using ℓ
2-regularization (2) we remove
the trivial templates from the sparse tracking method (3)we present a novel likelihood function that considers thereconstruction error which is concluded from the orthogonalleft-projection matrix and the orthogonal right-projectionmatrix Both qualitative and quantitative evaluation on videosequences demonstrate that the proposedmethod can handleocclusion illumination changes scale changes and no-rigid appearance changes effectively in a lower computationcomplexity and can run in real time
2 Object Representation via2DPCA and ℓ
2-Regularization
Principal component analysis (PCA) is a classical featureextraction and data representation technique widely usedin the areas of pattern recognition and computer visionCompared with PCA two-dimensional principal componentanalysis (2DPCA) [15] is based on 2Dmatrices rather than 1Dvectors So the image matrix does not need to be previouslytransformed into vector That is the extraction of imagefeatures is computationally more efficient using 2DPCA thanPCA In this paper we represent the object by using 2D basismatrices Given a series of image matrices [B
1B2 B
119870]
the projection coefficients matrices [A1A2 A
119870] can be
got by solving the following function
minUVA
1
119870
119870
sum
119894=1
10038171003817100381710038171003817B minus UAVT10038171003817100381710038171003817
2
119865 (1)
where sdot 119865denotes the Frobenius norm U represents the
orthogonal left-projection matrix V represents the orthogo-nal right-projection matrix
The cost function is set as an ℓ2-regularization quadratic
function
119869 (A) = 10038171003817100381710038171003817B minus UAVT100381710038171003817100381710038172
119865+ 120582 A2
119865
=1
2tr (B minus UAVT
)T(B minus UAVT
) + 120582 A2119865
=1
2tr (BT
minus VATUT) (B minus UAVT
) + 120582 A2119865
=1
2tr BTB minus BTUAVT
minus VATUTB + VATUTUAVT
+ 120582 A2119865
=1
2tr BTB minus tr BTUAVT
+1
2VATUTUAVT
+ 120582 A2119865
(2)
Here 120582 is a constant The solution of (2) is easily derived asfollows
Kronecker product vec(A) means the vector-version of thematrix A Therefore we can get the projection coefficientsmatrix A Let P = VTV otimes UTU + IT
2otimes 2120582I
2 Obviously
the projection matrix P is independent from B and wecan precalculate it in each frame before circulation for allcandidates When a new candidate comes we can simplycalculate P vec(UTBV) to obtain vec(A) which makes theproposed method very fast
Here we abandon the trivial templates completely whichmakes the target able to be represented by the 2DPCAsubspace fully The error matrix can be obtained by thefollowing equation after we get the projection coefficientsmatrix A from (3)
E = B minus UAVT (4)
So the error matrix can be calculated once
3 Tracking Framework Based on 2DPCA andℓ2-Regularization
Visual tracking is treated as a Bayesian inference task in aMarkov model with hidden state variables Given a series ofimage matrices 119861 = [B
where 119901(x119905| x119905minus1) is the motion model that represents
the state transition between two consecutive states 119901(B119905|
x119905) is the observation model which indicates the likelihood
function
Motion Model We apply an affine image warp to modelthe target motion between consecutive states Six parametersof the affine transform are used to model 119901(x
119905| x119905minus1)
of a tracked target Let x119905= 119909119905 119910119905 120579119905 119904119905 120572 120601119905 where 119909
119905
119910119905 120579119905 119904119905 120572 and 120601
119905denote 119909 and 119910 translations rotation
angle scale and aspect ration and skew respectively Thestate transition is formulated by random walk that is
Journal of Electrical and Computer Engineering 3
119901(x119905| x119905minus1) = 119873(x
119905 x119905minus1 Σ) where Σ is a diagonal covariance
matrix which indicates the variances of affine parameters
Observation Model If no occlusion occurs an image obser-vation B
119905can be generated by a 2DPCA subspace (spanned
by U and V and centered at 120583) Here we consider thepartial occlusion in the appearancemodel for robust trackingThus we assume that the centered image matrices B
119905(B119905=
B119905minus 120583) can be represented by the linear combination of the
projection matricesU and V Then we draw119873 candidates inthe state x
119905 For each of the observed imagematrices we solve
a ℓ2-regularization problem
minA119894
100381710038171003817100381710038171003817B119894 minus UA119894VT100381710038171003817100381710038171003817
where 119894 denotes the 119894th sample of the state x Thus we obtainA119894 and the likelihood can be measured by the reconstructionerror
119901 (B119894 | B119894) = exp(minus100381710038171003817100381710038171003817B119894 minus UA119894VT100381710038171003817100381710038171003817
2
119865
) (7)
However it is noted that just by penalizing error levelthe precise location of the tracked target can be benefitedTherefore we present a novel likelihood function whichconsiders both the reconstruction error and the level of errormatrix
119901 (B119894 | B119894) = exp(minus100381710038171003817100381710038171003817B119894 minus UA119894VT
minus E119894100381710038171003817100381710038171003817
2
119865
minus 12058210038171003817100381710038171003817E119894100381710038171003817100381710038171) (8)
where E119894 can be calculated by (9)
E119894 = B119894 minus UA119894VT (9)
Here A119894 is calculated by (3)
Online Update In order to handle the appearance changeof tracked target it is necessary to update the observa-tion model If some imprecise samples are used to updatethe tracked model may degrade Therefore we present anocclusion-radio-based update mechanism After obtainingthe best candidate state of each frame we compute thecorresponding error matrix and the occlusion ratio 120574 Twothresholds thr
1= 01 and thr
2= 06 are introduced to define
the degree of occlusion If 120574 lt thr1 the tracked target
is not occluded or a small part of it is occluded by thenoise Therefore the model with sample is updated directlyIf thr1lt 120574 lt thr
2 the tracked target is partially occluded
The occluded part is replaced by the average observationand the recovered candidate is used for update If 120574 gt
thr2 most part of the tracked target is occluded Therefore
the sample is discarded without update After we cumulateenough samples we use an incremental 2DPCA algorithm toupdate the tracker (left- and right-projection matrices)
4 Experiments
The proposed tracking algorithm is implemented in MAT-LAB which runs on a computer with Intel i5-3210 CPU
(25GHz) with 4GB memory The regularization 120582 is setto 005 The image observation is resized to pixels for theproposed 2DPCA representation For each sequence thelocation of the tracked target object is manually labeled inthe first frame 600 particles are adopted for the proposedalgorithm accounting for the trade-off between effectivenessand speed Our tracker is incrementally updated every 5frames
To demonstrate the effectiveness of the proposed trackingalgorithm we select six state-of-the-art trackers the ℓ
1
tracker [10] the PN tracker [16] the VTD tracker [17] theMIL tracker [1] the Frag tracker [18] and the 2DPCAℓ
1
tracker [14] for comparison on several challenging imagesequences including Occlusion 1 David Outdoor Caviar 2Girl Car 4 Car 11 Singer 1Deer Jumping and Lemming Thechallenging factors include severe occlusion pose changemotion blur illumination variation and background clutter
41 Qualitative Evaluation
Severe Occlusion We test four sequences (Occlusion 1 David-Outdoor Caviar 2 and Girl) with long time partial or heavyocclusion and scale change Figure 1(a) demonstrates that ℓ
1
algorithm Frag algorithm 2DPCAℓ1 and our algorithms
perform better since these methods take partial occlusioninto account ℓ
1algorithm 2DPCAℓ
1 and our algorithms
can handle occlusion by avoiding updating occluded pixelsinto the PCA basis and 2DPCA basis separately Frag algo-rithm can work well on some simple occlusion cases (egFigure 1(a) Occlusion 1) via the part-based representationHowever this method performs poorly on some more chal-lenging videos (eg Figure 1(b)DavidOutdoor) MIL trackeris not able to track the occluded target in DavidOutdoorand Caviar 2 since the Harr-like features the MIL methodadopted are less effective in distinguishing the similar objectsFor the Girl video the in- and out-of-plane rotation partialocclusion and the scale change make it difficult to track Itcan be seen that the Frag and the proposed tracker workbetter than the other methods
Illumination Change Figures 1(e) and 1(f) present trackingresults using the Car 4 Car 11 and Singer 1 sequenceswith significant change of illumination and scale as well asbackground clutter The ℓ
1tracker 2DPCAℓ
1tracker and
the proposed tracker perform well in the Car 4 sequenceswhereas the other trackers drift away when the target vehiclegoes underneath the overpass or the trees For Car 11sequences 2DPCAℓ
1and the proposed tracker can achieve
robust tracking results whereas the other trackers drift awaywhen drastic illumination change occurs or when similarobject appears In the Singer 1 sequence the drastic illumi-nation and scale change make it difficult to track It can beseen that the proposed tracker performs better than the othermethods
Motion Blur It is difficult for tracking algorithms to predictthe location of the tracked objects when the target movesabruptly Figures 1(h) and 1(i) demonstrate the trackingresults in theDeer and Jumping sequences InDeer sequences
4 Journal of Electrical and Computer Engineering
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(a)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(b)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(c)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(d)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(e)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(f)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(g)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(h)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(i)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(j)
Figure 1 Sampled tracking results of partial evaluated algorithms on ten challenging sequences
the animal appearance is almost indistinguishable due to thefast motion and most methods lost the target right at thebeginning of the video At frame 53 PN tracker locates thesimilar deer instead of the right object From the results wecan see that the VTD tracker and our tracker perform betterthan the other algorithms 2DPCAℓ
