Research Article Visual Tracking Using Max-Average Pooling and Weight-Selection Strategydownloads.hindawi.com/journals/jam/2014/828907.pdf · 2019-07-31 · Research Article Visual

Research ArticleVisual Tracking Using Max-Average Pooling andWeight-Selection Strategy

Suguo Zhu and Junping Du

Beijing Key Laboratory of Intelligent Telecommunication Software and Multimedia School of Computer ScienceBeijing University of Posts and Telecommunications Beijing 100876 China

Correspondence should be addressed to Junping Du junpingdu126com

Received 23 April 2014 Accepted 7 July 2014 Published 20 July 2014

Academic Editor Yantao Shen

Copyright copy 2014 S Zhu and J Du 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

Many modern visual tracking algorithms incorporate spatial pooling max pooling or average pooling which is to achieveinvariance to feature transformations and better robustness to occlusion illumination change and position variation In thispaper max-average pooling method and Weight-selection strategy are proposed with a hybrid framework which is combinedwith sparse representation and particle filter to exploit the spatial information of an object and make good compromises to ensurethe correctness of the results in this framework Challenges can be well considered by the proposed algorithm Experimental resultsdemonstrate the effectiveness and robustness of the proposed algorithm comparedwith the state-of-the-artmethods on challengingsequences

1 Introduction

Visual tracking has a wide range of applications in computervision such as space visual surveillance driver assistancesystem and visual navigation The challenges in designing arobust visual tracking algorithm are caused by the presenceof occlusion background clutter and illumination change

Recently many visual tracking algorithms have beendeveloped to tackle these challenges using sparsity of theimage They usually combine other sophisticated methods totrack the target object Examples are sparse representationcombined with learning [1ndash3] mean shift [4ndash6] Bayesianestimation [7 8] and particle filter [9] However theyoften ignore the pooling method and just take the maxpooling or average pooling method without analyzing it forexample Ross et al [3] do not refer to the pooling methodand employ the max pooling directly Actually the poolingmethod as an indispensable step in sparse representationdoes have an important influence on the performance ofthe algorithm For instance the pooling type is shown tomatter more than the careful unsupervised pretraining offeatures for classification problems with little training dataand good results with random features are obtained whenappropriate pooling is used [10] Yang et al [11] report much

better classification performance on several objects or sceneclassification benchmarks when using the maximum value ofa feature rather than its average to summarize its activity overa region of interest

However in spite of the successes of the previous workthere still exist many limitations As discussed by Boureauet al [12] the conditions max pooling and average poolingwork in are different for the former it is the soft codingmethods upon local descriptors and for the other it is ahard quantization method Boureau et al [13] discuss in thearea of visual recognition the differences of max pooling andaverage pooling and explain the link between the samplecardinality in a spatial pool and also provide results that maxpooling method is better than the average pooling methodthrough experiments except the resolution in visual trackingIn this paper we propose using max pooling and averagepooling together in sparse representation for the first stage ofthe algorithm called max-average pooling method We willdiscuss this method in Section 2

Another popular tracking method is the sequentialMonte Carlo methods also known as particle filters whichrecursively estimate target posterior with discrete sample-weight pairs in a dynamic Bayesian framework The basicidea was introduced by Sarkar [14] and developed into

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2014 Article ID 828907 10 pageshttpdxdoiorg1011552014828907

2 Journal of Applied Mathematics

various improved versions over the last decade Particle filterperforms well in visual areas It is usually merged with otheralgorithms to overcome the complicated situation such asthe color visual spectrum and thermal spectrum images arefused in a joint sparse representation which constructs theparticle filter [9] Unfortunately by the limitation of inferreddrift will not be avoided when the similar obstacle appearsGhosh and Manjunath [15] considers the process of learningthe representation of each particle as an exclusive task toincrease the robustness of the tracker and obtains goodresults however the speed of the algorithm is decreasedgreatly and the particle degeneration still exists

In our studies we found that there are some similaritiesbetween sparse representation and particle filter (1) theassumption is applied that the current tracking is based oncorrect result from the last frame which also means that theresult from every tracking is correct (2) before the analysisof the current frame they both sample particles (3) theycompute the weights for the particles to choose the best oneWe employ the similarities to propose a novel frameworkfor robust object tracking which merges the same stepsof sparse representation and particle filter The proposedframework samples particles around the result tracked fromthe last frame avoiding the particle degeneration The twoalgorithms are illustrated in Figure 1(a) and the proposedframework is shown in Figure 1(b) where the W-S strategyequals Weight-Selection (W-S) strategy it is proposed tobalance the tracking to be more robust and correct The W-Sstrategy will be hashed out in Section 4

In this paper we introduce a robust tracking methodusing a hybrid framework combined with sparse coding andparticle filter for which we propose max-average pooling toimprove the traditional pooling method and the Weight-Selection strategy to avoid drift during object tracking Therest of the paper is organized as follows Section 2 introducesmax-average poolingmethod Section 3 describes the particlefilter details on the framework of the proposed algorithmand analysis of the proposed Weight-Selection strategy arediscussed in Section 4 Subsequently the experiments areexplained in Section 5 In Section 6 the summary of thepaper is presented

2 Sparse Representation withMax-Average Pooling

A typical assumption underlying sparse representation is thatthe tracking result in the last frame is enough accurate thatthe tracker could utilize it for the current prediction Basedon this assumption we draw particles around the last resultthe center point of the bounding box from the last frameand make the dispersion of particles conforms to normaldistribution In this case the particles will disperse aroundthe result of the last frame

The local patches within the target region can be repre-sented as the linear combination of a few basic elements ofthe dictionary with the sparsity assumption For the data inthe current image 119909

119894isin 119883 the set of the basis vector can be

obtained by the following optimal formula

min119882119863

119873

sum

119894=1

1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2+ 120582

1003816100381610038161003816119908119894

1003816100381610038161003816

subject to 1003817100381710038171003817119889119896

1003817100381710038171003817

le 1 forall119896 = 1 2 119870

(1)

where a unit L2-norm constraint on 119908119896is typically applied

to avoid trivial solutions 119863 denotes the dictionary and 119908119894

=

1199081198941

1199081198942

119908119894119872

which contains many zeros to indicatethe sparsity of the image denotes the importance of the 119894thcolumn in the dictionary 119863 Normally the dictionary 119863 isan over-complete basis set that is 119870 gt 119873 The parameter120582 gt 0 is a scalar regularization parameter that balancesthe tradeoff between reconstruction error and sparsity Thereconstruction error indicates the reliability of the represen-tation Note that there are two unknown parameters 119882 and119863 The purpose of this section is to obtain the weight value119882 and the dictionary should be learned first

