review article a review on particle swarm optimization...

Review ArticleA Review on Particle Swarm Optimization Algorithm andIts Variants to Human Motion Tracking

Sanjay Saini Dayang Rohaya Bt Awang RambliM Nordin B Zakaria and Suziah Bt Sulaiman

Department of Computer amp Information Science Universiti Teknologi Petronas 31750 Tronoh Perak Malaysia

Correspondence should be addressed to Sanjay Saini sanjay1987sainigmailcom

Received 9 July 2014 Accepted 9 October 2014 Published 30 November 2014

Academic Editor Suh-Yuh Yang

Copyright copy 2014 Sanjay Saini 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

Automatic human motion tracking in video sequences is one of the most frequently tackled tasks in computer vision communityThe goal of human motion capture is to estimate the joints angles of human body at any time However this is one of the mostchallenging problem in computer vision and pattern recognition due to the high-dimensional search space self-occlusion andhigh variability in human appearance Several approaches have been proposed in the literature using different techniques Howeverconventional approaches such as stochastic particle filtering have shortcomings in computational cost slowness of convergencesuffers from the curse of dimensionality and demand a high number of evaluations to achieve accurate results Particle swarmoptimization (PSO) is a population-based globalized search algorithm which has been successfully applied to address humanmotion tracking problem and produced better results in high-dimensional search spaceThis paper presents a systematic literaturesurvey on the PSO algorithm and its variants to human motion tracking An attempt is made to provide a guide for the researchersworking in the field of PSO based human motion tracking from video sequences Additionally the paper also presents theperformance of various model evaluation search strategies within PSO tracking framework for 3D pose tracking

1 Introduction

Human motion tracking is a general requirement in manyreal-time applications including automatic smart securitysurveillance [1] human computer interaction (HCI) 3Danimation industries [2]medical rehabilitation [3] and sportscience (eg for movement and behaviour analysis) In orderto improve the feasibility in such applications the researchon articulated human motion tracking and pose estimationhas been continuously growing in the past few years [4ndash12]

The primary objective of markerless articulated humanmotion tracking is to automatically localize the pose andposition of a subject from the video stream (sequences ofimages) This task is formulated by rendering a human bodymodel on the images to identify themodels configuration thatis the best availablematch of the input images Onemajor lineof approach in the research is based on articulated models[4ndash12] The interest in this area owed two benefits firstly it

generates results in the form of model configuration for eachframe that can be useful for various higher-order processingtasks such as character animation and 3D movies Secondlythe human models are sufficiently capable to give abundantinformation of kinematic human body motion However thekey challenge in the approach is the high-dimensionality ofthe search space involved due to the large number of freedomtypically present in an articulated human body figure

The human motion tracking is a very complex task dueto the high-dimensional parametric search space and largenumber of degree of freedoms involved Other challengesinclude variation of cluttered background occlusion ambi-guity and illumination changes To address human motiontracking challengesmanymethods and algorithms have beenproposed in the literature using different techniquesThe firstsolutions emerging from the computer vision communityare particle filtering (PF) variants [4 5 13ndash15] In particularthe condensation algorithm is mostly widespread used in

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 704861 16 pageshttpdxdoiorg1011552014704861

2 Mathematical Problems in Engineering

human motion tracking [16] However it suffers from thedimensionality issue when used for the humanmotion track-ing problem To address this issue [5] introduced annealedparticle filter (APF) an approach that merges condensationand simulates annealing in an attempt to improve the trackingresults as well reduce the number of particles The APFperforms a multilayer particle evaluation where the fitnessfunctions in the initial layers are smoothed to avoid the searchfrom being trapped in local minima In the last layers fitnessfunction is more peaked in order to concentrate the particlesto solution regions To represent the posterior distributionadequately the particle filter solutions critically rely on alarge number of particles which consequently increases thecomputational complexity beyond practical use when a widevariety of motion is considered [6 7 11 12 17]

Partition sampling [15] is another approach to reduce thesystem complexity The technique was initially introduced in[18] to address the high cost effect of particle filters whiletrackingmultiple objects Later on it was successfully appliedin hand tracking In general terms partitioned sampling (PS)is a strategy that consists of dividing the complete state intoseveral substates ldquopartitionsrdquo consecutively employing thedynamics for every partition followed by a suitable weightedresampling procedure In point of fact partition samplingcan abbreviate the high dimensionality problem in anothersituation also

Thepartitioned sampling (PS) is different from theAPF ina way that it applies strong partition of the search space Themain problem consists of determining the optimal partitionIn an attempt to solve this Bandouch et al [13] proposed amethod that combines both PS and APF known as PSAPFThe APF is incorporated into a PS framework by utilizingan appropriate weighted resampling in each subspace Thisapproach is able to deal with high dimensionality but itsuffers from high cost of employing a very large number ofevaluations per frame (around 8000) Generally the commonhuman pose tracking approaches rely on filtering algorithmsbut the conventional filtering algorithms have some short-comings such as computational expensive slowness of theirconvergence and they suffer from the curse of dimensionalityand they need to rely on simple human models (which leadto suboptimal tracking results) or require a high number ofevaluation to achieve accurate results [6 7 11 12 19]

Many real-world problems such as the articulated humanmotion tracking and pose estimation problem can be formu-lated as multidimensional nonlinear optimization problemsof parameters with variables in continuous domains In thepast few years evolutionary computation approaches (egGA PSO DE etc) are most widely used to solve continuousoptimization problems including human motion trackingand pose estimation

Particle swarm optimization (PSO) [20] is a population-based stochastic optimization algorithm which is originallyinspired from social behaviour of bird flocking or fishschooling The PSO has a capability of simple computationand rapid convergence as a stochastic search scheme PSOhas been successfully applied in several areas includinghuman motion tracking and pose estimation [6ndash12] and inthe other optimization areas the PSO give competition to

the genetic algorithms Currently the PSO and its variantsare most extensively used in the literature for video-basedarticulated human motion tracking and pose estimation asthey offer several advantages for example ability to solvehighly nonlinear problem robust and reliable performanceglobal and local search capability and little or no priorinformation requirement and it has fewer parameters toadjust [6 7 11 12]

In the PSO tracking framework articulated humanmotion tracking problem is formulated as amultidimensionalnonlinear optimization problemThefinal tracking results arethen obtained by optimizing a fitness function that computesthe match between the observed image and the 3D bodymodel Generally the main aim of fitness function is toevaluate how well a candidate pose hypothesis matches theobservation that is the images from all cameras views ateach time instantMany fitness functions have been proposedin the literature including optical flow appearance modelskin color and contours-based fitness function Howevermost common approaches rely on silhouettes and edgesbased fitness function [4ndash7 11 12] because it provides anappropriate trade-off between robustness and speed Figure 1illustrates the general optimization framework Within thisframework many tracking task can be reformulated asa global optimization problem in which a metaheuristicalgorithm is used to the optimized model parameters In thispaper we employ the latter approach we find the optimalbody model configuration by maximizing a fitness functionrepresentative of the similarity between the model and imageobservation under investigation

The standard PSO is generally used to find a singleoptimum in a static search space In contrast the natureof pose estimation and tracking problem is dynamic whereoptimum changes over time or frames Thus the standardPSO cannot be used directly to the problem it is necessaryto modify the PSO algorithm to better suit this problem

PSO has the capability to find the best value for inter-acting particles unfortunately the standard PSO also suf-fers from the curse of dimensionality which has led tomany variants specifically adapted for pose tracking Alsoits convergence speed becomes very slow near the globaloptimum when it is applied to high-dimensional parametricsearch space Therefore PSO generally failed in searchingfor a global optimal solution The existence of local optimalsolutions is not the sole reason for this phenomenon Itis because the particles velocities sometimes failed intodegeneracy leading to the restriction of successive range inthe subplain of the whole search hyperplain In spite of itsreported success the second major issue in using PSO forarticulated humanmotion tracking problem is that of particlediversity loss Generally it occurs due to convergence of theprior level of optimization and all the particles may be closeto previous optimum position and the swarm has shrunkThe swarm may be able to find the optimum efficiently ifthe position of new optimum still lies within the region ofshrinking swarm because of its diversity However the trueoptimum can never be found if the current optimum liesoutside of the swarm because of the particles low velocitieswhichwill inhibit rediversification and tracking However in

Mathematical Problems in Engineering 3

New configuration

Model over image features fitness evaluation

Termination criteria met

Output 3D model

Deformed model

Yes

No

Optimization process

Image

3D model

Figure 1 Illustration of general optimization process

the dynamic optimization problem it is necessary to controlthe particle diversity within the swarm with respect to time

In order to overcome the above-mentioned issues severalvariants of PSO algorithm have been proposed for posetracking in the literature using different techniques such ashierarchical search optimization [6 7 11 12 21 22] andglobal-local refinement process [10 23] Some adaptive ver-sions of PSOhave been presented to incorporate the strengthsof other evolutionary and stochastic filtering algorithms likehybrid versions of PSO [23ndash26] or the adaptation of PSOparameters [27] Although these improvements lead to theavoidance of local optima the problem of early convergenceby the degeneracy of some dimensions still exists evenin the absence of local minima Thus the PSO algorithmperformance is still limited in high-dimensional parametricsearch space