1tracker may be able to
track the target again by chance after failure The appearancechanges of the Jumping sequences are drastic such that theℓ1 Frag and VTD tracker drift away from the object Our
tracker successfully keeps track of the object with small errors
whereas the MIL PN and 2DPCAℓ1can track the target in
some frames
Background Clutter Figure 1(j) illustrates the tracking resultsin the Lemming sequences with scale and pose change as wellas severe occlusion in cluttered background Frag tracker lostthe target object at the beginning of the sequence and whenthe target object moves quickly or rotates the VTD trackerfails too In contrast the proposed method can adapt to theheavy occlusion in-plane rotation and scale change
Journal of Electrical and Computer Engineering 5
0 100 200 300 400 500 600 700 800 9000
20406080
100120
Frame number
Cen
ter e
rror
Occlusion 1
0 50 100 150 200 250 3000
50100150200250300350400450
Frame number
Cen
ter e
rror
DavidOutdoor
0 50 100 150 200 250 300 350 400 450 5000
20406080
100120140160
Frame number
Cen
ter e
rror
Caviar 2
0 100 200 300 400 500 6000
50
100
150
200
250
Frame numberC
ente
r err
or
Girl
0 100 200 300 400 500 600 7000
50100150200250300350400
Frame number
Cen
ter e
rror
Car 4
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 350 4000
20406080
100120140160
Car 11
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 3500
20406080
100120
Singer 1
Frame number
Cen
ter e
rror
0 10 20 30 40 50 60 70 800
50100150200250300350
Deer
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 3500
20406080
100120140160180200
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Jumping
Frame number
Cen
ter e
rror
0 200 400 600 800 1000 1200 14000
50100150200250300350400450500
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Lemming
Figure 2 Center location error (in pixels) evaluation
6 Journal of Electrical and Computer Engineering
0 100 200 300 400 500 600 700 800 9000
010203040506070809
1
Ove
rlap
rate
Frame number
Occlusion 1
0 50 100 150 200 250 3000
010203040506070809
1
Ove
rlap
rate
Frame number
DavidOutdoor
0 50 100 150 200 250 300 350 400 450 5000
010203040506070809
1
Ove
rlap
rate
Frame number
Caviar 2
0 100 200 300 400 500 6000
010203040506070809
1
Ove
rlap
rate
Frame number
Girl
0 100 200 300 400 500 600 7000
010203040506070809
1
Ove
rlap
rate
Frame number
Car 4
0 50 100 150 200 250 300 350 4000
010203040506070809
1
Ove
rlap
rate
Frame number
Car 11
0 50 100 150 200 250 300 3500
010203040506070809
1
Ove
rlap
rate
Frame number
Singer 1
0 10 20 30 40 50 60 70 800
010203040506070809
1
Ove
rlap
rate
Frame number
Deer
0 50 100 150 200 250 300 3500
010203040506070809
1
Ove
rlap
rate
Frame number
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Jumping
0 200 400 600 800 1000 1200 14000
010203040506070809
1
Ove
rlap
rate
Frame number
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Lemming
Figure 3 Overlap rate evaluation
Journal of Electrical and Computer Engineering 7
42 Quantitative Evaluation To conduct quantitative com-parisons between the proposed tracking method and theother sate-of-the-art trackers we compute the differencebetween the predicted and the ground truth center locationerror in pixels and overlap rates which are most widelyused in quantitative evaluation The center location error isusually defined as the Euclidean distance between the centerlocations of tracked objects and their corresponding labeledground truth Figure 2 demonstrates the center error plotswhere a smaller center error means a more accurate resultin each frame Overlap rate score is defined as score =
area(119877119905cap 119877119892)area(119877
119905cup 119877119892) 119877119905is the tracked bounding
box of each frame and 119877119892is the corresponding ground
truth bounding box Figure 3 shows the overlap rates of eachtracking algorithm for all sequences Generally speaking ourtracker performs favorably against the other methods
43 Computational Complexity The most time consumingpart of the generative tracking algorithm is to compute thecoefficients using the basis vectors For the ℓ
1tracker the
computation of the coefficients using the LASSO algorithmis 119874(1198892 + 119889119896) 119889 is the dimension of subspace and 119896 is thenumber of basis vectorsThe load of the 2DPCAℓ
1tracker [10]
with ℓ1regularization is 119874(119898119889119896) 119898 stands for the number
of iterations (eg 10 on average) For our tracker the trivialtemplates are abandoned and square templates are not usedSo the load of our tracker is 119889119896 The tracking speed of ℓ
1
2DPCAℓ1 and our method is 025 fps 22 fps and 52 fps
separately (fps frame per second) Therefore we can getthat our tracker is more effective and much faster than theaforementioned trackers
5 Conclusion
In this paper we present a fast and effective tracking algo-rithm We first clarify the benefits of the utilizing 2DPCAbasis vectors Then we formulate the tracking process withthe ℓ
2-regularization Finally we update the appearance
model accounting for the partial occlusion Both qualitativeand quantitative evaluations on challenging image sequencedemonstrate that the proposed method outperforms severalstate-of-the-art trackers
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This project is supported by the Shandong Provincial NaturalScience Foundation China (no ZR2015FL009)
References
[1] B Babenko M H Yang and S Belongie ldquoVisual tracking withonline multiple instance learningrdquo in Proceedings of the 22thIEEE Conference on Computer Vision and Pattern Recognitioninpp 983ndash990 San Francisco Calif USA 2009
[2] K H Zhang L Zhang andMH Yang ldquoReal time compressivetrackingrdquo in Proceedings of 12th European Conference on Com-puter Vision pp 864ndash877 Florence Italy 2012
[3] JWright A Y Yang A Ganesh S S Sastry and YMa ldquoRobustface recognition via sparse representationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 31 no 2 pp210ndash227 2009
[4] J Yang J Wright T S Huang and Y Ma ldquoImage super-resolution via sparse representationrdquo IEEE Transactions onImage Processing vol 19 no 11 pp 2861ndash2873 2010
[5] J Mairal M Elad and G Sapiro ldquoSparse representation forcolor image restorationrdquo IEEETransactions on Image Processingvol 17 no 1 pp 53ndash69 2008
[6] Y Wu J Lim and M-H Yang ldquoOnline object tracking abenchmarkrdquo in Proceedings of the 26th IEEE Conference onComputer Vision and Pattern Recognition (CVPR rsquo13) pp 2411ndash2418 Portland Ore USA June 2013
[7] X Jia H Lu and M-H Yang ldquoVisual tracking via adaptivestructural local sparse appearance modelrdquo in Proceedings ofthe 2012 IEEE Conference on Computer Vision and PatternRecognition (CVPR rsquo12) pp 1822ndash1829 Providence RI USAJune 2012
[8] W Zhong H Lu and M-H Yang ldquoRobust object tracking viasparsity-based collaborative modelrdquo in Proceedings of the 25thIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo12) pp 1838ndash1845 Providence RI USA June 2012
[9] T Zhang B Ghanem S Liu and N Ahuja ldquoRobust visualtracking via multi-task sparse learningrdquo in Proceedings ofthe 25th IEEE Conference on Computer Vision and PatternRecognition pp 2042ndash2049 Providence RI USA 2012
[10] X Mei and H Ling ldquoRobust visual tracking using ℓ1minimiza-
tionrdquo in Proceedings of 12th IEEE International Conference onComputer Vision pp 1436ndash1443 Kyoto Japan September 2009
[11] D A Ross J Lim R-S Lin and M-H Yang ldquoIncrementallearning for robust visual trackingrdquo International Journal ofComputer Vision vol 77 no 1ndash3 pp 125ndash141 2008
[12] B H Zhuang H Lu Z Y Xiao and D Wang ldquoVisual trackingvia discriminative sparse similarity maprdquo IEEE Transactions onImage Processing vol 23 no 4 pp 1872ndash1881 2014
[13] C Qian Y B Zhuang and Z Z Xu ldquoVisual tracking withstructural appearance model based on extended incrementalnon-negative matrix factorizationrdquo Neurocomputing vol 136pp 327ndash336 2014
[14] D Wang and H Lu ldquoObject tracking via 2DPCA and l1-regularizationrdquo IEEE Signal Processing Letters vol 19 no 11 pp711ndash714 2012
[15] DWang H Lu and X Li ldquoTwo dimensional principal compo-nents of natural images and its applicationrdquo Neurocomputingvol 74 no 17 pp 2745ndash2753 2011
[16] Z Kalal JMatas andKMikolajczyk ldquoP-N learning bootstrap-ping binary classifiers by structural constraintsrdquo in Proceedingsof the IEEE Computer Society Conference on Computer Visionand Pattern Recognition (CVPR rsquo10) pp 49ndash56 San FranciscoCalif USA June 2010
[17] J Kwon and K M Lee ldquoVisual tracking decompositionrdquoin Proceedings of the IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR rsquo10) pp 1269ndash1276 IEEE San Francisco Calif USA June 2010
[18] A Adam E Rivlin and I Shimshoni ldquoRobust fragments-basedtracking using the integral histogramrdquo in Proceedings of the 19thIEEE Conference on Computer Vision and Pattern Recognitionpp 798ndash805 New York NY USA 2006
good performance among many scenes However the coeffi-cients and the sparse error matrix used in this method needan iterative algorithm to compute and the space and timecomplexity are too large to meet the real-time tracking
Motivated by the aforementioned work this paperpresents a robust and fast ℓ
2norm tracking algorithm with
adaptive appearance model The contributions of this workare threefold (1) we exploit the strength of 2DPCA sub-space representation using ℓ
2-regularization (2) we remove
the trivial templates from the sparse tracking method (3)we present a novel likelihood function that considers thereconstruction error which is concluded from the orthogonalleft-projection matrix and the orthogonal right-projectionmatrix Both qualitative and quantitative evaluation on videosequences demonstrate that the proposedmethod can handleocclusion illumination changes scale changes and no-rigid appearance changes effectively in a lower computationcomplexity and can run in real time
2 Object Representation via2DPCA and ℓ
2-Regularization
Principal component analysis (PCA) is a classical featureextraction and data representation technique widely usedin the areas of pattern recognition and computer visionCompared with PCA two-dimensional principal componentanalysis (2DPCA) [15] is based on 2Dmatrices rather than 1Dvectors So the image matrix does not need to be previouslytransformed into vector That is the extraction of imagefeatures is computationally more efficient using 2DPCA thanPCA In this paper we represent the object by using 2D basismatrices Given a series of image matrices [B