In many trackingmethods the earlier tracking results arestored longer than the newly acquired results since they areassumed to be more accurate [8 16 17] Accordingly we takethe objects from the first ten tracking results as the initialdictionary to solve the optimization problem Firstly with thehelp of the KNN algorithm which is also called 119896 nearestneighbor algorithm we track the first ten frames to obtain theobjects correctly and quickly For the object tracked from theframes we make affine transformations and save them intothe dictionary Finally the dictionary is constituted as (widthlowast height) lowast 10

The average pooling scheme for histogram generationused by He et al [18] is efficient yet the strategy may miss thespatial information of each patch For example if we changethe location of the left part and the right part of a human faceimage the average pooling scheme neglects the exchangeWhile it is proven by Carneiro and Nascimento [19] thatcompared with average pooling the method of max poolingis more accurate meanwhile max pooling will be moresuitable for the sufficient sparse conditions [13] Combiningthe advantages of the two poolingmethods we propose max-average pooling method to solve the above problems

119908119894

=

max 1199081198941

1199081198942

119908119894119895

119908119894119873

sum 119908119894119895

119895 = 1 2 119873

(2)

where 119908119894denotes the final 119894th pooling result which is

produced by max-average pooling method The proposedpooling method has two steps maximizing of the weightsin vector 119908

119894and then averaging it The denominator in

formula (2) indicates the first step of calculating the max-imization of the weights and the numerator is the sumof 1199081198941

1199081198942

119908119894119895

119908119894119873

which indicates the averagingstep Utilizing the proposedmax-average poolingmethod wemake reconstruction and calculate errors of the reconstruc-tion with patches the formula used for that is as follows

error = sum1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2

(3)

where error is a vector of 1 with 119873 and 119873 is the number ofthe particles Finally we choose the minimum one as the goal

Journal of Applied Mathematics 3

Optimal formula

Sparse coding

Pooling

Result Sample

Sparse representation

Particle filter

Sample

Similarity

Weights

Resample

Result

(a)

Sample

Sparse coding

Pooling

Similarity

Weights Result

W-S strategy

(b)

Figure 1 The illustrations for the algorithmic procedures and the proposed framework (a) algorithm procedures of sparse representationand particle filter and (b) the proposed framework

of our algorithm which corresponds to the tracking result ofthe current frame The algorithm process for one frame is asshown in the Algorithm 1

3 Particle Filter

The particle filter is a Bayesian sequential importance sam-pling technique for estimating the posterior distribution ofstate variables characterizing a dynamic system [14]

Let 119883119905denote the state variable of the object at time 119905

The procedure of particle filter is iterative where the initialstep is to sample 119873 particles from a set of previous particles119883119905minus1

proportionally to their likelihood 119908119894

119905minus1 according to

the distribution 119901(119909119905

| 119909119905minus1

1199111119905

) Subsequently a newstate 119883

119905is generated And that is the traditional sampling

means However the problem is that the new particles arealways affected by the likelihood 119908

119894

119905minus1 which is obtained

from the last state 119905 minus 1 That situation is called particledegeneracy which causes most of the particles concentratethe positions with bigger weights This condition is easyto cause drift In this paper the distribution of particlesis shared with sparse representation avoiding the weightchange caused by the particle degeneracy The reason is thatthere is a similar assumption between sparse representationand particle filters which is that the tracking results beforestate 119905 are all sufficiently exact that the subsequent statesutilize their results for prediction

To accomplish the tracking we compute and update theimportance weight of each particle The posterior 119901(119909

119905|

1199111119905minus1

) is approximated by the finite set of 119873 samples withimportance weights 119908

119894

119905 As is well known if the particle 119909

119894

119905is

the one the tracker predicts the background information inits bounding box will be less than the others and the weight isbigger Accordingly we take two steps to calculate the weight119908119894

119905of each particle An extra bounding box is settled in the

original one which is shown in Figure 2 The weights of theparticles are updated separately as

119908119894

119905119895= 119908119894

119905minus1

119901119895

(119911119905

| 119909119894

119905) 119901119895

(119909119894

119905| 119909119894

119905minus1)

119902119895

(119909119905

| 1199091119905minus1

1199111119905

)

119894 = 1 2 119873 119895 = 1 2

(4)

where 1199091119905minus1

denotes the random samples forming posteriorprobability distribution 119873 denotes the number of the sam-ples 119911

1119905denotes the observed values from the beginning to

time 119905 119909119894119905denotes the 119894th sample at time 119905119908119894

119905minus1denotes the 119894th

weight vector at time 119905minus1 (the last frame) 119902(119909119905

| 1199091119905minus1

1199111119905

) =

119901(119909119905

| 119909119905minus1

) is an importance distribution and the weightsbecome the observation likelihood 119901(119911

119905| 119909119905) Then one

weight is multiplied by the other for the final value Consider

119908119894

119905= 119908119894

1199051sdot 119908119894

1199052 (5)

The above idea can be illustrated in Figure 2 The weightsare calculated with two separated parts which are calledbounding-1 and bounding-2 The width of bounding-2 isa quarter of bounding-1 and the height is an eighth ofbounding-1 Note that bounding-1 is much bigger thanbounding-2 The improvement for the calculation of weightswill increase the accuracy of the prediction especially asthe position of object changes bounding-1 will conclude thechanges of object

4 Tracking with the Proposed Algorithm

41 Sparse Representation Jointed with Particle Filter Sparserepresentation and particle filter both have advantagesand disadvantages of their own The sparse representationmethod is more stable for tracking and able to considerthe spatial information while the particle filter has strongeradaptability for nonlinear and non-Gaussian distribution ofcontinuous system than the other state-of-the-art methodsNonetheless for the sparse representation method wrongreconstruction happens occasionally and it is the fatal prob-lem which could cause drift when shape distortion occurswhile particle degeneration is also hard to solve for theparticle filter


Input An image from the video sequences the center point of the bounding box the noise coefficient120582 and the number of particles 119873(1) Sample 119873 particles around the initial point of the bounding box and the distribution of the particles

is the normal distribution which is implemented by the function randn(2) Initialize the dictionary using tracking results of the first ten frames(3) Compute the formula to obtain the sparse codes min