There are many survey works that deliver an effectiveoverview of articulated human body pose estimation andanalysis [1 28ndash33] However these survey works cover onlygeneral overview of human motion tracking and pose esti-mation To the best of our knowledge there is no systematicsurvey in the literature that provides the details of PSO basedapproaches for human pose tracking Recently some surveyshave given the overview of PSO in data cluster analysisapplication [34 35]

In that point of view different variants of PSO withdifferent techniques have been proposed to improve theperformance of the PSO in pose tracking Therefore themain aim of this work is to present a systematic literaturesurvey by reviewing PSO algorithm and its variants as appliedto human pose tracking An attempt is made to provide aguide for the researchers who are working or planning towork in the field of PSO based human motion tracking fromvideo sequences Additionally the paper will also focus onthe various model evaluation search strategies within PSO

tracking framework for 3D pose tracking in order to identifytheir potential efficiency worth for effective pose recoveryin high-dimensional search space For example first is theholistic (global optimization) approach where all the humanbody parameters or variables are optimized jointly Secondis the hierarchical search optimization where articulatedstructure of human body considering independent branchesnamely the limbs and head is optimized Therefore it ispossible to apply a hierarchical search where there areindependent search processes working on smaller spaces andthen the problem can be more easily solved Finally one cansee the discussion of the evaluated work and it highlightsthe gaps for future work and provides directions of futureresearch

2 Particle Swarm Optimization (PSO)

A short perception of tracking process in a stochastic opti-mization prospective has been given in this section to indicatehow PSO will work on tracking application and how it is ableto achieve good performance The fundamental concept ofPSO algorithm with its variants also has been discussed

21 Motivation Fundamentally video-based tracking is theprocess of automatically localizing the subject pose andposition in a video stream In the PSO context the trackingproblem can be understood as follows imagine a certainobject (food) in the image (state space) being explored Aset of particles (birds) are randomly distributed in the imagespace (state space) None of the particles (birds) knows thelocation of the object (food) However every particle (birds)knows whether it is progressing closer to or further awayfrom the object (food) through an objective function (senseof smell or sight)The question arises as how to find the object


(food) effectively by utilizing collectively and efficiently allthe particles information The PSO algorithm is an attemptto provide a framework for the question

In video-based articulated human motion tracking thedata of concern is in a time sequence Thus the trackingprocess is considered as a dynamic optimization problem Inthis context the objectrsquos height and shape may change withtime the objective function is hence temporally dynamicSuch dynamic optimization problem can be solved by usingtwo effective principles firstly by utilizing the temporal con-tinuity information among two consecutive frames effectivelyand secondly by maintaining the particle diversity duringeach optimization process [6 7 11 12 27]

22 Standard Particle Swarm Optimization Before startingthe discussion on standard PSO algorithm we first intro-duce some necessary notations and assumptions which areused in PSO algorithm Assume an 119899-dimensional solutionspace Ω Let us consider that the 119894th particle position andvelocity are represented as x119894 = (1199091198941 1199091198942 119909119894119899) and v119894 =(V1198941 V1198942 V119894119899) respectively The individual best position(p119894) is originated by 119894th particle so far (personal best) andexpressed by p119894 = (1199011198941 1199011198942 119901119894119899) and overall best ofall the particle value (g) (global-best) is defined as g =(1198921 1198922 119892

119899) The standard particle swarm optimization

(PSO) can be briefly summarized in the following paragraphParticle swarm optimization (PSO) [20] is a population-

based stochastic optimization algorithm The main motiva-tion for the development of this algorithm was based on thesimulation of simplified animal social behaviors such as birdflocking or fish schooling The algorithmmaintains a swarmconsisting of 119873 particles where each particle is representinga candidate solution to the optimization problem underconsideration If the problem is described with 119899 variablesthen each particle denotes an 119899-dimensional point in thesearch space A cost (fitness) function is used in the searchspace to measure the fitness of particles The particles arerandomly generated in the solution search space havingits position adjusted according to its own personal bestexperience and best particle position of the swarm

The PSO is initialized with a set of random particlesx119894119873119894=1

(119873 number of particles) and the search for optimalsolution iteratively in the search space Each particle has acorresponding fitness value as well as its own velocity v119894The fitness value is calculated by an observation model andthe velocity provides the direction of particle movement Ineach iteration the 119894th particle movement depends on twokey factors first its individual best position (p119894) which isoriginated by 119894th particle so far and second the global bestposition (g) is the overall global best position that has beengenerated by entire swarm In the (119905 + 1)th iteration eachparticle updates the position and velocity by utilizing thefollowing equations

v119894119905+1= 120596v119894119905+ 12059311199031(p119894119905minus x119894119905) + 12059321199032(g119905minus x119894119905) (1)

x119894119905+1= x119894119905+ v119894119905+1 (2)

Swarminfluence

Current motioninfluence

Particle swarminfluence

parpos i

t+1

gbest

parval i

t+1

parpos i

t

pbest i

t

t

x

x

g

v

p

Figure 2 Illustration of particlersquos position update in PSO

where v119894119905and x119894

119905denote the velocity vector and the position

vector of 119894-particle respectively at t-iteration The particlevelocity constraint is one of the importantmechanismswhichis used for controlling particle movement in search space andis also useful for making balance between exploitation andexploration The specific acceleration parameters are 120593

1and

1205932which represent the positive constants which are called as

cognitive and social parameters both control the influencebalance of the personal best and global best particle posi-tion 119903

1 1199032are random numbers obtained from a uniformly

distribution function in the interval [0 1] 120596 is the inertiaweight parameter that has been used as velocity constraintmechanism [6]The inertia weight plays an important role forcontrolling the trade-off between global and local searchThehigh value of inertia weight 120596 promotes particles to explorein large space (global search) whereas small inertia weight 120596promotes particles to search in smaller area (local search)In the following at the starting of the search (120596 = 120596max)high inertia value is importedwhich decreases until it reaches(120596 = 120596min) the lowest value Figure 2 illustrates a schematicview of updating the position of a particle in two successiveiterations

Here at each iteration global best g and individual bestp119894 positions are computed after invoking the fitness function(cost function) at each position x119894

119905 Generally a greater

fitness value corresponds to a more optimal position Thebest position of a particle is updated only when the presentposition value is higher than the former best value Amongall of the individual best position values the position withthe highest fitness value is considered as global best It can beexpressed mathematically as follows

p119894119905=

x119894119905 if 119891 (x119894

119905gt 119891 (p119894

119905))

p119894119905 otherwise

g = argmaxp119894119905

119891 (p119894119905)

(3)

where 119891(p119894119905) is the fitness value at the position x119894

119905 The

processwill continue until the terminating conditions aremet(typically a maximum number of iterations)


The PSO has good balance between exploration andexploitation and plays an important role in avoiding prema-ture convergence during the optimization process In factin a number of works PSO has been successfully applied inarticulated human motion tracking and has been reported togive good accuracy with less computational cost in compari-son to particle filtering approach [6ndash12] Pseudocode for PSOalgorithm is presented in Algorithm 1

3 PSO to Human Motion Tracking

In the computer vision community articulated human posetracking is a long standing problem and still it is considered asa difficult problem because of themany challenges it presentsFirst it is a high-dimensional problem because large numberof variables is used to cover full human body pose estimationand to obtain accurate results This is a crucial problemin pose tracking The solution to this problem requires asearch strategy that can efficiently explore wide sections ofthe search space Second the computing power is a limitingfactor The operations needed to evaluate the solutions arecomputationally very expensive Therefore it is importantand essential to have good solutions in few iterations aspossible Finally an appropriate balance is needed betweenlocal and global search In most of the situations local searchcan deliver good solutions however the problemof occlusionand ambiguities in the configuration of camera lead us touse the global optimization so that a correct solution can beachieved after the conflicting situation is finished

As we have stated previously human pose tracking prob-lem can be formulated as a multidimensional nonlinear opti-mization problem that search the best possible joint angle ofthe human bodymodel given the information available in theprior and the current images [19] In the past decades variousstochastic filtering (eg PF APF PSAPF etc) and nature-inspired evolutionary algorithms (eg GA PSO PEA (prob-ability evolutionary algorithm) QICA (quantum-inspiredimmune cloning algorithm) QPSO (quantum-PSO) etc)have been developed for human pose tracking It has beenproven by many researchers that evolutionary algorithms areviable tool to solve complex optimization problems and canbe successfully implemented for solving human pose trackingproblem Among them the PSO algorithm gained popularityin the last few years in the domain of humanmotion trackingand pose estimation It is because of its simplicity flexibilityand self-organization The PSO also successfully combinedwith other techniques such as dimensionality reductionand subspace learning to address the human pose trackingproblem [7 36ndash38]

31 Literature Survey Initially Ivekovic and Trucco [22]have applied PSO for upper body pose estimation frommultiview video sequences The PSO algorithm is appliedin 20-dimensional search space The optimization process isexecuted in 6 hierarchical steps which are based on modelhierarchy However the approach is only performed in staticupper body pose estimation Similarly Robertson and Trucco[21] used an approach where the number of optimized

parameters is iteratively increased so that a superset ofthe previously optimized parameters is optimized at everyhierarchical stage