1B2 B
119870]
the projection coefficients matrices [A1A2 A
119870] can be
got by solving the following function
minUVA
1
119870
119870
sum
119894=1
10038171003817100381710038171003817B minus UAVT10038171003817100381710038171003817
2
119865 (1)
where sdot 119865denotes the Frobenius norm U represents the
orthogonal left-projection matrix V represents the orthogo-nal right-projection matrix
The cost function is set as an ℓ2-regularization quadratic
function
119869 (A) = 10038171003817100381710038171003817B minus UAVT100381710038171003817100381710038172
119865+ 120582 A2
119865
=1
2tr (B minus UAVT
)T(B minus UAVT
) + 120582 A2119865
=1
2tr (BT
minus VATUT) (B minus UAVT
) + 120582 A2119865
=1
2tr BTB minus BTUAVT
minus VATUTB + VATUTUAVT
+ 120582 A2119865
=1
2tr BTB minus tr BTUAVT
+1
2VATUTUAVT
+ 120582 A2119865
(2)
Here 120582 is a constant The solution of (2) is easily derived asfollows
Kronecker product vec(A) means the vector-version of thematrix A Therefore we can get the projection coefficientsmatrix A Let P = VTV otimes UTU + IT
2otimes 2120582I
2 Obviously
the projection matrix P is independent from B and wecan precalculate it in each frame before circulation for allcandidates When a new candidate comes we can simplycalculate P vec(UTBV) to obtain vec(A) which makes theproposed method very fast
Here we abandon the trivial templates completely whichmakes the target able to be represented by the 2DPCAsubspace fully The error matrix can be obtained by thefollowing equation after we get the projection coefficientsmatrix A from (3)
E = B minus UAVT (4)
So the error matrix can be calculated once
3 Tracking Framework Based on 2DPCA andℓ2-Regularization
Visual tracking is treated as a Bayesian inference task in aMarkov model with hidden state variables Given a series ofimage matrices 119861 = [B
where 119901(x119905| x119905minus1) is the motion model that represents
the state transition between two consecutive states 119901(B119905|
x119905) is the observation model which indicates the likelihood
function
Motion Model We apply an affine image warp to modelthe target motion between consecutive states Six parametersof the affine transform are used to model 119901(x
119905| x119905minus1)
of a tracked target Let x119905= 119909119905 119910119905 120579119905 119904119905 120572 120601119905 where 119909
119905
119910119905 120579119905 119904119905 120572 and 120601
119905denote 119909 and 119910 translations rotation
angle scale and aspect ration and skew respectively Thestate transition is formulated by random walk that is
Journal of Electrical and Computer Engineering 3
119901(x119905| x119905minus1) = 119873(x
119905 x119905minus1 Σ) where Σ is a diagonal covariance
matrix which indicates the variances of affine parameters
Observation Model If no occlusion occurs an image obser-vation B
119905can be generated by a 2DPCA subspace (spanned
by U and V and centered at 120583) Here we consider thepartial occlusion in the appearancemodel for robust trackingThus we assume that the centered image matrices B
119905(B119905=
B119905minus 120583) can be represented by the linear combination of the
projection matricesU and V Then we draw119873 candidates inthe state x
119905 For each of the observed imagematrices we solve
a ℓ2-regularization problem
minA119894
100381710038171003817100381710038171003817B119894 minus UA119894VT100381710038171003817100381710038171003817
where 119894 denotes the 119894th sample of the state x Thus we obtainA119894 and the likelihood can be measured by the reconstructionerror
119901 (B119894 | B119894) = exp(minus100381710038171003817100381710038171003817B119894 minus UA119894VT100381710038171003817100381710038171003817
2
119865
) (7)
However it is noted that just by penalizing error levelthe precise location of the tracked target can be benefitedTherefore we present a novel likelihood function whichconsiders both the reconstruction error and the level of errormatrix
119901 (B119894 | B119894) = exp(minus100381710038171003817100381710038171003817B119894 minus UA119894VT
minus E119894100381710038171003817100381710038171003817
2
119865
minus 12058210038171003817100381710038171003817E119894100381710038171003817100381710038171) (8)
where E119894 can be calculated by (9)
E119894 = B119894 minus UA119894VT (9)
Here A119894 is calculated by (3)
Online Update In order to handle the appearance changeof tracked target it is necessary to update the observa-tion model If some imprecise samples are used to updatethe tracked model may degrade Therefore we present anocclusion-radio-based update mechanism After obtainingthe best candidate state of each frame we compute thecorresponding error matrix and the occlusion ratio 120574 Twothresholds thr
1= 01 and thr
2= 06 are introduced to define
the degree of occlusion If 120574 lt thr1 the tracked target
is not occluded or a small part of it is occluded by thenoise Therefore the model with sample is updated directlyIf thr1lt 120574 lt thr
2 the tracked target is partially occluded
The occluded part is replaced by the average observationand the recovered candidate is used for update If 120574 gt
thr2 most part of the tracked target is occluded Therefore
the sample is discarded without update After we cumulateenough samples we use an incremental 2DPCA algorithm toupdate the tracker (left- and right-projection matrices)
4 Experiments
The proposed tracking algorithm is implemented in MAT-LAB which runs on a computer with Intel i5-3210 CPU
(25GHz) with 4GB memory The regularization 120582 is setto 005 The image observation is resized to pixels for theproposed 2DPCA representation For each sequence thelocation of the tracked target object is manually labeled inthe first frame 600 particles are adopted for the proposedalgorithm accounting for the trade-off between effectivenessand speed Our tracker is incrementally updated every 5frames
To demonstrate the effectiveness of the proposed trackingalgorithm we select six state-of-the-art trackers the ℓ
1
tracker [10] the PN tracker [16] the VTD tracker [17] theMIL tracker [1] the Frag tracker [18] and the 2DPCAℓ
1
tracker [14] for comparison on several challenging imagesequences including Occlusion 1 David Outdoor Caviar 2Girl Car 4 Car 11 Singer 1Deer Jumping and Lemming Thechallenging factors include severe occlusion pose changemotion blur illumination variation and background clutter
41 Qualitative Evaluation
Severe Occlusion We test four sequences (Occlusion 1 David-Outdoor Caviar 2 and Girl) with long time partial or heavyocclusion and scale change Figure 1(a) demonstrates that ℓ
1
algorithm Frag algorithm 2DPCAℓ1 and our algorithms
perform better since these methods take partial occlusioninto account ℓ
1algorithm 2DPCAℓ
1 and our algorithms
can handle occlusion by avoiding updating occluded pixelsinto the PCA basis and 2DPCA basis separately Frag algo-rithm can work well on some simple occlusion cases (egFigure 1(a) Occlusion 1) via the part-based representationHowever this method performs poorly on some more chal-lenging videos (eg Figure 1(b)DavidOutdoor) MIL trackeris not able to track the occluded target in DavidOutdoorand Caviar 2 since the Harr-like features the MIL methodadopted are less effective in distinguishing the similar objectsFor the Girl video the in- and out-of-plane rotation partialocclusion and the scale change make it difficult to track Itcan be seen that the Frag and the proposed tracker workbetter than the other methods
Illumination Change Figures 1(e) and 1(f) present trackingresults using the Car 4 Car 11 and Singer 1 sequenceswith significant change of illumination and scale as well asbackground clutter The ℓ
1tracker 2DPCAℓ
1tracker and
the proposed tracker perform well in the Car 4 sequenceswhereas the other trackers drift away when the target vehiclegoes underneath the overpass or the trees For Car 11sequences 2DPCAℓ
1and the proposed tracker can achieve
robust tracking results whereas the other trackers drift awaywhen drastic illumination change occurs or when similarobject appears In the Singer 1 sequence the drastic illumi-nation and scale change make it difficult to track It can beseen that the proposed tracker performs better than the othermethods
Motion Blur It is difficult for tracking algorithms to predictthe location of the tracked objects when the target movesabruptly Figures 1(h) and 1(i) demonstrate the trackingresults in theDeer and Jumping sequences InDeer sequences
4 Journal of Electrical and Computer Engineering
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(a)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(b)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(c)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(d)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(e)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(f)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(g)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(h)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(i)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(j)
Figure 1 Sampled tracking results of partial evaluated algorithms on ten challenging sequences
the animal appearance is almost indistinguishable due to thefast motion and most methods lost the target right at thebeginning of the video At frame 53 PN tracker locates thesimilar deer instead of the right object From the results wecan see that the VTD tracker and our tracker perform betterthan the other algorithms 2DPCAℓ
1tracker may be able to
track the target again by chance after failure The appearancechanges of the Jumping sequences are drastic such that theℓ1 Frag and VTD tracker drift away from the object Our
tracker successfully keeps track of the object with small errors
whereas the MIL PN and 2DPCAℓ1can track the target in
some frames
Background Clutter Figure 1(j) illustrates the tracking resultsin the Lemming sequences with scale and pose change as wellas severe occlusion in cluttered background Frag tracker lostthe target object at the beginning of the sequence and whenthe target object moves quickly or rotates the VTD trackerfails too In contrast the proposed method can adapt to theheavy occlusion in-plane rotation and scale change
Journal of Electrical and Computer Engineering 5
0 100 200 300 400 500 600 700 800 9000