119882 119863sum119873

119894=1

1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2

+ 1205821003816100381610038161003816119908119894

1003816100381610038161003816

Note that 1003817100381710038171003817119889119896

1003817100381710038171003817

le 1 and 119896 = 1 2 119870 where 119870 is the size of the patchrsquo width by height(4) Pool the features by computing 119908

119894= (max 119908

1198941 1199081198942

119908119894119895

119908119894119873

)(sum 119908119894119895

)

(5) Compute the error of reconstruction119890119903119903119900119903 = sum

1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2

(6) Finally obtain the particle which is corresponding to the minimum error

Algorithm 1 The proposed algorithm with max-average pooling

(Left top)

rectWidth

rectHeight

heightOffset

heightOffset

widthOffset

widthOffset

Bounding-1

Bounding-2

Object

(Right bottom)

(Left998400 top998400)

Figure 2 Two bounding boxes for weights

In this paper we combine the two methods for ourtracking Under the framework of particle filter we employthe sampling method of sparse representation in the phasesof initialization for each frame We solve the optimal math-ematical problem by using a popular tool called SPASMlibrary [20] with the dictionary obtained from the firstten frames The pooling method is used as mentioned inSection 2Through this we obtain one result about the objectSubsequently we compute theweights of all particles sampledat the sparse phase using weight computation method inparticle filter and it also generates a tracking result Actuallytwo tracking results are generated from the above phases andone should be chosen to be the tracking result The solutionwill be proposed in the next section

42 Weight-Selection Strategy Observing the two trackingprocedures we found that the results of sparse representationare more accurate than those of particle filter Howeverduring the tracking using the above method there have beenalways some results jumping far away from an object forexample Figure 3 shows this situation in the 95th frame and96th frame the green point denotes the result of sparse repre-sentation (SR) the yellow point denotes the result of particlefilter (PF) the blue points denote the sampled particles andthe red bounding box is the tracking result Note that the

result of sparse representation suddenly ldquojumpsrdquo to the pointaway from the object when the next frame comes while theone of particle filter just stays around the object though itis not exact enough It is obvious that the tracking result iswrong which means that the tracker drifts

Analyzing the problem above the proposed max-averagepooling method for the sparse reconstruction sometimesis not sufficiently accurate This problem also exists inmax pooling and average pooling method The primaryreason for tracking inaccuracy even for the drift is thesparse reconstruction error Figure 4(a) describes well therelationship between sparse reconstruction errors and theimage sequences as occlusion comes In image sequences theocclusions occur from about the 63rd to the 88th frame andthe 93rd to 150th frame In this figure the two-frame sectionshave the highest reconstruction errors which indicate thatwhen the occlusion comes reconstruction errors will be highenough which can influence the results of object trackingAfter the occlusions the errors drop down and stay below 01at almost the remaining time

To lower the impact caused by the reconstruction errorsZhang et al [16] employ a regularized variant of the L1norm to reconstruction of sparse error Cong et al [17]propose a criterion SRC (sparse representation cost) todetect abnormal event He et al [18] discuss the impactsof reconstruction errors for signal classification Althoughthese methods improve the accuracy of the tracker theyincrease the algorithm complexity For the considerationof the tracking speed and the advantages of particle filterfor tracking we propose Weight-Selection (W-S) strategy tosolve the above problem by choosing different results fordifferent track conditions

We compute the histograms in the bounding boxes whichtake tracking points as centers Comparing the histogramsrespectively with the result in the last frame we choose theone that has smaller distance Let 120582 to be a weight to remedythe inaccuracy cost by the sparse representation error If thesparse result is similar to the last result we will make nodifference otherwise calculate the result as

result = 120582 times sparse + (1 minus 120582) particle (6)where sparse denotes the tracking results of sparse represen-tation method particle denotes results of particle filter and


(a) The 95th frame (b) The 96th frame

Figure 3 Tracking results in ThreePostShop2cor with the problem (green result of SR yellow result of PF blue the sampled particles andred the final tracking result)

120582 is set to be 03 Here we do not put the particle resultto replace sparse representation directly since the particleresult is also not accurate at all the timeWe take compromiseto improve the predictive validity and achieve better dataprocessing When object distortion happens the chosenweight refrains from drifting and enhances the temporaryaccuracy of the tracking

Through W-S strategy we improve the performance ofour tracker The working situation about W-S strategy isshown in Figure 4(b) which is an experiment of ThreeP-astShop2cor sequence The value switches between 1 and2 to make different decisions If the value is 1 it meansthat the reconstruction error is so small that the currentprediction of sparse representation is more similar to theformer result and works as well as the tracking resultotherwise the reconstruction error is incorrect and the finalresult is obtained by (6) Note that it also switches from 1 to2 or from 2 to 1 even after the occlusions That is becauseW-S strategy makes a positive impact on tracking even afterthe occlusions to decrease the effect of pose and positionchanging

We demonstrate the proposed method on ThreePost-Shop2cor sequence The results of the 95th and 96th framesare shown in Figure 5 the green point denotes the result ofsparse representation (SR) the yellow point denotes the resultof particle filter (PF) the blue points denote the sampledparticles and the red bounding box denotes the final trackingresult Note that after using theWeight-Selection strategy wecorrect the jump error and improve the performance of ourtracker

43 Tracking Algorithm with the Proposed Method In thefollowing we provide a summary of the proposed trackingalgorithm

(1) Locate the target in the first frame either manuallyor by using an automated detector and use a singleparticle and a bounding box to indicate this location

(2) Initialize the dictionary with the results by trackingthe target object in the first ten frames using KNNmethod

(3) Advance to the next frame Draw particles accordingto the dynamical model

(4) For each particle extract the corresponding windowfrom the current frame calculate its reconstructionerror using max-average pooling and choose theparticle with the minimum error to be the temporaryresult of sparse representation method At the sametime calculate weights of every particle and choosethe best one as the result of particle filter according tothe particle filter principle

(5) Utilize Weight-Selection strategy and select the bestone to be the final result

(6) Go to Step (3)

Our tracker works as a collector at the very begin-ning when it initializes the dictionary which is also calledtemplates based on tracker Between the accuracy and thespeed of the algorithm there is actually a tradeoff In thenext section we will discuss the implementation issues andanalyze the experimental results