John et al [6] proposed a hierarchical version of PSO(HPSO) to the human motion tracking using a 31 DOF(degree-of-freedom) articulated model with great successIn order to overcome the high dimensionality the 31-dimensional search space is divided into 12 hierarchicalsubspaces Additionally the estimates obtained from eachsubspace are fixed in the following optimization stages Asthey have stated their approach results outperforms PFAPF and PSAPF HPSO algorithm reduces the computationcost massively in the comparisons of the stochastic filteringapproaches However this approach has some shortcomingthat the HPSO algorithm failed to escape the local maximacalculated in the previous hierarchical levels which as a resultmay produce inaccurate trackingMoreover the final solutiontends to drift away from the true pose especially at low framerates Zhang et al [11] applied the PSO stochastic algorithmto estimate the full articulated human body motion Thismethod also estimates pose in a hierarchical fashion byprescribing some space constraints into each suboptimizationstage To maintain the diversity of particles the swarmparticles are circulated according to a weak transition modeland the temporal continuity information is also utilized

Krzeszowski et al [10] present a global-local particleswarm optimization method for 3D human motion captureThis system divides the entire optimization cycle into twoparts the first part of optimization cycle estimates the wholebody and the second part refines the local limb poses usingless amount of particles A similar approach called global-local annealed PSO (GLAPSO) is presented by Kwolek et al[9] This algorithm maintains a pool of candidate instead ofselecting global best particle to improve the algorithm abilityto explore the search space One hybrid approach is presentedby Kwolek et al [23] in which particle swarm optimizationwith resampling is used to articulate human body trackingThe system employs a resampling method to select a recordof the best particle according to the weights of particlesmaking up the swarm which leads to the reduction of thepremature stagnation Kwolek [26] applied PSO algorithm totrack the human motion from multiview surveillance videoThis approach also estimates the body pose hierarchicallyKrzeszowski et al [39] proposed an approach which com-bines the PSO and PF (PF + PSO) where the particle swarmoptimization algorithm is employed in the particle filtering toshift the particles towards more promising region of humanbody model Similarly [24 25 40] introduced annealedPSO based particle filter (APSOPF) algorithm for articu-lated human motion tracking The sampling covariance andannealed factor are incorporated into the velocity-updatingequation of PSO which results in constraining particle tomost likely the reason of pose space and reducing generationof invalid particles However both of the above-discussedapproaches obtained good accuracy but are computationallyheavy

Ivekovic et al [41] proposed an adaptive particle swarmoptimization (APSO) to reduce the computational complex-ity of the system This system uses black-box property of


Set parameters 1198731205931 1205932 Vmax 120596max 120596min

InitializationInitialize a population of119873 particles with random position (x119894) and velocity (v119894)foreach Particle 119894 isin 1 rarr 119873 dop119894(0)= x119894

Compute the fitness value 119891end forInitialize the inertia weight 120596Select the best particle in the swarm p119894

(0)

Iteration processfor 119905 = 1 to maximum number of iterations doforeach particle 119894 isin 1 rarr 119873 do

update velocity v119894119905and position x119894

119905for the particles

employ the inertia weight update rulecompute particles fitness value 119891(x119894

119905)

update best particles p119894119905and g

119905

end forif convergence criteria are met thenExit from iteration process

end if

Algorithm 1 Pseudocode for particle swarm optimization (PSO)

HPSO in which it requires no parameters value input fromthe users and it adaptively changes the search parametersonline based on the types of pose estimation in the previousframe Yan et al [42] adopt annealed Gaussian based par-ticle swarm optimization (AGPSO) for 3D human motiontracking In this approach the observation is designed as aminimized Markov Random field (MRF) energy Kiran etal [43] present a hybrid PSO called (PSO + K) for humanposture classification Initially the PSO algorithm is appliedto search the optimal solution in parametric search space andthen it passed to K-means algorithm which has been usedto refine the final optimal solution Zhang [44] introducesanother hybrid PSO algorithm for humanmotion tracking inmonocular video In order to construct theweight function ofparticles color edge andmotion cues are integrated togetherTo escape from the local minima simulated annealing (SA)algorithm incorporated into PSOThis approach yields betterresults than both the standard PSO and APF algorithms

Ugolotti et al [17] introduced two algorithms for modelbased object detection namely particle swarm optimization(PSO) and differential evolution (DE) PSO is clearly andconsistently superior compared with the DE for model basedtracking Similarly Bolivar et al [19] report the comparisonsbetween evolutionary and particle filtering algorithms Asthey stated that for the human motion tracking the hier-archical version of PSO (H-PSO) is better than all filteringas well as evolutionary algorithms except hierarchical covari-ance matrix adaptation evolutionary strategy (H-CMAES)Their comparisons results are tested on HumanEva-I-IIdatasets Fleischmann et al [12] proposed a soft partitioningapproach with PSO (SPPSO) In this approach the optimiza-tion process is divided into two stages where in first stageimportant parameters (typically torso) are optimized and in

second stage all remaining parameters are optimized jointlyand called global optimization which refines the estimatesfrom the first stageThe approach obtained good results at lowframe rates (20 fps) sequences but at normal frame (60 fps) itreceived almost similar results as HPSO However they usedglobal optimization in second stage therefore the approachis computational costly

In the user-friendly human computer communicationnonintrusive human body tracking is a key issue This is oneof the most challenging problems in computer vision and atthe same time one of the most computationally demandingtasks Conventionally the human pose tracking approachesneed to execute the various tasks step-by-step to obtaingood tracking results (ie foregroundbackground removaledge detection and model rendering and optimization)Therefore the implementation of such techniques in CPU(central processing unit) leads to longer processing timeand higher computational cost From this point of view theGPU architecture benefits from the property of execution ofthousands of threads concurrently because of the massivefine grain parallelization In order to take GPU architecturesbenefit there are some publications that discuss the imple-mentation details of the PSO and its variants on GPU

Kwolek et al [8] proposed parallel version of PSO knownas latency tolerant parallel particle swarm optimization Inthis algorithm multiple swarms are present that are executedin parallel on multiple computers which are connectedthrough peer-to-peer network which exchange the informa-tion about the location of the best particles as well as itscorresponding fitness function of a subswarmThis informa-tion about the location of global particles and correspondingfitness value is transferred asynchronously after each opti-mization iteration without blocking the sending thread The


mutual exclusive memory is used to store these best valuesAfter each iteration the value of global particle is verifiedby processing thread for its performance over other particlesprovided by other computers If value is better than previousthen the value of best particle gets updated and optimizationprocess continues The main novelty of this work lies inthe asynchronous exchange mechanism for the best particleinformation during the multiple calls of PSO Their resultdemonstrates that latency tolerant parallel particle swarmoptimization is able to give real-time results Zhang andSeah [45] proposed another hybrid approach that is calledNiching swarm filtering (NSF) with local optimization Inthe NSF framework ring topology based bare bones particleswarm optimization algorithm (BBPSO) and particle filteralgorithms have been integrated This approach in trackingunconstrained human motions without using strong priorinformation of the dynamics and its GPU implementationshows that approach is able to give real-time results

Mussi et al [46] developed an approach to articulatedhuman body tracking from multiview video using PSOrunning on GPUTheir implementation is far from real-timeand roughly requires 7 sec per frame but they clearly demon-strate that the formulation of algorithm in GPU decreasesthe execution time prominently without compromising theaccuracy of post estimation Krzeszowski et al [47] reportGPU-accelerated articulated human motion tracking usingPSO and they show that their GPU implementation hasachieved a speedup of more than fifteen times than the CPUimplementation with a 26 DOF 3D model

Real-time tracking performance of human motion iscritical formany applications In order to compile this Zhanget al [48] introduced GPU-accelerated based multilayerframework for real-time full body motion tracking In theirmultilayer pose tracking framework first layer they appliedthe NSF stochastic search to fit the body model to imagesand in the second layer the estimation is refined hierarchi-cally using local optimization The volume with appearancereconstruction observation has been used to measure thepose hypothesis and 3D distance transform (DT) is employedto increase the algorithm speed The GPU implementationis done using CUDA (compute unified device architecture)which significantly accelerates the pose tracking processTheir results demonstrate that NFS algorithm outperformsother state-of-the-arts algorithms in CPU implementation aswell as in GPU Similarly Rymut and Kwolek [49] presenta GPU-accelerated PSO for real-time multiview humanmotion tracking In this approach they demonstrated howparticle swarm optimization algorithm works on GPU forarticulated human motion tracking and also demonstratedthe parallelization of the cost function