20406080
100120
Frame number
Cen
ter e
rror
Occlusion 1
0 50 100 150 200 250 3000
50100150200250300350400450
Frame number
Cen
ter e
rror
DavidOutdoor
0 50 100 150 200 250 300 350 400 450 5000
20406080
100120140160
Frame number
Cen
ter e
rror
Caviar 2
0 100 200 300 400 500 6000
50
100
150
200
250
Frame numberC
ente
r err
or
Girl
0 100 200 300 400 500 600 7000
50100150200250300350400
Frame number
Cen
ter e
rror
Car 4
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 350 4000
20406080
100120140160
Car 11
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 3500
20406080
100120
Singer 1
Frame number
Cen
ter e
rror
0 10 20 30 40 50 60 70 800
50100150200250300350
Deer
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 3500
20406080
100120140160180200
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Jumping
Frame number
Cen
ter e
rror
0 200 400 600 800 1000 1200 14000
50100150200250300350400450500
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Lemming
Figure 2 Center location error (in pixels) evaluation
6 Journal of Electrical and Computer Engineering
0 100 200 300 400 500 600 700 800 9000
010203040506070809
1
Ove
rlap
rate
Frame number
Occlusion 1
0 50 100 150 200 250 3000
010203040506070809
1
Ove
rlap
rate
Frame number
DavidOutdoor
0 50 100 150 200 250 300 350 400 450 5000
010203040506070809
1
Ove
rlap
rate
Frame number
Caviar 2
0 100 200 300 400 500 6000
010203040506070809
1
Ove
rlap
rate
Frame number
Girl
0 100 200 300 400 500 600 7000
010203040506070809
1
Ove
rlap
rate
Frame number
Car 4
0 50 100 150 200 250 300 350 4000
010203040506070809
1
Ove
rlap
rate
Frame number
Car 11
0 50 100 150 200 250 300 3500
010203040506070809
1
Ove
rlap
rate
Frame number
Singer 1
0 10 20 30 40 50 60 70 800
010203040506070809
1
Ove
rlap
rate
Frame number
Deer
0 50 100 150 200 250 300 3500
010203040506070809
1
Ove
rlap
rate
Frame number
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Jumping
0 200 400 600 800 1000 1200 14000
010203040506070809
1
Ove
rlap
rate
Frame number
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Lemming
Figure 3 Overlap rate evaluation
Journal of Electrical and Computer Engineering 7
42 Quantitative Evaluation To conduct quantitative com-parisons between the proposed tracking method and theother sate-of-the-art trackers we compute the differencebetween the predicted and the ground truth center locationerror in pixels and overlap rates which are most widelyused in quantitative evaluation The center location error isusually defined as the Euclidean distance between the centerlocations of tracked objects and their corresponding labeledground truth Figure 2 demonstrates the center error plotswhere a smaller center error means a more accurate resultin each frame Overlap rate score is defined as score =
area(119877119905cap 119877119892)area(119877
119905cup 119877119892) 119877119905is the tracked bounding
box of each frame and 119877119892is the corresponding ground
truth bounding box Figure 3 shows the overlap rates of eachtracking algorithm for all sequences Generally speaking ourtracker performs favorably against the other methods
43 Computational Complexity The most time consumingpart of the generative tracking algorithm is to compute thecoefficients using the basis vectors For the ℓ
1tracker the
computation of the coefficients using the LASSO algorithmis 119874(1198892 + 119889119896) 119889 is the dimension of subspace and 119896 is thenumber of basis vectorsThe load of the 2DPCAℓ
1tracker [10]
with ℓ1regularization is 119874(119898119889119896) 119898 stands for the number
of iterations (eg 10 on average) For our tracker the trivialtemplates are abandoned and square templates are not usedSo the load of our tracker is 119889119896 The tracking speed of ℓ
1
2DPCAℓ1 and our method is 025 fps 22 fps and 52 fps
separately (fps frame per second) Therefore we can getthat our tracker is more effective and much faster than theaforementioned trackers
5 Conclusion
In this paper we present a fast and effective tracking algo-rithm We first clarify the benefits of the utilizing 2DPCAbasis vectors Then we formulate the tracking process withthe ℓ
2-regularization Finally we update the appearance
model accounting for the partial occlusion Both qualitativeand quantitative evaluations on challenging image sequencedemonstrate that the proposed method outperforms severalstate-of-the-art trackers
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This project is supported by the Shandong Provincial NaturalScience Foundation China (no ZR2015FL009)
References
[1] B Babenko M H Yang and S Belongie ldquoVisual tracking withonline multiple instance learningrdquo in Proceedings of the 22thIEEE Conference on Computer Vision and Pattern Recognitioninpp 983ndash990 San Francisco Calif USA 2009
[2] K H Zhang L Zhang andMH Yang ldquoReal time compressivetrackingrdquo in Proceedings of 12th European Conference on Com-puter Vision pp 864ndash877 Florence Italy 2012
[3] JWright A Y Yang A Ganesh S S Sastry and YMa ldquoRobustface recognition via sparse representationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 31 no 2 pp210ndash227 2009
[4] J Yang J Wright T S Huang and Y Ma ldquoImage super-resolution via sparse representationrdquo IEEE Transactions onImage Processing vol 19 no 11 pp 2861ndash2873 2010
[5] J Mairal M Elad and G Sapiro ldquoSparse representation forcolor image restorationrdquo IEEETransactions on Image Processingvol 17 no 1 pp 53ndash69 2008
[6] Y Wu J Lim and M-H Yang ldquoOnline object tracking abenchmarkrdquo in Proceedings of the 26th IEEE Conference onComputer Vision and Pattern Recognition (CVPR rsquo13) pp 2411ndash2418 Portland Ore USA June 2013
[7] X Jia H Lu and M-H Yang ldquoVisual tracking via adaptivestructural local sparse appearance modelrdquo in Proceedings ofthe 2012 IEEE Conference on Computer Vision and PatternRecognition (CVPR rsquo12) pp 1822ndash1829 Providence RI USAJune 2012
[8] W Zhong H Lu and M-H Yang ldquoRobust object tracking viasparsity-based collaborative modelrdquo in Proceedings of the 25thIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo12) pp 1838ndash1845 Providence RI USA June 2012
[9] T Zhang B Ghanem S Liu and N Ahuja ldquoRobust visualtracking via multi-task sparse learningrdquo in Proceedings ofthe 25th IEEE Conference on Computer Vision and PatternRecognition pp 2042ndash2049 Providence RI USA 2012
[10] X Mei and H Ling ldquoRobust visual tracking using ℓ1minimiza-
tionrdquo in Proceedings of 12th IEEE International Conference onComputer Vision pp 1436ndash1443 Kyoto Japan September 2009
[11] D A Ross J Lim R-S Lin and M-H Yang ldquoIncrementallearning for robust visual trackingrdquo International Journal ofComputer Vision vol 77 no 1ndash3 pp 125ndash141 2008
[12] B H Zhuang H Lu Z Y Xiao and D Wang ldquoVisual trackingvia discriminative sparse similarity maprdquo IEEE Transactions onImage Processing vol 23 no 4 pp 1872ndash1881 2014
[13] C Qian Y B Zhuang and Z Z Xu ldquoVisual tracking withstructural appearance model based on extended incrementalnon-negative matrix factorizationrdquo Neurocomputing vol 136pp 327ndash336 2014
[14] D Wang and H Lu ldquoObject tracking via 2DPCA and l1-regularizationrdquo IEEE Signal Processing Letters vol 19 no 11 pp711ndash714 2012
[15] DWang H Lu and X Li ldquoTwo dimensional principal compo-nents of natural images and its applicationrdquo Neurocomputingvol 74 no 17 pp 2745ndash2753 2011
[16] Z Kalal JMatas andKMikolajczyk ldquoP-N learning bootstrap-ping binary classifiers by structural constraintsrdquo in Proceedingsof the IEEE Computer Society Conference on Computer Visionand Pattern Recognition (CVPR rsquo10) pp 49ndash56 San FranciscoCalif USA June 2010
[17] J Kwon and K M Lee ldquoVisual tracking decompositionrdquoin Proceedings of the IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR rsquo10) pp 1269ndash1276 IEEE San Francisco Calif USA June 2010
[18] A Adam E Rivlin and I Shimshoni ldquoRobust fragments-basedtracking using the integral histogramrdquo in Proceedings of the 19thIEEE Conference on Computer Vision and Pattern Recognitionpp 798ndash805 New York NY USA 2006
119905 x119905minus1 Σ) where Σ is a diagonal covariance
matrix which indicates the variances of affine parameters
Observation Model If no occlusion occurs an image obser-vation B
119905can be generated by a 2DPCA subspace (spanned
by U and V and centered at 120583) Here we consider thepartial occlusion in the appearancemodel for robust trackingThus we assume that the centered image matrices B
119905(B119905=
B119905minus 120583) can be represented by the linear combination of the
projection matricesU and V Then we draw119873 candidates inthe state x
119905 For each of the observed imagematrices we solve
a ℓ2-regularization problem
minA119894
100381710038171003817100381710038171003817B119894 minus UA119894VT100381710038171003817100381710038171003817
where 119894 denotes the 119894th sample of the state x Thus we obtainA119894 and the likelihood can be measured by the reconstructionerror
119901 (B119894 | B119894) = exp(minus100381710038171003817100381710038171003817B119894 minus UA119894VT100381710038171003817100381710038171003817
2
119865
) (7)
However it is noted that just by penalizing error levelthe precise location of the tracked target can be benefitedTherefore we present a novel likelihood function whichconsiders both the reconstruction error and the level of errormatrix
119901 (B119894 | B119894) = exp(minus100381710038171003817100381710038171003817B119894 minus UA119894VT
minus E119894100381710038171003817100381710038171003817
2
119865
minus 12058210038171003817100381710038171003817E119894100381710038171003817100381710038171) (8)
where E119894 can be calculated by (9)
E119894 = B119894 minus UA119894VT (9)
Here A119894 is calculated by (3)
Online Update In order to handle the appearance changeof tracked target it is necessary to update the observa-tion model If some imprecise samples are used to updatethe tracked model may degrade Therefore we present anocclusion-radio-based update mechanism After obtainingthe best candidate state of each frame we compute thecorresponding error matrix and the occlusion ratio 120574 Twothresholds thr
1= 01 and thr
2= 06 are introduced to define
the degree of occlusion If 120574 lt thr1 the tracked target
is not occluded or a small part of it is occluded by thenoise Therefore the model with sample is updated directlyIf thr1lt 120574 lt thr
2 the tracked target is partially occluded