5 Implementation and Experiments

The program of the proposed algorithm is implementedin Matlab r2012b and runs at about 15 frames per secondon an Intel Core 32 GHz with 4GB memory We applythe affine transformation with six parameters to model thetarget motion between two consecutive frames The sparsecoding problem is solved with the SPAMS package [20]and VLFeat open source library (httpwwwvlfeatorg) Foreach sequence we set 600 particles for every frame and thelocation of the target object is manually labeled in the firstframe To make the scenario a bit more realistic and morechallenging we use the same parameters for all the sequencefor instance the parameter 120582 used in the W-S strategy is setto be 03

We evaluate the performance of the proposedalgorithm on three different kinds of challenging videosequences from the previous work [8] CAVIAR data set(httphomepagesinfedacukrbfCAVIAR) and our own


0 50 100 150 200 250 300 3500

005

01

015

02

025

X 88

Frames of sequence

Reco

nstr

uctio

n er

rors

for s

pars

e rep

rese

ntat

ion

Occlusion 2Occlusion 1

X 63

X 93

Y 009694

Y 01246

X 146Y 01377

X 145Y 01202

Y 009671

X 150Y 0113

X 292Y 006501

X 260Y 009223

X 193Y 006491

X 178Y 01028

X 167Y 01049

X 183Y 008949

(a) Reconstruction errors for sparse representation

Opt

ion

for s

witc

hing

1 o

r 2

Occlusion2

Occlusion1

X = 63

Y = 1 Y = 1

X = 88

Y = 1 Y = 1

Y = 2 Y = 2 Y = 2 Y = 2

Y = 2

Y = 2

X = 92 X = 145

Y = 1

Y = 1

Y = 1 Y = 1 Y = 1 Y = 1

X = 150

X = 146

X = 179

X = 167 X = 193

X = 183

X = 292

X = 315

X = 331

X = 260 X = 293 X = 328

0 50 100 150 200 250 30005

1

15

2

25

Frames of sequence

(b) Weight-Selection strategy for tracking

Figure 4 Data analysis about reconstruction errors (a) It illustrates the relationships between sparse reconstruction errors and the imagesequences as occlusions come (b) it describes the function ofWeight-Selection strategy which decreases the impacts of reconstruction errorsduring the tracking Value 1 or 2 represents the option for W-S strategy

The challenges of these sequences include factors that aregenerally considered to be of importance by the scholarssuch as occlusion illumination change posescale variationand background clutter The compared algorithms includetwo state-of-the-art tracking methods tracking-learning-detection (TLD) tracker [2] and incremental learning forvisual tracking (ILVT) tracker [3] which are provided by theauthors used for fair comparison For a better comparisonthe parameters for the comparison algorithms and theproposed algorithm are set to be the same which will ensurethat the conditions are the same for all of the algorithms totrack the object

51 Quantitative Evaluation Evaluation criteria are em-ployed to quantitatively assess the performance of the

trackers Figure 6 presents the relative position errors whichis calculated (in pixels) against the manually labeled groundtruth Let

error =

1

119873

119873

sum

119894=1

radic(119909119872119894

minus 119909gt119894)2

+ (119910119872119894

minus 119910gt119894)2 (7)

where error denotes the relative position error of the trackingresult (119909

119872119894 119910119872119894

) and the ground truth (119909gt119894 119910gt119894) 119872 meansthe tracking algorithm 119872 119873 denotes the frame number ofthe tested video sequences and 119894 indicates the 119894th frame Thedetail of the errors is shown in Figure 6

Overall the proposed algorithmperformswell against thestate-of-the-art methods It is able to overcome the influencesof the occlusions illumination change and pose variation



Figure 5 Tracking results in ThreePostShop2cor with Weight-Selection strategy (green result of SR yellow result of PF blue the sampledparticles and red the final tracking result)

The performance of our method can be attributed to theefficient pooling method and W-S strategy

52 Qualitative Evaluation The first sequence ThreePast-Shop2cor has been used in several recent tracking papers[1 8] and it presents the challenging issues such as occlusionsand scale and pose changes Especially for occlusions thesequence shows a process of no occlusion presenting occlu-sion and the occlusion disappeared and the occlusions arefrom the 63rd to the 88th frame and the 93rd to 150th frameThe occlusion happens twice and the two persons nearbyare similar to the object especially the one on the rightIn Figure 7 we use a red rectangle to denote our proposedmethod blue to TLD method and green to ILVT methodNote that during the object (the person) moving from theclose to the distant the comparison methods begin to driftor deviate from the object while the proposed method isalways able to track the object even occlusions appear twiceThe TLD tracker shows inaccuracy at about the 70th framealthough its rectangle (blue) includes the object it containstoomuch background information which could lead to errorfor the computation of the similarity between two histogramsand make the forward or backward error not exact ILVTmethod occurs incorrectly as the red person blocks the targetobject at about the 63rd frameThe reason is that in the 78thframe the object disappeared temporally at the same timeILVT tracker could not search for it and make the new errorinformation be the target object For the next frames ILVTmethod drifts completely In the proposed method max-average pooling not only considers the space constructionbut also chooses the best patches which could represent thecharacters of the object The proposed tracker is able to trackthe object correctly and exactly even the occlusions occurtwice

The second sequence Car4 shown in Figure 6 containsa car driven in the sunlight and in the middle of thesequence the shadow changes appearance of the car for ashort time The illumination change will disturb the trackingbecause it makes the appearance and texture of the object

different Note that before the shadow came the trackerscould always track the object though TLD method containsmore background information than ILVT method and theproposed method As the shadow comes TLDmethod is notable to maintain the earlier situation It loses the object andthe drift shows up At the end of the sequence TLDmethod isable to recapture the target after drifting into the backgroundbut with higher tracking errors and lower success rate(Figure 8)

We notice that during the whole tracking ILVT methodand the proposed method track the object all the time Theproposed method is not as steady as ILVT method Thereason is the influence of ldquojumprdquo As long as it jumps to theplace far away from the object the W-S strategy makes goodcompromise which can ensure the correctness of themethodThe error of the proposedmethod is similar to ILVTmethodIf we do not consider the W-S strategy the tracker will driftFrom the overall perspective although the proposed methodis not as steady as ILVT method it is able to track the objectand its rectangle includes much less background informationthan ILVT method