As we have indicated previously the PSO also is success-fully combined with other techniques such as dimensionalityreduction and subspace to address the human pose trackingproblem For example John et al 2010 [7] introduceda hybrid generative-discriminative approach for marker-less human motion capture using charting and manifoldconstrained particle swam optimization [7] The chartingalgorithm has been used to learn the common motion in alow-dimensional latent search space and the pose tracking

is executed by a modified PSO called manifold constrainedPSO Mainly this PSO variant is designed to polarize thesearch space for the best next pose Similarly Saini et al[37] proposed a low-dimensional manifold learning (LDML)approach for human pose tracking where a hierarchical-charting dimension reduction technique has been used tolearn motion model In order to escape from local minimathe quantum-behaved particle swarm optimization (QPSO)has been used for pose tracking in low-dimensional searchspace Li and Sun [50] proposed a generative methodfor articulated human motion tracking using sequentialannealed particle swarm optimization (SAPSO) Simulatedannealed principle has been integrated into traditional PSOto get global optimum solution more efficiently The mainnovelty of their approach is the use of principal componentanalysis (PCA) to reduce the dimensionality and learn thelatent space human motions

Note that most of the above-discussed PSO basedapproaches rely on silhouette and edge based fitness function[4ndash11 24 25 40 41] The main reason is that both genericfeatures have been shown to deliver an appropriate trade-offbetween robustness and speedHowever in some approachesthe use of skin color leads to failure because of the influence oflightning on skin color which varies from person to personTable 1 summarizes the above research contributions

32 Discussion PSO has been applied in a number of areasas a technique to solve large nonlinear complex optimizationproblems However the applications of PSO in computervision and graphics are still rather limited [52] Few PSO vari-ants have been developed with different techniques for posetracking According to literature review in most of the casesthe hierarchical version of PSO (HPSO) is most effective forpose tracking To get fast and real-time tracking results manyvariants of PSO have been implemented on GPU Howeverthe PSO still requires much investigation to improve thetracking performance and also other key features that wouldmake such algorithms techniques suitable for pose trackingFurthermore many variants of PSO have not been used yetin pose tracking such as multiobjective PSO multiswam PSOas well as many others which have been discussed [34] Somefuture works and research trends to address the pose trackingproblem are as follows development of multiswarm PSOalgorithm subswarm method such as [53] developing newfitness and measuring functions new approach for searchspace partitioning some dimensional reduction techniqueswhich can be easily incorporated to PSO new sensitivityanalysis of PSO parameters and others

4 Pose Evaluation Techniques

In the last decade many stochastic filtering and nature-inspired algorithms have been proposed in the literatureusing different techniques for human pose tracking Amongthe many nature-inspired algorithms pose tracking withparticle swarm optimization techniques has found success insolving pose tracking problem because PSO is well suited forparameter-optimization problems like pose tracking In order


Table 1 Resume of the research description and the contribution by different authors Methods are listed in the chronological order by thefirst author

Publications Pose evaltechniques

Number ofstages Algorithm DOF Remarks

Ivekovic and Trucco (2006) [22] HP 6 PSO 20 The approach is only performed for upper bodypose estimation

Robertson and Trucco (2006) [21] HP 6 Parallel PSO 24 The approach is only performed for upper bodypose estimation

John et al (2010) [6] HP 12 HPSO 31

The algorithm is unable to escape from localmaxima which is calculated in the previoushierarchical levels However the approach iscomputationally more efficient than thecompeting techniques

Ivekovic et al (2010) [41] HP 12 APSO 31 Computationally very inexpensive that isuseful for real-time applications

Mussi et al (2010) [46] HP 11 PSO 32

The approach has been implemented in GPUwhich significantly saves the computationalcost when compared to sequentialimplementation

John et al (2010) [7] HP 12Manifold

constrainedPSO

31

Charting a nonlinear dimension reductionalgorithm has been used to learn motion modelin low-dimensional search space However theapproach has not been tested with publicavailable dataset

Krzeszowski et al (2010) [39] Holistic lowast PF + PSO 26

Mobility limitation is imposed to the bodymodel and is computationally expensiveMoreover approach has not been tested withpublicly available dataset

Zhang et al (2010) [40] Holistic lowast APSOPF 31The approach is able to alleviate the problem ofinconsistency between the observation modeland the true model

Yan et al (2010) [42] Holistic lowast AGPSO 29 Computationally very expensive

Kiran et al (2010) [43] mdash mdash PSO + K mdash The approach is only tested for postureclassification

Zhang et al (2011) [11] HP 5 PSO 29The approach produces good tracking resultsbut suffers from heavy computational cost dueto more numbers of fitness evaluation

Krzeszowski et al (2011) [10] HP 2 GLPSO 26

The approach suffers from error accumulationand mobility limitation is imposed to the bodymodel Moreover approach was not tested withpublicly available dataset

Kwolek et al (2011) [9] HP 2 GLAPSO 26

The approach saves the computational cost byusing 4 core processor computing powersHowever the approach was not tested withpublicly available dataset

Kwolek et al (2011) [8] Global lowast

latencytolerant

parallel PSO26

The approach demonstrates the parallel natureof PSO and its strength in computational costas compared to multiple PC (8) versus singlePC (1)

Kwolek (2011) [26] HP 3 PSO 26Tracking in surveillance videos which cancontribute toward the view-invariant actionrecognition

Kwolek et al (2012) [23] Holistic lowast

RAPSOAPSO 26

The approach produced better results than PFand APF but suffers from large computationalcost

Zhang and Seah (2011) [45] HP 5 NFS BBPSO 36NFS algorithm produces good tracking resultsand their GPU implementation is able to givereal-time results


Table 1 Continued



Ugolotti et al (2013) [17] HP 11 PSO DE 32Article demonstrates the strengths of twoevolutionary approaches (PSO and DE) onGPU implementation

Fleischmann et al (2012) [12] SP 2 SPPSO 31The soft partitioning strategy overcomes theerror accumulation issue However SPPSOsuffers from heavy computation cost

Li and Sun (2012) [50] mdash mdash SAPSO mdash

Principal component analysis (PCA) has beenused to reduce the dimensionality and learnthe latent space human motion which is themain novelty of the work

Saini et al (2012 2013) [37 38] HP 12 QPSO 31

H-charting algorithm has been used to reducethe search space and learn the motion modelProposed QPSO algorithm is able to escapefrom local minima

Zhang et al (2013) [48] HP 2 NFS 36

New generative sampling algorithm with arefinement step of local optimization has beenproposed Moreover the approach does notrely on prior strong motion Due to GPUimplementation approach it is able to givereal-time performance

Nguyen et al (2013) [51] HP 10 HAPSOPF mdashThe body pose is optimized hierarchicalmanner in order to reduce the computationalcost of APSOPF

Zhang (2014) [44] Holistic lowast SAPSO mdashThe main novelty of work is color edge andmotion cue are integrated together to constructthe weight function

Rymut and Kwolek (2014) [49] Holistic lowast PSO 26

Parallelization of the cost function is the mainnovelty of the work Furthermore CPU versusGPU performance has been demonstrated forhuman motion tracking

lowastindicate that all the parameters are optimized together (globalholistic optimization) HP represents the hard partitioning and SP represents the softpartitioning The number of stages indicates the stages which are used by authors to obtain the solution

to improve the efficiency of PSO algorithms researchers haveproposed different variants of PSO algorithm with differenttechniques such as hierarchical optimization different fitnessfunctions different search space partitioning and differentpose refinement process

The complexity of the human kinematic structure andthe large variability in body shape between individuals implythat there are many parameters that need to be estimatedfor a full body model that is often over 35 (in our case31) even for coarse models When defining the problemas an optimization of an objective function over the modelparameters the search space becomes very high dimensionalHowever exploring high-dimensional state space in practicaltime becomes problematic Therefore in order to reducethe complexity different types of search strategy have beenutilized in pose space within PSO tracking framework such ashierarchical search with soft and hard partitioning Accord-ing to the literature review there are two techniques thatcan be applied to solve the problem holistic and hierarchicaltechniques Figure 3 illustrates the taxonomy of pose trackingapproaches within PSO tracking framework The graphical

Pose tracking problem in PSO tracking framework

Holistic approach Hierarchical search approach

Hard search space partitioning (HP) Soft search space partitioning (SP)

Figure 3 Detailed taxonomy of pose tracking approaches withinPSO tracking framework

representation of different partitioning strategy is illustratedin Figure 4 [12]

41 Holistic Optimization In the holistic approach all humanpose parameters are optimized jointly also known as globaloptimization Fundamentally this approach is more appro-priate because it makes no assumptions about the indepen-dence of the body parts which results in more robustness to


1

1

0

0

X2

X1

t

tminus1

x

x

(a)

1

0

tminus1

t

X2

10

X1

x

x

(b)

tminus1

t

1

0

X2

10

X1

x

x

(c)

Figure 4 Illustration of different partitioning strategy using two level optimizationwhere x119905minus1

represents the initial and x119905the new estimation

error In practical due to high dimensionality the recoveryof complete 3D body pose parameters jointly is very difficultespecially in real-time situation because this process requiredmore computing time to evaluate the solutionThe exponen-tial growth of the search space with large number of variablesis the main drawback of the holistic approach Furthermorea small deviation in the higher nodes of the hierarchy affectstheir lower children However good quality results can bereceived in the early search stages for the lower nodes butit might be discarded later by changes in one of their parentsFinally the main drawback of global optimization is that itis computationally very expensive Figure 4(a) demonstratesthe global optimization process where the optimizer searchesthe whole search space (grey) at once