The occluded part is replaced by the average observationand the recovered candidate is used for update If 120574 gt
thr2 most part of the tracked target is occluded Therefore
the sample is discarded without update After we cumulateenough samples we use an incremental 2DPCA algorithm toupdate the tracker (left- and right-projection matrices)
4 Experiments
The proposed tracking algorithm is implemented in MAT-LAB which runs on a computer with Intel i5-3210 CPU
(25GHz) with 4GB memory The regularization 120582 is setto 005 The image observation is resized to pixels for theproposed 2DPCA representation For each sequence thelocation of the tracked target object is manually labeled inthe first frame 600 particles are adopted for the proposedalgorithm accounting for the trade-off between effectivenessand speed Our tracker is incrementally updated every 5frames
To demonstrate the effectiveness of the proposed trackingalgorithm we select six state-of-the-art trackers the ℓ
1
tracker [10] the PN tracker [16] the VTD tracker [17] theMIL tracker [1] the Frag tracker [18] and the 2DPCAℓ
1
tracker [14] for comparison on several challenging imagesequences including Occlusion 1 David Outdoor Caviar 2Girl Car 4 Car 11 Singer 1Deer Jumping and Lemming Thechallenging factors include severe occlusion pose changemotion blur illumination variation and background clutter
41 Qualitative Evaluation
Severe Occlusion We test four sequences (Occlusion 1 David-Outdoor Caviar 2 and Girl) with long time partial or heavyocclusion and scale change Figure 1(a) demonstrates that ℓ
1
algorithm Frag algorithm 2DPCAℓ1 and our algorithms
perform better since these methods take partial occlusioninto account ℓ
1algorithm 2DPCAℓ
1 and our algorithms
can handle occlusion by avoiding updating occluded pixelsinto the PCA basis and 2DPCA basis separately Frag algo-rithm can work well on some simple occlusion cases (egFigure 1(a) Occlusion 1) via the part-based representationHowever this method performs poorly on some more chal-lenging videos (eg Figure 1(b)DavidOutdoor) MIL trackeris not able to track the occluded target in DavidOutdoorand Caviar 2 since the Harr-like features the MIL methodadopted are less effective in distinguishing the similar objectsFor the Girl video the in- and out-of-plane rotation partialocclusion and the scale change make it difficult to track Itcan be seen that the Frag and the proposed tracker workbetter than the other methods
Illumination Change Figures 1(e) and 1(f) present trackingresults using the Car 4 Car 11 and Singer 1 sequenceswith significant change of illumination and scale as well asbackground clutter The ℓ
1tracker 2DPCAℓ
1tracker and
the proposed tracker perform well in the Car 4 sequenceswhereas the other trackers drift away when the target vehiclegoes underneath the overpass or the trees For Car 11sequences 2DPCAℓ
1and the proposed tracker can achieve
robust tracking results whereas the other trackers drift awaywhen drastic illumination change occurs or when similarobject appears In the Singer 1 sequence the drastic illumi-nation and scale change make it difficult to track It can beseen that the proposed tracker performs better than the othermethods
Motion Blur It is difficult for tracking algorithms to predictthe location of the tracked objects when the target movesabruptly Figures 1(h) and 1(i) demonstrate the trackingresults in theDeer and Jumping sequences InDeer sequences
4 Journal of Electrical and Computer Engineering
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(a)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(b)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(c)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(d)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(e)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(f)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(g)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(h)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(i)
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
(j)
Figure 1 Sampled tracking results of partial evaluated algorithms on ten challenging sequences
the animal appearance is almost indistinguishable due to thefast motion and most methods lost the target right at thebeginning of the video At frame 53 PN tracker locates thesimilar deer instead of the right object From the results wecan see that the VTD tracker and our tracker perform betterthan the other algorithms 2DPCAℓ
1tracker may be able to
track the target again by chance after failure The appearancechanges of the Jumping sequences are drastic such that theℓ1 Frag and VTD tracker drift away from the object Our
tracker successfully keeps track of the object with small errors
whereas the MIL PN and 2DPCAℓ1can track the target in
some frames
Background Clutter Figure 1(j) illustrates the tracking resultsin the Lemming sequences with scale and pose change as wellas severe occlusion in cluttered background Frag tracker lostthe target object at the beginning of the sequence and whenthe target object moves quickly or rotates the VTD trackerfails too In contrast the proposed method can adapt to theheavy occlusion in-plane rotation and scale change
Journal of Electrical and Computer Engineering 5
0 100 200 300 400 500 600 700 800 9000
20406080
100120
Frame number
Cen
ter e
rror
Occlusion 1
0 50 100 150 200 250 3000
50100150200250300350400450
Frame number
Cen
ter e
rror
DavidOutdoor
0 50 100 150 200 250 300 350 400 450 5000
20406080
100120140160
Frame number
Cen
ter e
rror
Caviar 2
0 100 200 300 400 500 6000
50
100
150
200
250
Frame numberC
ente
r err
or
Girl
0 100 200 300 400 500 600 7000
50100150200250300350400
Frame number
Cen
ter e
rror
Car 4
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 350 4000
20406080
100120140160
Car 11
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 3500
20406080
100120
Singer 1
Frame number
Cen
ter e
rror
0 10 20 30 40 50 60 70 800
50100150200250300350
Deer
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 3500
20406080
100120140160180200
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Jumping
Frame number
Cen
ter e
rror
0 200 400 600 800 1000 1200 14000
50100150200250300350400450500
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Lemming
Figure 2 Center location error (in pixels) evaluation
6 Journal of Electrical and Computer Engineering
0 100 200 300 400 500 600 700 800 9000
010203040506070809
1
Ove
rlap
rate
Frame number
Occlusion 1
0 50 100 150 200 250 3000
010203040506070809
1
Ove
rlap
rate
Frame number
DavidOutdoor
0 50 100 150 200 250 300 350 400 450 5000
010203040506070809
1
Ove
rlap
rate
Frame number
Caviar 2
0 100 200 300 400 500 6000
010203040506070809
1
Ove
rlap
rate
Frame number
Girl
0 100 200 300 400 500 600 7000
010203040506070809
1
Ove
rlap
rate
Frame number
Car 4
0 50 100 150 200 250 300 350 4000
010203040506070809
1
Ove
rlap
rate
Frame number
Car 11
0 50 100 150 200 250 300 3500
010203040506070809
1
Ove
rlap
rate
Frame number
Singer 1
0 10 20 30 40 50 60 70 800
010203040506070809
1
Ove
rlap
rate
Frame number
Deer
0 50 100 150 200 250 300 3500
010203040506070809
1
Ove
rlap
rate
Frame number
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Jumping
0 200 400 600 800 1000 1200 14000
010203040506070809
1
Ove
rlap
rate
Frame number
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Lemming
Figure 3 Overlap rate evaluation
Journal of Electrical and Computer Engineering 7
42 Quantitative Evaluation To conduct quantitative com-parisons between the proposed tracking method and theother sate-of-the-art trackers we compute the differencebetween the predicted and the ground truth center locationerror in pixels and overlap rates which are most widelyused in quantitative evaluation The center location error isusually defined as the Euclidean distance between the centerlocations of tracked objects and their corresponding labeledground truth Figure 2 demonstrates the center error plotswhere a smaller center error means a more accurate resultin each frame Overlap rate score is defined as score =
area(119877119905cap 119877119892)area(119877
119905cup 119877119892) 119877119905is the tracked bounding
box of each frame and 119877119892is the corresponding ground
truth bounding box Figure 3 shows the overlap rates of eachtracking algorithm for all sequences Generally speaking ourtracker performs favorably against the other methods
43 Computational Complexity The most time consumingpart of the generative tracking algorithm is to compute thecoefficients using the basis vectors For the ℓ
1tracker the
computation of the coefficients using the LASSO algorithmis 119874(1198892 + 119889119896) 119889 is the dimension of subspace and 119896 is thenumber of basis vectorsThe load of the 2DPCAℓ
1tracker [10]
with ℓ1regularization is 119874(119898119889119896) 119898 stands for the number
of iterations (eg 10 on average) For our tracker the trivialtemplates are abandoned and square templates are not usedSo the load of our tracker is 119889119896 The tracking speed of ℓ
1
2DPCAℓ1 and our method is 025 fps 22 fps and 52 fps
separately (fps frame per second) Therefore we can getthat our tracker is more effective and much faster than theaforementioned trackers
5 Conclusion
In this paper we present a fast and effective tracking algo-rithm We first clarify the benefits of the utilizing 2DPCAbasis vectors Then we formulate the tracking process withthe ℓ
2-regularization Finally we update the appearance
model accounting for the partial occlusion Both qualitativeand quantitative evaluations on challenging image sequencedemonstrate that the proposed method outperforms severalstate-of-the-art trackers
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This project is supported by the Shandong Provincial NaturalScience Foundation China (no ZR2015FL009)
References
[1] B Babenko M H Yang and S Belongie ldquoVisual tracking withonline multiple instance learningrdquo in Proceedings of the 22thIEEE Conference on Computer Vision and Pattern Recognitioninpp 983ndash990 San Francisco Calif USA 2009
[2] K H Zhang L Zhang andMH Yang ldquoReal time compressivetrackingrdquo in Proceedings of 12th European Conference on Com-puter Vision pp 864ndash877 Florence Italy 2012
[3] JWright A Y Yang A Ganesh S S Sastry and YMa ldquoRobustface recognition via sparse representationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 31 no 2 pp210ndash227 2009