The last video was taken on the bus in the eveningwhich is shown in Figure 9 We try to track the bus infront of the camera The lighting is dark the contrastbetween the target and the background is low and it isvery difficult for the general algorithm to track the targetobject exactly However the proposed method performswell in tracking the bus while the other two methods driftinto the cluttered background when drastic illuminationvariation occurs This can be attributed to the strategyof Weight-Selection which is able to capture the correctappearance change due to lighting changesWith the distancebetween the bus and the camera becoming further andfurther the size of the proposed tracking box reduces TLDmethod and ILVT method contain more information thanthe proposed method as the illumination changes drasticallyand the distance becomes far As time passes by the twocompared methods lose the target object gradually Mean-while the proposed method tracks the target object all thetime


0 50 100 150 200 2500

20

40

60

80

100

120

Frame

Erro

rThreePastShop2cor

ILVTTLD

OURS

(a)

0 50 100 150 200 2500

20

40

60

80

100

Frame

Erro

r

Car4

ILVTTLD

OURS

(b)

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

Frame

Erro

r

Bjbus103

ILVTTLD

OURS

(c)

Figure 6 Quantitative evaluation of the trackers in terms of position errors (in pixels) The center errors of the proposed algorithm (red) incomparison with ILVT (green) and TLD (blue) algorithm at three sequences

6 Conclusions

In this paper we propose an efficient tracking algorithmbased on sparse representation and particle filter usingthe proposed max-average pooling and Weight-Selectionstrategy The proposed method exploits both spatial andlocal information of the target by max-average poolingand avoids the drift resulting from sparse reconstructionerrors using Weight-Selection strategy This helps opti-mization of the spatial and local information In additionthe combination of the sparse representation and parti-cle filter avoids the particle degeneration highlights their

respective advantages and improves the performance ofthe algorithm Experimental results demonstrate the effec-tiveness and robustness of the proposed algorithm com-pared with the state-of-the-art methods on challengingsequences

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


Figure 7 ThreePastShop2cor the challenges are occlusions and pose variation (red the proposed method blue TLD method and greenILVT method)

Figure 8 Car4 a car moving underneath an overpass and trees The challenges are the illumination change and pose variation (red theproposed method blue TLD method green ILVT method)

Figure 9 Bjbus103 the sequence is captured on the bus in the evening The target object is the bus in front of the camera The challenges arethe illumination change and pose variation (red the proposed method blue TLD method green ILVT method)


Acknowledgments

This work is supported by the National Basic ResearchProgram of China (973Program) 2012CB821200 (Grant no2012CB821206) and the National Natural Science Foundationof China (Grant no 61320106006)

References

[1] D Wang H Lu and M Yang ldquoOnline object tracking withsparse prototypesrdquo IEEE Transactions on Image Processing vol22 no 1 pp 314ndash325 2013

[2] Z Kalal K Mikolajczyk and J Matas ldquoFace-TLD tracking-learning-detection applied to facesrdquo in Proceedings of the 17thIEEE International Conference on Image Processing (ICIP rsquo10)pp 3789ndash3792 Hong Kong China September 2010

[3] D A Ross J Lim R Lin and M Yang ldquoIncremental learningfor robust visual trackingrdquo International Journal of ComputerVision vol 77 no 1ndash3 pp 125ndash141 2008

[4] D Comaniciu and P Meer ldquoMean shift a robust approachtoward feature space analysisrdquo IEEE Transactions on PatternAnalysis and Machine Intelligence vol 24 no 5 pp 603ndash6192002

[5] B Liu J Huang L Yang and C Kulikowsk ldquoRobust trackingusing local sparse appearance model and K-selectionrdquo inProceedings of the IEEE Conference on Computer Vision andPattern Recognition (CVPR 11) pp 1313ndash1320 Providence RIUSA June 2011

[6] D Comaniciu V Ramesh and P Meer ldquoReal-time tracking ofnon-rigid objects using mean shiftrdquo in Proceedings of the IEEEConference on Computer Vision and Pattern Recognition (CVPR00) pp 142ndash149 Hilton Head Island SC USA June 2000

[7] B Li W Xiong W Hu et al ldquoIllumination estimation basedon bilayer sparse codingrdquo in Proceedings of the IEEE Conferenceon Computer Vision and Pattern Recognition pp 1423ndash1429Portland Ore USA 2013

[8] X Jia H Lu and M Yang ldquoVisual tracking via adaptivestructural local sparse appearance modelrdquo in Proceedings of theIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo12) pp 1822ndash1829 Providence RI USA June 2012

[9] H P Liu and F C Sun ldquoFusion tracking in color and infraredimages using joint sparse representationrdquo Science China Infor-mation Sciences vol 55 no 3 pp 590ndash599 2012

[10] K Jarrett K Kavukcuoglu M Ranzato and Y LeCun ldquoWhatis the best multi-stage architecture for object recognitionrdquo inProceedings of IEEE 12th International Conference on ComputerVision (ICCV rsquo09) pp 2146ndash2153 Kyoto Japan October 2009

[11] J Yang K Yu Y Gong and T Huang ldquoLinear spatial pyra-mid matching using sparse coding for image classificationrdquoin Proceedings of the IEEE Computer Society Conference onComputer Vision and Pattern Recognition Workshops (CVPRrsquo09) pp 1794ndash1801 Miami Fla USA June 2009

[12] Y-L Boureau F Bach Y LeCun and J Ponce ldquoLearningmid-level features for recognitionrdquo in Proceedings of the IEEEComputer Society Conference on Computer Vision and PatternRecognition (CVPR 10) pp 2559ndash2566 San Francisco CalifUSA June 2010

[13] Y Boureau J Ponce and Y Lecun ldquoA theoretical analysis offeature pooling in visual recognitionrdquo in Proceedings of the 27thInternational Conference on Machine Learning (ICML rsquo10) pp111ndash118 Haifa Israel June 2010

[14] P Sarkar ldquoSequential Monte Carlo methods in practicerdquo Tech-nometrics vol 45 no 1 p 106 2003

[15] P Ghosh and B S Manjunath ldquoRobust simultaneous registra-tion and segmentation with sparse error reconstructionrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol35 no 2 pp 425ndash436 2013

[16] T Zhang B Ghanem S Liu and N Ahuja ldquoRobust visualtracking via multi-task sparse learningrdquo in Proceedings of theIEEE Conference on Computer Vision and Pattern Recognition(CVPR rsquo12) pp 2042ndash2049 Providence RI USA June 2012