42 Hierarchical Search Approach Computational complex-ity of global optimization approach is very high due to large

number of variables to cover full human body pose estima-tion In this situation the hierarchical search takes advantageby considering the each human body parts independentlyTherefore it is possible to apply a hierarchical search inwhich there are independent search processes working onsmaller spaces Despite this several researchers have appliedhierarchical partitioning schemes in the search space accord-ing to the limb hierarchy to reduce the complexity of high-dimensional search [6 7 11 21 41 46 51] and also they provedthat hierarchical search approaches is more appropriate thanholistic approachesThe hierarchical search approach furthercan be classified in two classes hard search space partitioning(HP) and soft search space partitioning (SP)

421 Hard Search Space Partitioning (HP) Hierarchical opti-mization along with the global-local PSO which divides theoptimization process intomultiple stages in which a subset of


parameters is optimized while the rest of the parameters arefixed disabling the optimizer from refining the suboptimalestimate from the initial stage In other words in hierarchicalschemes the search space is partitioned according to themodel hierarchy The most important parameters are opti-mized first (typically torso) while the less important are keptconstant This is termed as hard partitioning of the searchspace Figure 4(b) illustrates the hierarchical optimizationwhere in first stage parameter 119909

1is optimized and 119909

2is kept

constant Similarly during the second stage parameter 1199092is

optimized and 1199091is kept constant

422 Soft Search Space Partitioning (SP) Hierarchical hardsearch space partitioning (HP) approaches are very effectiveto reduce the effect of computational complexity [6 7 1121 46] But the pose estimation approach which is dividedinto hierarchical stageswith hard partitions suffers from erroraccumulation especially low frame rate sequences The erroraccumulation occurs due to objective function for one stagebeing unable to evaluate completely independently fromsubsequent stages To avoid error accumulation issue someof the researchers have applied soft partitioning approach insearch space [12]

The major difference between hard and soft partitioningis that previous optimized level (parameters) allowed somevariation in the following level to refine their suboptimalfrom the initial stage The soft partitioning approach reducesthe search space not as much as hard partitioning but thesearch space is much smaller than in a global optimizationFigure 4(c) demonstrates the soft partitioning scheme wherethe initial stage is equivalent to the hierarchical schemebut 119909

1allowed some variation during the second stage

optimization which results in the optimizer to find a betterestimate

Hierarchical search approaches are very effective toreduce the effect of computational complexity [6 7 1121] However hierarchical search approach also has manydrawbacks Firstly incorrect pose estimation (due to noiseor occlusion) for the initial segment can distort the poseestimates for subsequent limbs Therefore an error in theestimation of the first node compromises the rest of the nodesirrevocably [13] Secondly the optimal partitioning may notbe obvious and itmay change according to time Table 1 showsthe summary of some popular PSO based approaches andalso display their pose evaluation techniques along with thenumber of stages used to evaluate the solution

43 Discussion Wenotice that each author has used differentnumber of stages in hierarchical search optimization toestimate a complete human body However based on theliterature it is still unclear how many hierarchical partitionsare sufficient to obtain good quality of results and alsowhich order of partition is the best (eg which body partneeds to be estimated first leg or arms) In the noisefree data this does not make a sense but in noisy dataobservation practices it makes inaccurate estimation in theearly partition which results in inaccurate next partitionoutcome Additionally many researchers have proved that

hierarchical search approaches are very effective to reduce theeffect of computational complexity [6 7 11 21 46] Howeverstill it is not clear which hierarchical search space partitioningis effective for pose tracking

In order to investigate above mention issues we haveimplemented PSO algorithm using Brown University com-putational tracking framework [4] This framework coversthe APF implementation We substituted our PSO trackingcode in their framework in place of the APF code whileother parts of the framework are kept the same Firstly wehave tested various model evaluation search strategies in 3Dpose tracking to identify their potential efficiency worth foreffective pose recovery in high-dimensional search spaceSecondly we also have investigated different order of bodypartitions for PSO (ie first leg or arms and vise verse) andfinally we have tested different hierarchical body partitions toidentify howmany hierarchical partitions are good enough toget good quality results with considerable computational cost

5 Quantitative and Visual Results

In this section we have shown some results of the test that wehave performed using PSO algorithmThe parameter settingsfor PSO algorithm are presented in Table 2 Additionally forthe global PSO optimization 60 particles and 60 iterationsare used The presented PSO algorithm is run in Brown Uni-versity framework with windows 320GHz processor Thequantitative comparison is carried out in three prospective(1)Comparison of holistic and hierarchical algorithms searchwith both soft partitioning and hard partitioning (2) anextensive experimental study of PSO over range of valuesof its parameters and (3) computation time The completeexperiment was carried out using Lee walk dataset [4] Thisdataset was captured by using four synchronized grey scalecameras with 640 times 480 resolutions The main reason to useLee walk dataset is that it contains ground-truth articulatedmotion which is allowed for a quantitative comparison ofthe tracking results As in [54] the error metric calculated isdefined as the average absolute distance between the 119899markeractual position 119909 and the estimated position 119909

119889 (119909 119909) =

1

119899

119899

sum

119894=1

1003817100381710038171003817119909119894minus 119909119894

1003817100381710038171003817 (4)

Equation (4) gives an error measure for a single frame ofthe sequence The tracking error of the whole sequence iscalculated by averaging that for all the frames

In hierarchical search we have divided complete searchspace into 6 different subspaces and correspondingly exe-cuted the hierarchical optimization in 6 steps in which wehave considered that it will provide an appropriate balancebetween global and local search The six steps are the globalposition and orientation of the root followed by torso andhead and finally the branches corresponding to the limbs (asillustrated in Figure 5 where LUA and LLA represent the leftupper arm and left lower arm resp similarly LUL and LLLrepresent the left upper leg and left lower leg respectivelysimilar representation is on right side for the right bodyparts) which are optimized independently In hierarchical


Table 2 Setting for PSO algorithm

Algorithm Parameters Fitness function Body model

PSO119873 = 20 120593

1 1205932= 20

120596max = 20 120596min =

01Max iteration = 30

Silhouette + edge119891 = 119891

119890+ 119891119904

Truncated cones (Balan et al(2005) [4]

31 DOF (John et al (2010) [6]Fleischmann et al (2012) [12])

Chain 2 Chain 3 Chain 4 Chain 5

HeadLUL

LLL

RUL

RLL

RUA

RLA

TOR

LUA

LLA

Figure 5 Standard kinematic tree representation of human model

search with hard partitioning the estimate obtained for eachsubspace is unchanged once it is generated and only one limbsegment at a time is optimized and the results are propagateddown to the kinematic tree While in soft partitioning thepreviously optimized parameterswhich are positioned higherin the Kinematic tree allowed some variation in the followingoptimization stageThus the current estimates can be refinedfrom their parents The variations in the previous optimizedparameters are set empirically

51 Accuracy Figure 6 shows the average 3D tracking errorgraph between ground-truth pose and estimated pose with3600 evaluation per frame on Lee walk sequences Thehierarchical search with soft partitioning approach performsbetter than the other two approaches particularly at 20 fpsHowever the difference is very less pronounced at 60 fpsThehighest fluctuations correspond to the fast limbs movementsespecially the lower arms and legs As we have noticed thatas the number of evaluation increases the likely range ofvariation in the 3D error becomes narrower and it increasesthe tracking performance Table 3 displays the average 3Dtracking error for Lee walk sequences and Figure 7 showseach evaluating approach tracking results for a few frameswith corresponding 3D error

52 Varying the Number of Particles We have evaluated thePSO performance by varying the number of particles for bothhierarchical hard and soft partitioning However to keep thecomputational time feasible on our hardware the range of119873

Table 3 3D distance tracking error calculated for Lee walksequences (5 runs)

Search strategies Error [mm] 20 fps Error [mm] 60 fpsHolistic (global PSO) 8400 plusmn 1700mm 4820 plusmn 800mmHierarchical searchwith hard partitioning(H-HP)

6820 plusmn 1400mm 46 plusmn 620mm

Hierarchical searchwith soft partitioning(H-SP)


Table 4 PSOrsquos 3D error in mm on Lee walk 20 fps with varyingnumbers of particles and likelihood evaluation

Algorithm

Hierarchical searchwith hardpartitioning(H-HP)

Hierarchical searchwith soft

partitioning(S-HP)

PSO (30 particles) 5880 plusmn 1600mm 4210 plusmn 1080mmPSO (40 particles) 5210 plusmn 1200mm 3840 plusmn 1410mmPSO (50 particles) 5060 plusmn 600mm 3420 plusmn 1280mm

is limited The experiments have been tested with 30 40 and50 particles for over five trials Table 4 shows the results Aspredicted we notice that the accuracy and consistency havebeen improved as the value of 119873 increases and also it hasincreased the computational time More number of particlesin PSO is able to estimate pose more accurately and avoidthe error propagation However the number of likelihoodevaluations per frame and computational cost increases with119873 (ie 30 particles result in 5400 likelihood evaluations 40particles in 7200 and 50 particles in 9000 evaluations perframe)The complete set of experiments to evaluate the valuesof119873 after which no significant benefit happens is beyond thescope of our hardware