[4] J Yang J Wright T S Huang and Y Ma ldquoImage super-resolution via sparse representationrdquo IEEE Transactions onImage Processing vol 19 no 11 pp 2861ndash2873 2010
[5] J Mairal M Elad and G Sapiro ldquoSparse representation forcolor image restorationrdquo IEEETransactions on Image Processingvol 17 no 1 pp 53ndash69 2008
[6] Y Wu J Lim and M-H Yang ldquoOnline object tracking abenchmarkrdquo in Proceedings of the 26th IEEE Conference onComputer Vision and Pattern Recognition (CVPR rsquo13) pp 2411ndash2418 Portland Ore USA June 2013
[7] X Jia H Lu and M-H Yang ldquoVisual tracking via adaptivestructural local sparse appearance modelrdquo in Proceedings ofthe 2012 IEEE Conference on Computer Vision and PatternRecognition (CVPR rsquo12) pp 1822ndash1829 Providence RI USAJune 2012
[8] W Zhong H Lu and M-H Yang ldquoRobust object tracking viasparsity-based collaborative modelrdquo in Proceedings of the 25thIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo12) pp 1838ndash1845 Providence RI USA June 2012
[9] T Zhang B Ghanem S Liu and N Ahuja ldquoRobust visualtracking via multi-task sparse learningrdquo in Proceedings ofthe 25th IEEE Conference on Computer Vision and PatternRecognition pp 2042ndash2049 Providence RI USA 2012
[10] X Mei and H Ling ldquoRobust visual tracking using ℓ1minimiza-
tionrdquo in Proceedings of 12th IEEE International Conference onComputer Vision pp 1436ndash1443 Kyoto Japan September 2009
[11] D A Ross J Lim R-S Lin and M-H Yang ldquoIncrementallearning for robust visual trackingrdquo International Journal ofComputer Vision vol 77 no 1ndash3 pp 125ndash141 2008
[12] B H Zhuang H Lu Z Y Xiao and D Wang ldquoVisual trackingvia discriminative sparse similarity maprdquo IEEE Transactions onImage Processing vol 23 no 4 pp 1872ndash1881 2014
[13] C Qian Y B Zhuang and Z Z Xu ldquoVisual tracking withstructural appearance model based on extended incrementalnon-negative matrix factorizationrdquo Neurocomputing vol 136pp 327ndash336 2014
[14] D Wang and H Lu ldquoObject tracking via 2DPCA and l1-regularizationrdquo IEEE Signal Processing Letters vol 19 no 11 pp711ndash714 2012
[15] DWang H Lu and X Li ldquoTwo dimensional principal compo-nents of natural images and its applicationrdquo Neurocomputingvol 74 no 17 pp 2745ndash2753 2011
[16] Z Kalal JMatas andKMikolajczyk ldquoP-N learning bootstrap-ping binary classifiers by structural constraintsrdquo in Proceedingsof the IEEE Computer Society Conference on Computer Visionand Pattern Recognition (CVPR rsquo10) pp 49ndash56 San FranciscoCalif USA June 2010
[17] J Kwon and K M Lee ldquoVisual tracking decompositionrdquoin Proceedings of the IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR rsquo10) pp 1269ndash1276 IEEE San Francisco Calif USA June 2010
[18] A Adam E Rivlin and I Shimshoni ldquoRobust fragments-basedtracking using the integral histogramrdquo in Proceedings of the 19thIEEE Conference on Computer Vision and Pattern Recognitionpp 798ndash805 New York NY USA 2006
Figure 1 Sampled tracking results of partial evaluated algorithms on ten challenging sequences
the animal appearance is almost indistinguishable due to thefast motion and most methods lost the target right at thebeginning of the video At frame 53 PN tracker locates thesimilar deer instead of the right object From the results wecan see that the VTD tracker and our tracker perform betterthan the other algorithms 2DPCAℓ
1tracker may be able to
track the target again by chance after failure The appearancechanges of the Jumping sequences are drastic such that theℓ1 Frag and VTD tracker drift away from the object Our
tracker successfully keeps track of the object with small errors
whereas the MIL PN and 2DPCAℓ1can track the target in
some frames
Background Clutter Figure 1(j) illustrates the tracking resultsin the Lemming sequences with scale and pose change as wellas severe occlusion in cluttered background Frag tracker lostthe target object at the beginning of the sequence and whenthe target object moves quickly or rotates the VTD trackerfails too In contrast the proposed method can adapt to theheavy occlusion in-plane rotation and scale change
Journal of Electrical and Computer Engineering 5
0 100 200 300 400 500 600 700 800 9000
20406080
100120
Frame number
Cen
ter e
rror
Occlusion 1
0 50 100 150 200 250 3000
50100150200250300350400450
Frame number
Cen
ter e
rror
DavidOutdoor
0 50 100 150 200 250 300 350 400 450 5000
20406080
100120140160
Frame number
Cen
ter e
rror
Caviar 2
0 100 200 300 400 500 6000
50
100
150
200
250
Frame numberC
ente
r err
or
Girl
0 100 200 300 400 500 600 7000
50100150200250300350400
Frame number
Cen
ter e
rror
Car 4
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 350 4000
20406080
100120140160
Car 11
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 3500
20406080
100120
Singer 1
Frame number
Cen
ter e
rror
0 10 20 30 40 50 60 70 800
50100150200250300350
Deer
Frame number
Cen
ter e
rror
0 50 100 150 200 250 300 3500
20406080
100120140160180200
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Jumping
Frame number
Cen
ter e
rror
0 200 400 600 800 1000 1200 14000
50100150200250300350400450500
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Lemming
Figure 2 Center location error (in pixels) evaluation
6 Journal of Electrical and Computer Engineering
0 100 200 300 400 500 600 700 800 9000
010203040506070809
1
Ove
rlap
rate
Frame number
Occlusion 1
0 50 100 150 200 250 3000
010203040506070809
1
Ove
rlap
rate
Frame number
DavidOutdoor
0 50 100 150 200 250 300 350 400 450 5000
010203040506070809
1
Ove
rlap
rate
Frame number
Caviar 2
0 100 200 300 400 500 6000
010203040506070809
1
Ove
rlap
rate
Frame number
Girl
0 100 200 300 400 500 600 7000
010203040506070809
1
Ove
rlap
rate
Frame number
Car 4
0 50 100 150 200 250 300 350 4000
010203040506070809
1
Ove
rlap
rate
Frame number
Car 11
0 50 100 150 200 250 300 3500
010203040506070809
1
Ove
rlap
rate
Frame number
Singer 1
0 10 20 30 40 50 60 70 800
010203040506070809
1
Ove
rlap
rate
Frame number
Deer
0 50 100 150 200 250 300 3500
010203040506070809
1
Ove
rlap
rate
Frame number
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Jumping
0 200 400 600 800 1000 1200 14000
010203040506070809
1
Ove
rlap
rate
Frame number
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Lemming
Figure 3 Overlap rate evaluation
Journal of Electrical and Computer Engineering 7
42 Quantitative Evaluation To conduct quantitative com-parisons between the proposed tracking method and theother sate-of-the-art trackers we compute the differencebetween the predicted and the ground truth center locationerror in pixels and overlap rates which are most widelyused in quantitative evaluation The center location error isusually defined as the Euclidean distance between the centerlocations of tracked objects and their corresponding labeledground truth Figure 2 demonstrates the center error plotswhere a smaller center error means a more accurate resultin each frame Overlap rate score is defined as score =
area(119877119905cap 119877119892)area(119877
119905cup 119877119892) 119877119905is the tracked bounding
box of each frame and 119877119892is the corresponding ground
truth bounding box Figure 3 shows the overlap rates of eachtracking algorithm for all sequences Generally speaking ourtracker performs favorably against the other methods
43 Computational Complexity The most time consumingpart of the generative tracking algorithm is to compute thecoefficients using the basis vectors For the ℓ
1tracker the
computation of the coefficients using the LASSO algorithmis 119874(1198892 + 119889119896) 119889 is the dimension of subspace and 119896 is thenumber of basis vectorsThe load of the 2DPCAℓ
1tracker [10]
with ℓ1regularization is 119874(119898119889119896) 119898 stands for the number
of iterations (eg 10 on average) For our tracker the trivialtemplates are abandoned and square templates are not usedSo the load of our tracker is 119889119896 The tracking speed of ℓ
1
2DPCAℓ1 and our method is 025 fps 22 fps and 52 fps
separately (fps frame per second) Therefore we can getthat our tracker is more effective and much faster than theaforementioned trackers
5 Conclusion
In this paper we present a fast and effective tracking algo-rithm We first clarify the benefits of the utilizing 2DPCAbasis vectors Then we formulate the tracking process withthe ℓ
2-regularization Finally we update the appearance
model accounting for the partial occlusion Both qualitativeand quantitative evaluations on challenging image sequencedemonstrate that the proposed method outperforms severalstate-of-the-art trackers
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This project is supported by the Shandong Provincial NaturalScience Foundation China (no ZR2015FL009)
References
[1] B Babenko M H Yang and S Belongie ldquoVisual tracking withonline multiple instance learningrdquo in Proceedings of the 22thIEEE Conference on Computer Vision and Pattern Recognitioninpp 983ndash990 San Francisco Calif USA 2009
[2] K H Zhang L Zhang andMH Yang ldquoReal time compressivetrackingrdquo in Proceedings of 12th European Conference on Com-puter Vision pp 864ndash877 Florence Italy 2012
[3] JWright A Y Yang A Ganesh S S Sastry and YMa ldquoRobustface recognition via sparse representationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 31 no 2 pp210ndash227 2009
[4] J Yang J Wright T S Huang and Y Ma ldquoImage super-resolution via sparse representationrdquo IEEE Transactions onImage Processing vol 19 no 11 pp 2861ndash2873 2010
[5] J Mairal M Elad and G Sapiro ldquoSparse representation forcolor image restorationrdquo IEEETransactions on Image Processingvol 17 no 1 pp 53ndash69 2008
[6] Y Wu J Lim and M-H Yang ldquoOnline object tracking abenchmarkrdquo in Proceedings of the 26th IEEE Conference onComputer Vision and Pattern Recognition (CVPR rsquo13) pp 2411ndash2418 Portland Ore USA June 2013
[7] X Jia H Lu and M-H Yang ldquoVisual tracking via adaptivestructural local sparse appearance modelrdquo in Proceedings ofthe 2012 IEEE Conference on Computer Vision and PatternRecognition (CVPR rsquo12) pp 1822ndash1829 Providence RI USAJune 2012
[8] W Zhong H Lu and M-H Yang ldquoRobust object tracking viasparsity-based collaborative modelrdquo in Proceedings of the 25thIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo12) pp 1838ndash1845 Providence RI USA June 2012
[9] T Zhang B Ghanem S Liu and N Ahuja ldquoRobust visualtracking via multi-task sparse learningrdquo in Proceedings ofthe 25th IEEE Conference on Computer Vision and PatternRecognition pp 2042ndash2049 Providence RI USA 2012