[17] Y Cong J Yuan and J Liu ldquoSparse reconstruction cost forabnormal event detectionrdquo in Proceedings of the IEEE Confer-ence on Computer Vision and Pattern Recognition (CVPR 11)pp 3449ndash3456 Providence RI USA June 2011

[18] S He Q Yang W H R Lau et al ldquoVisual tracking via localitysensitive histogramsrdquo in Proceedings of the IEEE Conferenceon Computer Vision and Pattern Recognition pp 2427ndash2434Portland Ore USA 2013

[19] G Carneiro and J C Nascimento ldquoThe fusion of deep learningarchitectures and particle filtering applied to lip trackingrdquo inProceedings of the 20th International Conference on PatternRecognition (ICPR 10) pp 2065ndash2068 Istanbul Turkey August2010

[20] J Mairal F Bach J Ponce and G Sapiro ldquoOnline learningfor matrix factorization and sparse codingrdquo Journal of MachineLearning Research vol 11 pp 19ndash60 2010

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Differential EquationsInternational Journal of

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Applied MathematicsJournal of


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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


various improved versions over the last decade Particle filterperforms well in visual areas It is usually merged with otheralgorithms to overcome the complicated situation such asthe color visual spectrum and thermal spectrum images arefused in a joint sparse representation which constructs theparticle filter [9] Unfortunately by the limitation of inferreddrift will not be avoided when the similar obstacle appearsGhosh and Manjunath [15] considers the process of learningthe representation of each particle as an exclusive task toincrease the robustness of the tracker and obtains goodresults however the speed of the algorithm is decreasedgreatly and the particle degeneration still exists

In our studies we found that there are some similaritiesbetween sparse representation and particle filter (1) theassumption is applied that the current tracking is based oncorrect result from the last frame which also means that theresult from every tracking is correct (2) before the analysisof the current frame they both sample particles (3) theycompute the weights for the particles to choose the best oneWe employ the similarities to propose a novel frameworkfor robust object tracking which merges the same stepsof sparse representation and particle filter The proposedframework samples particles around the result tracked fromthe last frame avoiding the particle degeneration The twoalgorithms are illustrated in Figure 1(a) and the proposedframework is shown in Figure 1(b) where the W-S strategyequals Weight-Selection (W-S) strategy it is proposed tobalance the tracking to be more robust and correct The W-Sstrategy will be hashed out in Section 4

In this paper we introduce a robust tracking methodusing a hybrid framework combined with sparse coding andparticle filter for which we propose max-average pooling toimprove the traditional pooling method and the Weight-Selection strategy to avoid drift during object tracking Therest of the paper is organized as follows Section 2 introducesmax-average poolingmethod Section 3 describes the particlefilter details on the framework of the proposed algorithmand analysis of the proposed Weight-Selection strategy arediscussed in Section 4 Subsequently the experiments areexplained in Section 5 In Section 6 the summary of thepaper is presented

2 Sparse Representation withMax-Average Pooling

A typical assumption underlying sparse representation is thatthe tracking result in the last frame is enough accurate thatthe tracker could utilize it for the current prediction Basedon this assumption we draw particles around the last resultthe center point of the bounding box from the last frameand make the dispersion of particles conforms to normaldistribution In this case the particles will disperse aroundthe result of the last frame

The local patches within the target region can be repre-sented as the linear combination of a few basic elements ofthe dictionary with the sparsity assumption For the data inthe current image 119909

119894isin 119883 the set of the basis vector can be

obtained by the following optimal formula

min119882119863

119873

sum

119894=1

1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2+ 120582

1003816100381610038161003816119908119894

1003816100381610038161003816

subject to 1003817100381710038171003817119889119896

1003817100381710038171003817

le 1 forall119896 = 1 2 119870

(1)

where a unit L2-norm constraint on 119908119896is typically applied

to avoid trivial solutions 119863 denotes the dictionary and 119908119894

=

1199081198941

1199081198942

119908119894119872

which contains many zeros to indicatethe sparsity of the image denotes the importance of the 119894thcolumn in the dictionary 119863 Normally the dictionary 119863 isan over-complete basis set that is 119870 gt 119873 The parameter120582 gt 0 is a scalar regularization parameter that balancesthe tradeoff between reconstruction error and sparsity Thereconstruction error indicates the reliability of the represen-tation Note that there are two unknown parameters 119882 and119863 The purpose of this section is to obtain the weight value119882 and the dictionary should be learned first

In many trackingmethods the earlier tracking results arestored longer than the newly acquired results since they areassumed to be more accurate [8 16 17] Accordingly we takethe objects from the first ten tracking results as the initialdictionary to solve the optimization problem Firstly with thehelp of the KNN algorithm which is also called 119896 nearestneighbor algorithm we track the first ten frames to obtain theobjects correctly and quickly For the object tracked from theframes we make affine transformations and save them intothe dictionary Finally the dictionary is constituted as (widthlowast height) lowast 10

The average pooling scheme for histogram generationused by He et al [18] is efficient yet the strategy may miss thespatial information of each patch For example if we changethe location of the left part and the right part of a human faceimage the average pooling scheme neglects the exchangeWhile it is proven by Carneiro and Nascimento [19] thatcompared with average pooling the method of max poolingis more accurate meanwhile max pooling will be moresuitable for the sufficient sparse conditions [13] Combiningthe advantages of the two poolingmethods we propose max-average pooling method to solve the above problems

119908119894

=

max 1199081198941

1199081198942

119908119894119895

119908119894119873

sum 119908119894119895

119895 = 1 2 119873

(2)

where 119908119894denotes the final 119894th pooling result which is

produced by max-average pooling method The proposedpooling method has two steps maximizing of the weightsin vector 119908

119894and then averaging it The denominator in

formula (2) indicates the first step of calculating the max-imization of the weights and the numerator is the sumof 1199081198941

1199081198942

119908119894119895

119908119894119873

which indicates the averagingstep Utilizing the proposedmax-average poolingmethod wemake reconstruction and calculate errors of the reconstruc-tion with patches the formula used for that is as follows

error = sum1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2

(3)

where error is a vector of 1 with 119873 and 119873 is the number ofthe particles Finally we choose the minimum one as the goal


Optimal formula

Sparse coding

Pooling

Result Sample


Particle filter

Sample

Similarity

Weights

Resample

Result

(a)