53 Computation Time The computation time is the majorfactor in the pose tracking Generally it takes from secondsto minutes to estimate the pose in one frame for MATLABimplementations [4 6 7 54] This means that tracking anentire sequence may take hours However the computationtime vastly depends on the number of likelihood evaluationand model rendering As we have used the same num-ber of likelihood evaluation for all search strategies thecomputation time for holistic is much higher than otherhierarchical search approaches Furthermore when it comesto a hierarchical search approaches the hard partitioning


50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)

Distance error overall particle

H-SPH-HPGlobal-PSO

(a)

50 100 150Frame index

H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)

Figure 6 The distance error graph for hierarchical soft partitioning hard partitioning and holistic (global) strategies using Lee walksequence at 20 fps (a) and 60 fps (b)

computation time is less than soft partitioning The com-mutation time can be massively cut down by using morenumbers of partitioning in the search space (similar to[6 41 46]) Thus the conclusions can be drawn based onthe experimental results the hierarchical search with hardpartitioning approach is more useful than the other twoapproaches to reach near to real-time performance Howeverthe PSO results are still far from being real time which wouldbe necessary for many applications The fast and real-timeperformance can be obtained by using graphics processinghardware

In our experiment we have investigated different orderof body partitions for PSO (ie first arms or legs) We havetested both cases but the order of partitioning did not haveany influence on the quality of tracking in our experimentsFinally in order to identify that how many hierarchical bodypartitions are good enough to get good quality results andwhich can have considerable computational load we havetested PSO algorithm with different optimization stages Wehave tested that two-stage optimization similar to [8ndash10 1223] five-stage optimization [11] six-stage optimization [19]seven-stage optimization [13] and twelve-stage optimization[6 7 41] In our experimental results we found that six-stage optimization provides good tracking accuracy thanthe other optimization stages It is because the six stagesprovide more appropriate balance between global and localsearch than others However there is no significant differencein tracking accuracy between six optimization stages andthe other stages The approaches which uses more numberof optimization stages like [6 7 41 46] are able to cutdown computational cost massively While the two stageoptimization approaches [8ndash10 12 23] suffer from high

computational cost because of the involvement of globaloptimization in the second stage Therefore the approachis not suitable for real-time applications Furthermore thetracking accuracy strongly depends on the quality of theimage likelihood The best tracking performance is obtainedcombining silhouette and edge in the likelihood evaluationWhen it comes to an individual likelihood evaluation thesilhouette likelihood evaluation is reported to perform better

54 Discussion Based on the experimental results a setof conclusion can be drawn First the hierarchical searchapproaches are more appropriate than holistic (global) interms of high and robust tracking accuracy with veryless computational cost The hierarchical search with softpartitioning approach is only suitable for low frame ratessequences but in high frame rates it produces very nearresults as hard partitioning approach The soft partitioningapproach has more computational cost than hard partition-ing Second the PSO algorithm did not have any influenceon the tracking quality when the order of partitioning ischanged (ie first leg or arms and vise verse) Finally the six-stage optimization provides an appropriate balance betweenglobal-local search therefore it has good accuracy than otherstages

6 Conclusion

This paper has presented a review of previous researchworks in the field of particle swarm optimization and itsvariants to pose tracking problem Additionally the paperhas presented the performance of various model evaluation


Frame 15-28 mm Frame 77-54 mm Frame 110-49 mm Frame 149-60 mm

(a)


(b)


(c)

Figure 7 Tracking results are shown for a few frames with corresponding 3D error and typical results are obtained on Lee walk sequencesat 20 fps ((a) hierarchical soft partitioning (b) hierarchical hard partitioning and (c) global PSO)

search strategies in 3D pose tracking using PSO algorithmResearch shows that PSO algorithm applied to pose trackingin multidimensional search space has shown outstandingperformance as compared to the stochastic particle filteringalgorithms However convergence speed is still limited whenthe search is for global optima Furthermore the modifiedPSO and its hybridization with other algorithms such as par-ticle filter simulated annealed etc andor the combinationswith other techniques such as dimensional reduction andfeature selection can be successfully applied to pose tracking

problem and provides better results Our implementationof PSO algorithm results shows that the hierarchical searchapproach is very effective for pose tracking and it can reducethe computation cost massively and produce robust andreliable tracking results

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper


Acknowledgments

This work is supported by ERGSGrant (ERGS12013ICT07UTP0203) funded by the Government of Malaysia Theauthors would like to thank Leonid Sigal for many usefuldiscussions regarding Brown University framework and alsoformaintaining the online evaluation for theHumanEva (Leewalk sequence) dataset

References

[1] T B Moeslund A Hilton and V Kruger ldquoA survey of advancesin vision-based humanmotion capture and analysisrdquo ComputerVision and Image Understanding vol 104 no 2-3 pp 90ndash1262006

[2] F Multon R Kulpa L Hoyet and T Komura ldquoInteractiveanimation of virtual humans based on motion capture datardquoComputer Animation and Virtual Worlds vol 20 no 5-6 pp491ndash500 2009

[3] S Saini D R A Rambli S Sulaiman M N Zakaria and SR M Shukri ldquoA low-cost game framework for a home-basedstroke rehabilitation systemrdquo in Proceedings of the InternationalConference on Computer amp Information Science (ICCIS rsquo12) pp55ndash60 Kuala Lumpeu Malaysia June 2012

[4] A O Balan L Sigal and M J Black ldquoA quantitative evaluationof video-based 3D person trackingrdquo in Proceedings of the 2ndJoint IEEE International Workshop on Visual Surveillance andPerformance Evaluation of Tracking and Surveillance pp 349ndash356 October 2005

[5] J Deutscher and I Reid ldquoArticulated body motion capture bystochastic searchrdquo International Journal of Computer Vision vol61 no 2 pp 185ndash205 2005

[6] V John E Trucco and S Ivekovic ldquoMarkerless human articu-lated tracking using hierarchical particle swarm optimisationrdquoImage and Vision Computing vol 28 no 11 pp 1530ndash1547 2010

[7] V John E Trucco and SMcKenna ldquoMarkerless humanmotioncapture using charting and manifold constrained particleswarm optimisationrdquo in Proceedings of the 21st British MachineVision Conference (BMVC rsquo10) September 2010

[8] B Kwolek T Krzeszowski and K Wojciechowski ldquoReal-timemulti-view humanmotion tracking using 3Dmodel and latencytolerant parallel particle swarm optimizationrdquo in ComputerVisionComputer Graphics Collaboration Techniques pp 169ndash180 2011

[9] B Kwolek T Krzeszowski and K Wojciechowski ldquoSwarmintelligence based searching schemes for articulated 3D bodymotion trackingrdquo in Advances Concepts for Intelligent VisionSystems pp 115ndash126 Springer New York NY USA 2011

[10] T Krzeszowski B Kwolek and K Wojciechowski ldquoModel-based 3D human motion capture using global-local particleswarm optimizationsrdquo in Computer Recognition Systems 4 vol95 of Advances in Intelligent and Soft Computing pp 297ndash306Springer Berlin Germany 2011

[11] Z Zhang H S Seah and C K Quah ldquoParticle swarmoptimization for markerless full body motion capturerdquo inHandbook of Swarm Intelligence vol 8 of Adaptation Learningand Optimization pp 201ndash220 Springer Berlin Germany 2011

[12] P Fleischmann I Austvoll and B Kwolek ldquoParticle swarmoptimizationwith soft search space partitioning for video-basedmarkerless pose trackingrdquo in Advanced Concepts for IntelligentVision Systems vol 7517 of Lecture Notes in Computer Sciencepp 479ndash490 2012

[13] J Bandouch F Engstler and M Beetz ldquoEvaluation of hier-archical sampling strategies in 3D human pose estimationrdquoin Proceedings of the 19th British Machine Vision Conference(BMVC rsquo08) pp 1ndash10 September 2008

[14] J Gall B Rosenhahn T Brox and H-P Seidel ldquoOptimizationand filtering for human motion capturerdquo International Journalof Computer Vision vol 87 no 1-2 pp 75ndash92 2010

[15] J MacCormick andM Isard ldquoPartitioned sampling articulatedobjects and interface-quality hand trackingrdquo in ComputerVisionmdashECCV 2000 vol 1843 of Lecture Notes in ComputerScience pp 3ndash19 Springer Berlin Germany 2000

[16] M Isard and A Blake ldquoCondensationmdashconditional densitypropagation for visual trackingrdquo International Journal of Com-puter Vision vol 29 no 1 pp 5ndash28 1998

[17] R Ugolotti Y S G Nashed P Mesejo S Ivekovic L Mussiand S Cagnoni ldquoParticle swarm optimization and differentialevolution for model-based object detectionrdquo Applied Soft Com-puting Journal vol 13 no 6 pp 3092ndash3150 2013

[18] J MacCormick and A Blake ldquoProbabilistic exclusion principlefor trackingmultiple objectsrdquo International Journal of ComputerVision vol 39 no 1 pp 57ndash71 2000