[10] X Mei and H Ling ldquoRobust visual tracking using ℓ1minimiza-
tionrdquo in Proceedings of 12th IEEE International Conference onComputer Vision pp 1436ndash1443 Kyoto Japan September 2009
[11] D A Ross J Lim R-S Lin and M-H Yang ldquoIncrementallearning for robust visual trackingrdquo International Journal ofComputer Vision vol 77 no 1ndash3 pp 125ndash141 2008
[12] B H Zhuang H Lu Z Y Xiao and D Wang ldquoVisual trackingvia discriminative sparse similarity maprdquo IEEE Transactions onImage Processing vol 23 no 4 pp 1872ndash1881 2014
[13] C Qian Y B Zhuang and Z Z Xu ldquoVisual tracking withstructural appearance model based on extended incrementalnon-negative matrix factorizationrdquo Neurocomputing vol 136pp 327ndash336 2014
[14] D Wang and H Lu ldquoObject tracking via 2DPCA and l1-regularizationrdquo IEEE Signal Processing Letters vol 19 no 11 pp711ndash714 2012
[15] DWang H Lu and X Li ldquoTwo dimensional principal compo-nents of natural images and its applicationrdquo Neurocomputingvol 74 no 17 pp 2745ndash2753 2011
[16] Z Kalal JMatas andKMikolajczyk ldquoP-N learning bootstrap-ping binary classifiers by structural constraintsrdquo in Proceedingsof the IEEE Computer Society Conference on Computer Visionand Pattern Recognition (CVPR rsquo10) pp 49ndash56 San FranciscoCalif USA June 2010
[17] J Kwon and K M Lee ldquoVisual tracking decompositionrdquoin Proceedings of the IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR rsquo10) pp 1269ndash1276 IEEE San Francisco Calif USA June 2010
[18] A Adam E Rivlin and I Shimshoni ldquoRobust fragments-basedtracking using the integral histogramrdquo in Proceedings of the 19thIEEE Conference on Computer Vision and Pattern Recognitionpp 798ndash805 New York NY USA 2006
Figure 2 Center location error (in pixels) evaluation
6 Journal of Electrical and Computer Engineering
0 100 200 300 400 500 600 700 800 9000
010203040506070809
1
Ove
rlap
rate
Frame number
Occlusion 1
0 50 100 150 200 250 3000
010203040506070809
1
Ove
rlap
rate
Frame number
DavidOutdoor
0 50 100 150 200 250 300 350 400 450 5000
010203040506070809
1
Ove
rlap
rate
Frame number
Caviar 2
0 100 200 300 400 500 6000
010203040506070809
1
Ove
rlap
rate
Frame number
Girl
0 100 200 300 400 500 600 7000
010203040506070809
1
Ove
rlap
rate
Frame number
Car 4
0 50 100 150 200 250 300 350 4000
010203040506070809
1
Ove
rlap
rate
Frame number
Car 11
0 50 100 150 200 250 300 3500
010203040506070809
1
Ove
rlap
rate
Frame number
Singer 1
0 10 20 30 40 50 60 70 800
010203040506070809
1
Ove
rlap
rate
Frame number
Deer
0 50 100 150 200 250 300 3500
010203040506070809
1
Ove
rlap
rate
Frame number
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Jumping
0 200 400 600 800 1000 1200 14000
010203040506070809
1
Ove
rlap
rate
Frame number
PNVTDMIL
Frag2DPCA9857471
Ours
9857471
Lemming
Figure 3 Overlap rate evaluation
Journal of Electrical and Computer Engineering 7
42 Quantitative Evaluation To conduct quantitative com-parisons between the proposed tracking method and theother sate-of-the-art trackers we compute the differencebetween the predicted and the ground truth center locationerror in pixels and overlap rates which are most widelyused in quantitative evaluation The center location error isusually defined as the Euclidean distance between the centerlocations of tracked objects and their corresponding labeledground truth Figure 2 demonstrates the center error plotswhere a smaller center error means a more accurate resultin each frame Overlap rate score is defined as score =
area(119877119905cap 119877119892)area(119877
119905cup 119877119892) 119877119905is the tracked bounding
box of each frame and 119877119892is the corresponding ground
truth bounding box Figure 3 shows the overlap rates of eachtracking algorithm for all sequences Generally speaking ourtracker performs favorably against the other methods
43 Computational Complexity The most time consumingpart of the generative tracking algorithm is to compute thecoefficients using the basis vectors For the ℓ
1tracker the
computation of the coefficients using the LASSO algorithmis 119874(1198892 + 119889119896) 119889 is the dimension of subspace and 119896 is thenumber of basis vectorsThe load of the 2DPCAℓ
1tracker [10]
with ℓ1regularization is 119874(119898119889119896) 119898 stands for the number
of iterations (eg 10 on average) For our tracker the trivialtemplates are abandoned and square templates are not usedSo the load of our tracker is 119889119896 The tracking speed of ℓ
1
2DPCAℓ1 and our method is 025 fps 22 fps and 52 fps
separately (fps frame per second) Therefore we can getthat our tracker is more effective and much faster than theaforementioned trackers
5 Conclusion
In this paper we present a fast and effective tracking algo-rithm We first clarify the benefits of the utilizing 2DPCAbasis vectors Then we formulate the tracking process withthe ℓ
2-regularization Finally we update the appearance
model accounting for the partial occlusion Both qualitativeand quantitative evaluations on challenging image sequencedemonstrate that the proposed method outperforms severalstate-of-the-art trackers
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This project is supported by the Shandong Provincial NaturalScience Foundation China (no ZR2015FL009)
References
[1] B Babenko M H Yang and S Belongie ldquoVisual tracking withonline multiple instance learningrdquo in Proceedings of the 22thIEEE Conference on Computer Vision and Pattern Recognitioninpp 983ndash990 San Francisco Calif USA 2009
[2] K H Zhang L Zhang andMH Yang ldquoReal time compressivetrackingrdquo in Proceedings of 12th European Conference on Com-puter Vision pp 864ndash877 Florence Italy 2012
[3] JWright A Y Yang A Ganesh S S Sastry and YMa ldquoRobustface recognition via sparse representationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 31 no 2 pp210ndash227 2009
[4] J Yang J Wright T S Huang and Y Ma ldquoImage super-resolution via sparse representationrdquo IEEE Transactions onImage Processing vol 19 no 11 pp 2861ndash2873 2010
[5] J Mairal M Elad and G Sapiro ldquoSparse representation forcolor image restorationrdquo IEEETransactions on Image Processingvol 17 no 1 pp 53ndash69 2008
[6] Y Wu J Lim and M-H Yang ldquoOnline object tracking abenchmarkrdquo in Proceedings of the 26th IEEE Conference onComputer Vision and Pattern Recognition (CVPR rsquo13) pp 2411ndash2418 Portland Ore USA June 2013
[7] X Jia H Lu and M-H Yang ldquoVisual tracking via adaptivestructural local sparse appearance modelrdquo in Proceedings ofthe 2012 IEEE Conference on Computer Vision and PatternRecognition (CVPR rsquo12) pp 1822ndash1829 Providence RI USAJune 2012
[8] W Zhong H Lu and M-H Yang ldquoRobust object tracking viasparsity-based collaborative modelrdquo in Proceedings of the 25thIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo12) pp 1838ndash1845 Providence RI USA June 2012
[9] T Zhang B Ghanem S Liu and N Ahuja ldquoRobust visualtracking via multi-task sparse learningrdquo in Proceedings ofthe 25th IEEE Conference on Computer Vision and PatternRecognition pp 2042ndash2049 Providence RI USA 2012
[10] X Mei and H Ling ldquoRobust visual tracking using ℓ1minimiza-
tionrdquo in Proceedings of 12th IEEE International Conference onComputer Vision pp 1436ndash1443 Kyoto Japan September 2009
[11] D A Ross J Lim R-S Lin and M-H Yang ldquoIncrementallearning for robust visual trackingrdquo International Journal ofComputer Vision vol 77 no 1ndash3 pp 125ndash141 2008
[12] B H Zhuang H Lu Z Y Xiao and D Wang ldquoVisual trackingvia discriminative sparse similarity maprdquo IEEE Transactions onImage Processing vol 23 no 4 pp 1872ndash1881 2014
[13] C Qian Y B Zhuang and Z Z Xu ldquoVisual tracking withstructural appearance model based on extended incrementalnon-negative matrix factorizationrdquo Neurocomputing vol 136pp 327ndash336 2014
[14] D Wang and H Lu ldquoObject tracking via 2DPCA and l1-regularizationrdquo IEEE Signal Processing Letters vol 19 no 11 pp711ndash714 2012
[15] DWang H Lu and X Li ldquoTwo dimensional principal compo-nents of natural images and its applicationrdquo Neurocomputingvol 74 no 17 pp 2745ndash2753 2011
[16] Z Kalal JMatas andKMikolajczyk ldquoP-N learning bootstrap-ping binary classifiers by structural constraintsrdquo in Proceedingsof the IEEE Computer Society Conference on Computer Visionand Pattern Recognition (CVPR rsquo10) pp 49ndash56 San FranciscoCalif USA June 2010
[17] J Kwon and K M Lee ldquoVisual tracking decompositionrdquoin Proceedings of the IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR rsquo10) pp 1269ndash1276 IEEE San Francisco Calif USA June 2010
[18] A Adam E Rivlin and I Shimshoni ldquoRobust fragments-basedtracking using the integral histogramrdquo in Proceedings of the 19thIEEE Conference on Computer Vision and Pattern Recognitionpp 798ndash805 New York NY USA 2006
42 Quantitative Evaluation To conduct quantitative com-parisons between the proposed tracking method and theother sate-of-the-art trackers we compute the differencebetween the predicted and the ground truth center locationerror in pixels and overlap rates which are most widelyused in quantitative evaluation The center location error isusually defined as the Euclidean distance between the centerlocations of tracked objects and their corresponding labeledground truth Figure 2 demonstrates the center error plotswhere a smaller center error means a more accurate resultin each frame Overlap rate score is defined as score =
area(119877119905cap 119877119892)area(119877
119905cup 119877119892) 119877119905is the tracked bounding
box of each frame and 119877119892is the corresponding ground
truth bounding box Figure 3 shows the overlap rates of eachtracking algorithm for all sequences Generally speaking ourtracker performs favorably against the other methods
43 Computational Complexity The most time consumingpart of the generative tracking algorithm is to compute thecoefficients using the basis vectors For the ℓ
1tracker the
computation of the coefficients using the LASSO algorithmis 119874(1198892 + 119889119896) 119889 is the dimension of subspace and 119896 is thenumber of basis vectorsThe load of the 2DPCAℓ
1tracker [10]
with ℓ1regularization is 119874(119898119889119896) 119898 stands for the number
of iterations (eg 10 on average) For our tracker the trivialtemplates are abandoned and square templates are not usedSo the load of our tracker is 119889119896 The tracking speed of ℓ