Sample

Sparse coding

Pooling

Similarity

Weights Result

W-S strategy

(b)



3 Particle Filter







| 119909119905minus1

1199111119905




119894




119905|

1199111119905minus1


119894


119894

119905is




119908119894

119905119895= 119908119894

119905minus1

119901119895

(119911119905

| 119909119894

119905) 119901119895

(119909119894

119905| 119909119894

119905minus1)

119902119895

(119909119905

| 1199091119905minus1

1199111119905

)

119894 = 1 2 119873 119895 = 1 2

(4)







| 1199091119905minus1

1199111119905

) =

119901(119909119905

| 119909119905minus1


119905| 119909119905) Then one


119908119894

119905= 119908119894

1199051sdot 119908119894

1199052 (5)







119882 119863sum119873

119894=1

1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2

+ 1205821003816100381610038161003816119908119894

1003816100381610038161003816

Note that 1003817100381710038171003817119889119896

1003817100381710038171003817


119894= (max 119908

1198941 1199081198942

119908119894119895

119908119894119873

)(sum 119908119894119895

)


1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2



(Left top)

rectWidth

rectHeight

heightOffset

heightOffset

widthOffset

widthOffset

Bounding-1

Bounding-2

Object

(Right bottom)

(Left998400 top998400)





















(6) Go to Step (3)






0 50 100 150 200 250 300 3500

005

01

015

02

025

X 88

Frames of sequence

Reco

nstr

uctio

n er

rors

for s

pars

e rep

rese

ntat

ion


X 63

X 93

Y 009694

Y 01246

X 146Y 01377

X 145Y 01202

Y 009671

X 150Y 0113

X 292Y 006501

X 260Y 009223

X 193Y 006491

X 178Y 01028

X 167Y 01049

X 183Y 008949


Opt

ion

for s

witc

hing

1 o

r 2

Occlusion2

Occlusion1

X = 63

Y = 1 Y = 1

X = 88

Y = 1 Y = 1

Y = 2 Y = 2 Y = 2 Y = 2

Y = 2

Y = 2

X = 92 X = 145

Y = 1

Y = 1

Y = 1 Y = 1 Y = 1 Y = 1

X = 150

X = 146

X = 179

X = 167 X = 193

X = 183

X = 292

X = 315

X = 331

X = 260 X = 293 X = 328

0 50 100 150 200 250 30005

1

15

2

25

Frames of sequence






error =

1

119873

119873

sum

119894=1

radic(119909119872119894

minus 119909gt119894)2

+ (119910119872119894

minus 119910gt119894)2 (7)


119872119894 119910119872119894













0 50 100 150 200 2500

20

40

60

80

100

120

Frame

Erro

rThreePastShop2cor

ILVTTLD

OURS

(a)

0 50 100 150 200 2500

20

40

60

80

100

Frame

Erro

r

Car4

ILVTTLD

OURS

(b)

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

Frame

Erro

r

Bjbus103

ILVTTLD

OURS

(c)


6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Optimal formula

Sparse coding

Pooling

Result Sample


Particle filter

Sample

Similarity

Weights

Resample

Result

(a)

Sample

Sparse coding

Pooling

Similarity

Weights Result

W-S strategy

(b)



3 Particle Filter







| 119909119905minus1

1199111119905




119894




119905|

1199111119905minus1


119894


119894

119905is




119908119894

119905119895= 119908119894

119905minus1

119901119895

(119911119905

| 119909119894

119905) 119901119895

(119909119894

119905| 119909119894

119905minus1)

119902119895

(119909119905

| 1199091119905minus1

1199111119905

)

119894 = 1 2 119873 119895 = 1 2

(4)







| 1199091119905minus1

1199111119905

) =

119901(119909119905

| 119909119905minus1


119905| 119909119905) Then one


119908119894

119905= 119908119894

1199051sdot 119908119894

1199052 (5)







119882 119863sum119873

119894=1

1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2

+ 1205821003816100381610038161003816119908119894

1003816100381610038161003816

Note that 1003817100381710038171003817119889119896

1003817100381710038171003817


119894= (max 119908

1198941 1199081198942

119908119894119895

119908119894119873

)(sum 119908119894119895

)


1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2



(Left top)

rectWidth

rectHeight

heightOffset

heightOffset

widthOffset

widthOffset

Bounding-1

Bounding-2

Object

(Right bottom)

(Left998400 top998400)





















(6) Go to Step (3)






0 50 100 150 200 250 300 3500

005

01

015

02

025

X 88

Frames of sequence

Reco

nstr

uctio

n er

rors

for s

pars

e rep

rese

ntat

ion


X 63

X 93

Y 009694

Y 01246

X 146Y 01377

X 145Y 01202

Y 009671

X 150Y 0113

X 292Y 006501

X 260Y 009223

X 193Y 006491

X 178Y 01028

X 167Y 01049

X 183Y 008949


Opt

ion

for s

witc

hing

1 o

r 2

Occlusion2

Occlusion1

X = 63

Y = 1 Y = 1

X = 88

Y = 1 Y = 1

Y = 2 Y = 2 Y = 2 Y = 2

Y = 2

Y = 2

X = 92 X = 145

Y = 1

Y = 1

Y = 1 Y = 1 Y = 1 Y = 1

X = 150

X = 146

X = 179

X = 167 X = 193

X = 183

X = 292

X = 315

X = 331

X = 260 X = 293 X = 328

0 50 100 150 200 250 30005

1

15

2

25

Frames of sequence






error =

1

119873

119873

sum

119894=1

radic(119909119872119894

minus 119909gt119894)2

+ (119910119872119894

minus 119910gt119894)2 (7)


119872119894 119910119872119894













0 50 100 150 200 2500

20

40

60

80

100

120

Frame

Erro

rThreePastShop2cor

ILVTTLD

OURS

(a)

0 50 100 150 200 2500

20

40

60

80

100

Frame

Erro

r

Car4

ILVTTLD

OURS

(b)

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

Frame

Erro

r

Bjbus103

ILVTTLD

OURS

(c)


6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119882 119863sum119873

119894=1

1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2

+ 1205821003816100381610038161003816119908119894

1003816100381610038161003816

Note that 1003817100381710038171003817119889119896

1003817100381710038171003817


119894= (max 119908

1198941 1199081198942

119908119894119895

119908119894119873

)(sum 119908119894119895

)