[19] E Yeguas-Bolivar R Munoz-Salinas R Medina-Carnicer andA Carmona-Poyato ldquoComparing evolutionary algorithms andparticle filters for Markerless HumanMotion Capturerdquo AppliedSoft Computing Journal vol 17 pp 153ndash166 2014

[20] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceedings of the IEEE International Conference on Neural Net-works pp 1942ndash1948 Piscat-away Perth Australia December1995

[21] C Robertson and E Trucco ldquoHuman body posture via hierar-chical evolutionary optimizationrdquo in Proceedings of the BritishMachine Vision Conference (BMVC rsquo06) pp 999ndash1008 Edin-burgh UK September 2006

[22] S Ivekovic and E Trucco ldquoHuman body pose estimation withPSOrdquo in Proceedings of the IEEE Congress on EvolutionaryComputation (CEC rsquo06) pp 1256ndash1263 July 2006

[23] B Kwolek T Krzeszowski A Gagalowicz K Wojciechowskiand H Josinski ldquoReal-time multi-view humanmotion trackingusing particle swarm optimization with resamplingrdquo in Articu-latedMotion and Deformable Objects pp 92ndash101 Springer NewYork NY USA 2012

[24] XWangWWan X Zhang and X Yu ldquoAnnealed particle filterbased on particle swarm optimization for articulated three-dimensional human motion trackingrdquoOptical Engineering vol49 no 1 Article ID 017204 2010

[25] X Wang X Zou W Wan and X Yu ldquoArticulated 3D humanpose estimation with particle filter based particle swarm opti-mizationrdquo in Proceedings of the International Conference onAudio Language and Image Processing (ICALIP rsquo10) pp 1094ndash1099 November 2010

[26] B Kwolek ldquoMultiple views based human motion tracking insurveillance videosrdquo in Proceedings of the 8th IEEE InternationalConference on Advanced Video and Signal Based Surveillance(AVSS rsquo11) pp 492ndash497 September 2011

[27] X Zhang W Hu S Maybank X Li and M Zhu ldquoSequentialparticle swarm optimization for visual trackingrdquo in Proceedingsof the 26th IEEE Conference on Computer Vision and PatternRecognition (CVPR rsquo08) pp 1ndash8 June 2008

[28] T B Moeslund and E Granum ldquoA survey of computer vision-based human motion capturerdquo Computer Vision and ImageUnderstanding vol 81 no 3 pp 231ndash268 2001


[29] D M Gavrila ldquoThe visual analysis of human movement asurveyrdquo Computer Vision and Image Understanding vol 73 no1 pp 82ndash98 1999

[30] R Poppe ldquoVision-based human motion analysis an overviewrdquoComputer Vision and Image Understanding vol 108 no 1-2 pp4ndash18 2007

[31] J K Aggarwal and Q Cai ldquoHuman motion analysis a reviewrdquoin Proceedings of the IEEE Nonrigid and Articulated MotionWorkshop pp 90ndash102 San Juan Puerto Rico USA June 1997

[32] L Wang W Hu and T Tan ldquoRecent developments in humanmotion analysisrdquo Pattern Recognition vol 36 no 3 pp 585ndash6012003

[33] J K Aggarwal and M S Ryoo ldquoHuman activity analysis areviewrdquo ACM Computing Surveys vol 43 no 3 article 16 2011

[34] A A A Esmin R A Coelho and S Matwin ldquoA reviewon particle swarm optimization algorithm and its variants toclustering high-dimensional datardquoArtificial Intelligence Review2013

[35] M J Abul Hasan and S Ramakrishnan ldquoA survey hybrid evo-lutionary algorithms for cluster analysisrdquo Artificial IntelligenceReview vol 36 no 3 pp 179ndash204 2011

[36] V John and E Trucco ldquoCharting-based subspace learning forvideo-based human action classificationrdquo Machine Vision andApplications vol 25 no 1 pp 119ndash132 2014

[37] S Saini D R B A Rambli S B Sulaiman and M N BZakaria ldquoHuman pose tracking in low-dimensional subspaceusing manifold learning by chartingrdquo in Proceedings of the 3rdIEEE International Conference on Signal and Image ProcessingApplications (ICSIPA rsquo13) pp 258ndash263 October 2013

[38] S Saini D R B A Rambli S B SulaimanMN B Zakaria andS Rohkmah ldquoMarkerless multi-view human motion trackingusing manifold model learning by chartingrdquo Procedia Engineer-ing vol 41 pp 664ndash670 2012

[39] T Krzeszowski B Kwolek and K Wojciechowski ldquoArticulatedbody motion tracking by combined particle swarm optimiza-tion and particle filteringrdquo in Computer Vision and Graphicsvol 6374 pp 147ndash154 Springer Berlin Germany 2010

[40] X Zhang W Hu X Wang et al ldquoA swarm intelligence basedsearching strategy for articulated 3D human body trackingrdquoin Proceedings of the IEEE Computer Society Conference onComputer Vision and Pattern Recognition Workshops (CVPRWrsquo10) pp 45ndash50 San Francisco Calif USA June 2010

[41] S Ivekovic V John and E Trucco ldquoMarkerless multi-viewarticulated pose estimation using adaptive hierarchical particleswarm optimisationrdquo in Applications of Evolutionary Computa-tion pp 241ndash250 Springer New York NY USA 2010

[42] J Yan J Song L Wang and Y Liu ldquoModel-based 3D humanmotion tracking and voxel reconstruction from sparse viewsrdquo inProceedings of the 17th IEEE International Conference on ImageProcessing (ICIP rsquo10) pp 3265ndash3268 September 2010

[43] M Kiran S L Teng C S Chan andW K Lai ldquoHuman postureclassification using hybrid Particle Swarm Optimizationrdquo inPeoceedings of the 10th International Conference on InformationSciences Signal Processing andTheirApplications (ISSPA rsquo10) pp778ndash781 May 2010

[44] B J Zhang ldquoMonocular video human motion tracking basedon hybrid PSOrdquo Journal of Multimedia vol 9 pp 106ndash113 2014

[45] Z Zhang and H S Seah ldquoReal-time tracking of unconstrainedfull-body motion using niching swarm filtering combinedwith local optimizationrdquo in Proceedings of the IEEE ComputerSociety Conference on Computer Vision and Pattern RecognitionWorkshops (CVPRW rsquo11) pp 23ndash28 June 2011

[46] L Mussi S Ivekovic and S Cagnoni ldquoMarkerless articulatedhuman body tracking from multi-view video with GPU-PSOrdquoin Evolvable Systems From Biology to Hardware vol 6274 ofLecture Notes in Computer Science pp 97ndash108 Springer BerlinGermany 2010

[47] T Krzeszowski B Kwolek and K Wojciechowski ldquoGPU-accelerated tracking of the motion of 3D articulated figurerdquo inComputer Vision andGraphics pp 155ndash162 Springer NewYorkNY USA 2010

[48] Z Zhang H S Seah C K Quah and J Sun ldquoGPU-acceleratedreal-time tracking of full-bodymotion withmulti-layer searchrdquoIEEE Transactions on Multimedia vol 15 no 1 pp 106ndash1192013

[49] B Rymut and B Kwolek ldquoReal-time multiview human bodytracking usingGPU-accelerated PSOrdquo in Parallel Processing andApplied Mathematics pp 458ndash468 Springer Berlin Germany2014

[50] Y Li and Z Sun ldquoArticulated human motion tracking bysequential annealed particle swarm optimizationrdquo in PatternRecognition pp 153ndash161 Springer New York NY USA 2012

[51] X S Nguyen S Dubuisson and C Gonzales ldquoHierarchicalannealed particle swarm optimization for articulated objecttrackingrdquo inComputerAnalysis of Images andPatterns vol 8047of Lecture Notes in Computer Science pp 319ndash326 SpringerBerlin Germany 2013

[52] R Poli An Analysis of Publications on Particle Swarm Pptimiza-tion Applications Department of Computer Science Universityof Essex Essex UK 2007

[53] F van den Bergh andA P Engelbrecht ldquoA cooperative approachto participle swam optimizationrdquo IEEE Transactions on Evolu-tionary Computation vol 8 no 3 pp 225ndash239 2004

[54] L Sigal A O Balan andM J Black ldquoHumanEva synchronizedvideo and motion capture dataset and baseline algorithm forevaluation of articulated human motionrdquo International Journalof Computer Vision vol 87 no 1-2 pp 4ndash27 2010

Submit your manuscripts athttpwwwhindawicom

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MathematicsJournal of


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Differential EquationsInternational Journal of

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Stochastic AnalysisInternational Journal of


human motion tracking [16] However it suffers from thedimensionality issue when used for the humanmotion track-ing problem To address this issue [5] introduced annealedparticle filter (APF) an approach that merges condensationand simulates annealing in an attempt to improve the trackingresults as well reduce the number of particles The APFperforms a multilayer particle evaluation where the fitnessfunctions in the initial layers are smoothed to avoid the searchfrom being trapped in local minima In the last layers fitnessfunction is more peaked in order to concentrate the particlesto solution regions To represent the posterior distributionadequately the particle filter solutions critically rely on alarge number of particles which consequently increases thecomputational complexity beyond practical use when a widevariety of motion is considered [6 7 11 12 17]