1
2DPCAℓ1 and our method is 025 fps 22 fps and 52 fps
separately (fps frame per second) Therefore we can getthat our tracker is more effective and much faster than theaforementioned trackers
5 Conclusion
In this paper we present a fast and effective tracking algo-rithm We first clarify the benefits of the utilizing 2DPCAbasis vectors Then we formulate the tracking process withthe ℓ
2-regularization Finally we update the appearance
model accounting for the partial occlusion Both qualitativeand quantitative evaluations on challenging image sequencedemonstrate that the proposed method outperforms severalstate-of-the-art trackers
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This project is supported by the Shandong Provincial NaturalScience Foundation China (no ZR2015FL009)
References
[1] B Babenko M H Yang and S Belongie ldquoVisual tracking withonline multiple instance learningrdquo in Proceedings of the 22thIEEE Conference on Computer Vision and Pattern Recognitioninpp 983ndash990 San Francisco Calif USA 2009
[2] K H Zhang L Zhang andMH Yang ldquoReal time compressivetrackingrdquo in Proceedings of 12th European Conference on Com-puter Vision pp 864ndash877 Florence Italy 2012
[3] JWright A Y Yang A Ganesh S S Sastry and YMa ldquoRobustface recognition via sparse representationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 31 no 2 pp210ndash227 2009
[4] J Yang J Wright T S Huang and Y Ma ldquoImage super-resolution via sparse representationrdquo IEEE Transactions onImage Processing vol 19 no 11 pp 2861ndash2873 2010
[5] J Mairal M Elad and G Sapiro ldquoSparse representation forcolor image restorationrdquo IEEETransactions on Image Processingvol 17 no 1 pp 53ndash69 2008
[6] Y Wu J Lim and M-H Yang ldquoOnline object tracking abenchmarkrdquo in Proceedings of the 26th IEEE Conference onComputer Vision and Pattern Recognition (CVPR rsquo13) pp 2411ndash2418 Portland Ore USA June 2013
[7] X Jia H Lu and M-H Yang ldquoVisual tracking via adaptivestructural local sparse appearance modelrdquo in Proceedings ofthe 2012 IEEE Conference on Computer Vision and PatternRecognition (CVPR rsquo12) pp 1822ndash1829 Providence RI USAJune 2012
[8] W Zhong H Lu and M-H Yang ldquoRobust object tracking viasparsity-based collaborative modelrdquo in Proceedings of the 25thIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo12) pp 1838ndash1845 Providence RI USA June 2012
[9] T Zhang B Ghanem S Liu and N Ahuja ldquoRobust visualtracking via multi-task sparse learningrdquo in Proceedings ofthe 25th IEEE Conference on Computer Vision and PatternRecognition pp 2042ndash2049 Providence RI USA 2012
[10] X Mei and H Ling ldquoRobust visual tracking using ℓ1minimiza-
tionrdquo in Proceedings of 12th IEEE International Conference onComputer Vision pp 1436ndash1443 Kyoto Japan September 2009
[11] D A Ross J Lim R-S Lin and M-H Yang ldquoIncrementallearning for robust visual trackingrdquo International Journal ofComputer Vision vol 77 no 1ndash3 pp 125ndash141 2008
[12] B H Zhuang H Lu Z Y Xiao and D Wang ldquoVisual trackingvia discriminative sparse similarity maprdquo IEEE Transactions onImage Processing vol 23 no 4 pp 1872ndash1881 2014
[13] C Qian Y B Zhuang and Z Z Xu ldquoVisual tracking withstructural appearance model based on extended incrementalnon-negative matrix factorizationrdquo Neurocomputing vol 136pp 327ndash336 2014
[14] D Wang and H Lu ldquoObject tracking via 2DPCA and l1-regularizationrdquo IEEE Signal Processing Letters vol 19 no 11 pp711ndash714 2012
[15] DWang H Lu and X Li ldquoTwo dimensional principal compo-nents of natural images and its applicationrdquo Neurocomputingvol 74 no 17 pp 2745ndash2753 2011
[16] Z Kalal JMatas andKMikolajczyk ldquoP-N learning bootstrap-ping binary classifiers by structural constraintsrdquo in Proceedingsof the IEEE Computer Society Conference on Computer Visionand Pattern Recognition (CVPR rsquo10) pp 49ndash56 San FranciscoCalif USA June 2010
[17] J Kwon and K M Lee ldquoVisual tracking decompositionrdquoin Proceedings of the IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR rsquo10) pp 1269ndash1276 IEEE San Francisco Calif USA June 2010
[18] A Adam E Rivlin and I Shimshoni ldquoRobust fragments-basedtracking using the integral histogramrdquo in Proceedings of the 19thIEEE Conference on Computer Vision and Pattern Recognitionpp 798ndash805 New York NY USA 2006
42 Quantitative Evaluation To conduct quantitative com-parisons between the proposed tracking method and theother sate-of-the-art trackers we compute the differencebetween the predicted and the ground truth center locationerror in pixels and overlap rates which are most widelyused in quantitative evaluation The center location error isusually defined as the Euclidean distance between the centerlocations of tracked objects and their corresponding labeledground truth Figure 2 demonstrates the center error plotswhere a smaller center error means a more accurate resultin each frame Overlap rate score is defined as score =
area(119877119905cap 119877119892)area(119877
119905cup 119877119892) 119877119905is the tracked bounding
box of each frame and 119877119892is the corresponding ground
truth bounding box Figure 3 shows the overlap rates of eachtracking algorithm for all sequences Generally speaking ourtracker performs favorably against the other methods
43 Computational Complexity The most time consumingpart of the generative tracking algorithm is to compute thecoefficients using the basis vectors For the ℓ
1tracker the
computation of the coefficients using the LASSO algorithmis 119874(1198892 + 119889119896) 119889 is the dimension of subspace and 119896 is thenumber of basis vectorsThe load of the 2DPCAℓ
1tracker [10]
with ℓ1regularization is 119874(119898119889119896) 119898 stands for the number
of iterations (eg 10 on average) For our tracker the trivialtemplates are abandoned and square templates are not usedSo the load of our tracker is 119889119896 The tracking speed of ℓ
1
2DPCAℓ1 and our method is 025 fps 22 fps and 52 fps
separately (fps frame per second) Therefore we can getthat our tracker is more effective and much faster than theaforementioned trackers
5 Conclusion
In this paper we present a fast and effective tracking algo-rithm We first clarify the benefits of the utilizing 2DPCAbasis vectors Then we formulate the tracking process withthe ℓ
2-regularization Finally we update the appearance
model accounting for the partial occlusion Both qualitativeand quantitative evaluations on challenging image sequencedemonstrate that the proposed method outperforms severalstate-of-the-art trackers
Competing Interests
The authors declare that they have no competing interests
Acknowledgments
This project is supported by the Shandong Provincial NaturalScience Foundation China (no ZR2015FL009)
References
[1] B Babenko M H Yang and S Belongie ldquoVisual tracking withonline multiple instance learningrdquo in Proceedings of the 22thIEEE Conference on Computer Vision and Pattern Recognitioninpp 983ndash990 San Francisco Calif USA 2009
[2] K H Zhang L Zhang andMH Yang ldquoReal time compressivetrackingrdquo in Proceedings of 12th European Conference on Com-puter Vision pp 864ndash877 Florence Italy 2012
[3] JWright A Y Yang A Ganesh S S Sastry and YMa ldquoRobustface recognition via sparse representationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 31 no 2 pp210ndash227 2009
[4] J Yang J Wright T S Huang and Y Ma ldquoImage super-resolution via sparse representationrdquo IEEE Transactions onImage Processing vol 19 no 11 pp 2861ndash2873 2010
[5] J Mairal M Elad and G Sapiro ldquoSparse representation forcolor image restorationrdquo IEEETransactions on Image Processingvol 17 no 1 pp 53ndash69 2008
[6] Y Wu J Lim and M-H Yang ldquoOnline object tracking abenchmarkrdquo in Proceedings of the 26th IEEE Conference onComputer Vision and Pattern Recognition (CVPR rsquo13) pp 2411ndash2418 Portland Ore USA June 2013
[7] X Jia H Lu and M-H Yang ldquoVisual tracking via adaptivestructural local sparse appearance modelrdquo in Proceedings ofthe 2012 IEEE Conference on Computer Vision and PatternRecognition (CVPR rsquo12) pp 1822ndash1829 Providence RI USAJune 2012
[8] W Zhong H Lu and M-H Yang ldquoRobust object tracking viasparsity-based collaborative modelrdquo in Proceedings of the 25thIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo12) pp 1838ndash1845 Providence RI USA June 2012
[9] T Zhang B Ghanem S Liu and N Ahuja ldquoRobust visualtracking via multi-task sparse learningrdquo in Proceedings ofthe 25th IEEE Conference on Computer Vision and PatternRecognition pp 2042ndash2049 Providence RI USA 2012
[10] X Mei and H Ling ldquoRobust visual tracking using ℓ1minimiza-
tionrdquo in Proceedings of 12th IEEE International Conference onComputer Vision pp 1436ndash1443 Kyoto Japan September 2009
[11] D A Ross J Lim R-S Lin and M-H Yang ldquoIncrementallearning for robust visual trackingrdquo International Journal ofComputer Vision vol 77 no 1ndash3 pp 125ndash141 2008
[12] B H Zhuang H Lu Z Y Xiao and D Wang ldquoVisual trackingvia discriminative sparse similarity maprdquo IEEE Transactions onImage Processing vol 23 no 4 pp 1872ndash1881 2014
[13] C Qian Y B Zhuang and Z Z Xu ldquoVisual tracking withstructural appearance model based on extended incrementalnon-negative matrix factorizationrdquo Neurocomputing vol 136pp 327ndash336 2014
[14] D Wang and H Lu ldquoObject tracking via 2DPCA and l1-regularizationrdquo IEEE Signal Processing Letters vol 19 no 11 pp711ndash714 2012
[15] DWang H Lu and X Li ldquoTwo dimensional principal compo-nents of natural images and its applicationrdquo Neurocomputingvol 74 no 17 pp 2745ndash2753 2011
[16] Z Kalal JMatas andKMikolajczyk ldquoP-N learning bootstrap-ping binary classifiers by structural constraintsrdquo in Proceedingsof the IEEE Computer Society Conference on Computer Visionand Pattern Recognition (CVPR rsquo10) pp 49ndash56 San FranciscoCalif USA June 2010
[17] J Kwon and K M Lee ldquoVisual tracking decompositionrdquoin Proceedings of the IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR rsquo10) pp 1269ndash1276 IEEE San Francisco Calif USA June 2010
[18] A Adam E Rivlin and I Shimshoni ldquoRobust fragments-basedtracking using the integral histogramrdquo in Proceedings of the 19thIEEE Conference on Computer Vision and Pattern Recognitionpp 798ndash805 New York NY USA 2006