1003817100381710038171003817119909119894

minus 119908119894119863

1003817100381710038171003817

2



(Left top)

rectWidth

rectHeight

heightOffset

heightOffset

widthOffset

widthOffset

Bounding-1

Bounding-2

Object

(Right bottom)

(Left998400 top998400)





















(6) Go to Step (3)






0 50 100 150 200 250 300 3500

005

01

015

02

025

X 88

Frames of sequence

Reco

nstr

uctio

n er

rors

for s

pars

e rep

rese

ntat

ion


X 63

X 93

Y 009694

Y 01246

X 146Y 01377

X 145Y 01202

Y 009671

X 150Y 0113

X 292Y 006501

X 260Y 009223

X 193Y 006491

X 178Y 01028

X 167Y 01049

X 183Y 008949


Opt

ion

for s

witc

hing

1 o

r 2

Occlusion2

Occlusion1

X = 63

Y = 1 Y = 1

X = 88

Y = 1 Y = 1

Y = 2 Y = 2 Y = 2 Y = 2

Y = 2

Y = 2

X = 92 X = 145

Y = 1

Y = 1

Y = 1 Y = 1 Y = 1 Y = 1

X = 150

X = 146

X = 179

X = 167 X = 193

X = 183

X = 292

X = 315

X = 331

X = 260 X = 293 X = 328

0 50 100 150 200 250 30005

1

15

2

25

Frames of sequence






error =

1

119873

119873

sum

119894=1

radic(119909119872119894

minus 119909gt119894)2

+ (119910119872119894

minus 119910gt119894)2 (7)


119872119894 119910119872119894













0 50 100 150 200 2500

20

40

60

80

100

120

Frame

Erro

rThreePastShop2cor

ILVTTLD

OURS

(a)

0 50 100 150 200 2500

20

40

60

80

100

Frame

Erro

r

Car4

ILVTTLD

OURS

(b)

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

Frame

Erro

r

Bjbus103

ILVTTLD

OURS

(c)


6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





















(6) Go to Step (3)






0 50 100 150 200 250 300 3500

005

01

015

02

025

X 88

Frames of sequence

Reco

nstr

uctio

n er

rors

for s

pars

e rep

rese

ntat

ion


X 63

X 93

Y 009694

Y 01246

X 146Y 01377

X 145Y 01202

Y 009671

X 150Y 0113

X 292Y 006501

X 260Y 009223

X 193Y 006491

X 178Y 01028

X 167Y 01049

X 183Y 008949


Opt

ion

for s

witc

hing

1 o

r 2

Occlusion2

Occlusion1

X = 63

Y = 1 Y = 1

X = 88

Y = 1 Y = 1

Y = 2 Y = 2 Y = 2 Y = 2

Y = 2

Y = 2

X = 92 X = 145

Y = 1

Y = 1

Y = 1 Y = 1 Y = 1 Y = 1

X = 150

X = 146

X = 179

X = 167 X = 193

X = 183

X = 292

X = 315

X = 331

X = 260 X = 293 X = 328

0 50 100 150 200 250 30005

1

15

2

25

Frames of sequence






error =

1

119873

119873

sum

119894=1

radic(119909119872119894

minus 119909gt119894)2

+ (119910119872119894

minus 119910gt119894)2 (7)


119872119894 119910119872119894













0 50 100 150 200 2500

20

40

60

80

100

120

Frame

Erro

rThreePastShop2cor

ILVTTLD

OURS

(a)

0 50 100 150 200 2500

20

40

60

80

100

Frame

Erro

r

Car4

ILVTTLD

OURS

(b)

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

Frame

Erro

r

Bjbus103

ILVTTLD

OURS

(c)


6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 50 100 150 200 250 300 3500

005

01

015

02

025

X 88

Frames of sequence

Reco

nstr

uctio

n er

rors

for s

pars

e rep

rese

ntat

ion


X 63

X 93

Y 009694

Y 01246

X 146Y 01377

X 145Y 01202

Y 009671

X 150Y 0113

X 292Y 006501

X 260Y 009223

X 193Y 006491

X 178Y 01028

X 167Y 01049

X 183Y 008949


Opt

ion

for s

witc

hing

1 o

r 2

Occlusion2

Occlusion1

X = 63

Y = 1 Y = 1

X = 88

Y = 1 Y = 1

Y = 2 Y = 2 Y = 2 Y = 2

Y = 2

Y = 2

X = 92 X = 145

Y = 1

Y = 1

Y = 1 Y = 1 Y = 1 Y = 1

X = 150

X = 146

X = 179

X = 167 X = 193

X = 183

X = 292

X = 315

X = 331

X = 260 X = 293 X = 328

0 50 100 150 200 250 30005

1

15

2

25

Frames of sequence






error =

1

119873

119873

sum

119894=1

radic(119909119872119894

minus 119909gt119894)2

+ (119910119872119894

minus 119910gt119894)2 (7)


119872119894 119910119872119894













0 50 100 150 200 2500

20

40

60

80

100

120

Frame

Erro

rThreePastShop2cor

ILVTTLD

OURS

(a)

0 50 100 150 200 2500

20

40

60

80

100

Frame

Erro

r

Car4

ILVTTLD

OURS

(b)

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

Frame

Erro

r

Bjbus103

ILVTTLD

OURS

(c)


6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















0 50 100 150 200 2500

20

40

60

80

100

120

Frame

Erro

rThreePastShop2cor

ILVTTLD

OURS

(a)

0 50 100 150 200 2500

20

40

60

80

100

Frame

Erro

r

Car4

ILVTTLD

OURS

(b)

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

Frame

Erro

r

Bjbus103

ILVTTLD

OURS

(c)


6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 50 100 150 200 2500

20

40

60

80

100

120

Frame

Erro

rThreePastShop2cor

ILVTTLD

OURS

(a)

0 50 100 150 200 2500

20

40

60

80

100

Frame

Erro

r

Car4

ILVTTLD

OURS

(b)

0 50 100 150 200 2500

10

20

30

40

50

60

70

80

Frame

Erro

r

Bjbus103

ILVTTLD

OURS

(c)


6 Conclusions










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Acknowledgments


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article Visual Tracking Using Max-Average Pooling and Weight-Selection Strategydownloads.hindawi.com/journals/jam/2014/828907.pdf · 2019-07-31 · Research Article Visual