Partition sampling [15] is another approach to reduce thesystem complexity The technique was initially introduced in[18] to address the high cost effect of particle filters whiletrackingmultiple objects Later on it was successfully appliedin hand tracking In general terms partitioned sampling (PS)is a strategy that consists of dividing the complete state intoseveral substates ldquopartitionsrdquo consecutively employing thedynamics for every partition followed by a suitable weightedresampling procedure In point of fact partition samplingcan abbreviate the high dimensionality problem in anothersituation also

Thepartitioned sampling (PS) is different from theAPF ina way that it applies strong partition of the search space Themain problem consists of determining the optimal partitionIn an attempt to solve this Bandouch et al [13] proposed amethod that combines both PS and APF known as PSAPFThe APF is incorporated into a PS framework by utilizingan appropriate weighted resampling in each subspace Thisapproach is able to deal with high dimensionality but itsuffers from high cost of employing a very large number ofevaluations per frame (around 8000) Generally the commonhuman pose tracking approaches rely on filtering algorithmsbut the conventional filtering algorithms have some short-comings such as computational expensive slowness of theirconvergence and they suffer from the curse of dimensionalityand they need to rely on simple human models (which leadto suboptimal tracking results) or require a high number ofevaluation to achieve accurate results [6 7 11 12 19]

Many real-world problems such as the articulated humanmotion tracking and pose estimation problem can be formu-lated as multidimensional nonlinear optimization problemsof parameters with variables in continuous domains In thepast few years evolutionary computation approaches (egGA PSO DE etc) are most widely used to solve continuousoptimization problems including human motion trackingand pose estimation

Particle swarm optimization (PSO) [20] is a population-based stochastic optimization algorithm which is originallyinspired from social behaviour of bird flocking or fishschooling The PSO has a capability of simple computationand rapid convergence as a stochastic search scheme PSOhas been successfully applied in several areas includinghuman motion tracking and pose estimation [6ndash12] and inthe other optimization areas the PSO give competition to

the genetic algorithms Currently the PSO and its variantsare most extensively used in the literature for video-basedarticulated human motion tracking and pose estimation asthey offer several advantages for example ability to solvehighly nonlinear problem robust and reliable performanceglobal and local search capability and little or no priorinformation requirement and it has fewer parameters toadjust [6 7 11 12]

In the PSO tracking framework articulated humanmotion tracking problem is formulated as amultidimensionalnonlinear optimization problemThefinal tracking results arethen obtained by optimizing a fitness function that computesthe match between the observed image and the 3D bodymodel Generally the main aim of fitness function is toevaluate how well a candidate pose hypothesis matches theobservation that is the images from all cameras views ateach time instantMany fitness functions have been proposedin the literature including optical flow appearance modelskin color and contours-based fitness function Howevermost common approaches rely on silhouettes and edgesbased fitness function [4ndash7 11 12] because it provides anappropriate trade-off between robustness and speed Figure 1illustrates the general optimization framework Within thisframework many tracking task can be reformulated asa global optimization problem in which a metaheuristicalgorithm is used to the optimized model parameters In thispaper we employ the latter approach we find the optimalbody model configuration by maximizing a fitness functionrepresentative of the similarity between the model and imageobservation under investigation

The standard PSO is generally used to find a singleoptimum in a static search space In contrast the natureof pose estimation and tracking problem is dynamic whereoptimum changes over time or frames Thus the standardPSO cannot be used directly to the problem it is necessaryto modify the PSO algorithm to better suit this problem

PSO has the capability to find the best value for inter-acting particles unfortunately the standard PSO also suf-fers from the curse of dimensionality which has led tomany variants specifically adapted for pose tracking Alsoits convergence speed becomes very slow near the globaloptimum when it is applied to high-dimensional parametricsearch space Therefore PSO generally failed in searchingfor a global optimal solution The existence of local optimalsolutions is not the sole reason for this phenomenon Itis because the particles velocities sometimes failed intodegeneracy leading to the restriction of successive range inthe subplain of the whole search hyperplain In spite of itsreported success the second major issue in using PSO forarticulated humanmotion tracking problem is that of particlediversity loss Generally it occurs due to convergence of theprior level of optimization and all the particles may be closeto previous optimum position and the swarm has shrunkThe swarm may be able to find the optimum efficiently ifthe position of new optimum still lies within the region ofshrinking swarm because of its diversity However the trueoptimum can never be found if the current optimum liesoutside of the swarm because of the particles low velocitieswhichwill inhibit rediversification and tracking However in


New configuration



Output 3D model

Deformed model

Yes

No


Image

3D model




















x119894119905+1= x119894119905+ v119894119905+1 (2)

Swarminfluence



parpos i

t+1

gbest

parval i

t+1

parpos i

t

pbest i

t

t

x

x

g

v

p


where v119894119905and x119894



1and








p119894119905=

x119894119905 if 119891 (x119894

119905gt 119891 (p119894

119905))


g = argmaxp119894119905

119891 (p119894119905)

(3)


119905 The
















(0)





119905)


119905


end if


























Mussi et al (2010) [46] HP 11 PSO 32



constrainedPSO

31













latencytolerant

parallel PSO26




RAPSOAPSO 26




Table 1 Continued

























1

1

0

0

X2

X1

t

tminus1

x

x

(a)

1

0

tminus1

t

X2

10

X1

x

x

(b)

tminus1

t

1

0

X2

10

X1

x

x

(c)










2is kept













119889 (119909 119909) =

1

119899

119899

sum

119894=1

1003817100381710038171003817119909119894minus 119909119894

1003817100381710038171003817 (4)






PSO119873 = 20 120593

1 1205932= 20

120596max = 20 120596min =



119890+ 119891119904




HeadLUL

LLL

RUL

RLL

RUA

RLA

TOR

LUA

LLA











Algorithm



partitioning(S-HP)





50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)


H-SPH-HPGlobal-PSO

(a)


H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)






6 Conclusion




(a)


(b)


(c)







Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










New configuration



Output 3D model

Deformed model

Yes

No


Image

3D model




















x119894119905+1= x119894119905+ v119894119905+1 (2)

Swarminfluence



parpos i

t+1

gbest

parval i

t+1

parpos i

t

pbest i

t

t

x

x

g

v

p


where v119894119905and x119894



1and








p119894119905=

x119894119905 if 119891 (x119894

119905gt 119891 (p119894

119905))


g = argmaxp119894119905

119891 (p119894119905)

(3)


119905 The
















(0)





119905)


119905


end if


























Mussi et al (2010) [46] HP 11 PSO 32



constrainedPSO

31













latencytolerant

parallel PSO26




RAPSOAPSO 26




Table 1 Continued

























1

1

0

0

X2

X1

t

tminus1

x

x

(a)

1

0

tminus1

t

X2

10

X1

x

x

(b)

tminus1

t

1

0

X2

10

X1

x

x

(c)










2is kept













119889 (119909 119909) =

1

119899

119899

sum

119894=1

1003817100381710038171003817119909119894minus 119909119894

1003817100381710038171003817 (4)






PSO119873 = 20 120593

1 1205932= 20

120596max = 20 120596min =



119890+ 119891119904




HeadLUL

LLL

RUL

RLL

RUA

RLA

TOR

LUA

LLA











Algorithm



partitioning(S-HP)





50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)


H-SPH-HPGlobal-PSO

(a)


H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)






6 Conclusion




(a)


(b)


(c)







Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















x119894119905+1= x119894119905+ v119894119905+1 (2)

Swarminfluence



parpos i

t+1

gbest

parval i

t+1

parpos i

t

pbest i

t

t

x

x

g

v

p


where v119894119905and x119894



1and








p119894119905=

x119894119905 if 119891 (x119894

119905gt 119891 (p119894

119905))


g = argmaxp119894119905

119891 (p119894119905)

(3)


119905 The
















(0)





119905)


119905


end if


























Mussi et al (2010) [46] HP 11 PSO 32



constrainedPSO

31













latencytolerant

parallel PSO26




RAPSOAPSO 26




Table 1 Continued

























1

1

0

0

X2

X1

t

tminus1

x

x

(a)

1

0

tminus1

t

X2

10

X1

x

x

(b)

tminus1

t

1

0

X2

10

X1

x

x

(c)










2is kept













119889 (119909 119909) =

1

119899

119899

sum

119894=1

1003817100381710038171003817119909119894minus 119909119894

1003817100381710038171003817 (4)






PSO119873 = 20 120593

1 1205932= 20

120596max = 20 120596min =



119890+ 119891119904




HeadLUL

LLL

RUL

RLL

RUA

RLA

TOR

LUA

LLA











Algorithm



partitioning(S-HP)





50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)


H-SPH-HPGlobal-PSO

(a)


H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)






6 Conclusion




(a)


(b)


(c)







Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra























(0)





119905)


119905


end if


























Mussi et al (2010) [46] HP 11 PSO 32



constrainedPSO

31













latencytolerant

parallel PSO26




RAPSOAPSO 26




Table 1 Continued

























1

1

0

0

X2

X1

t

tminus1

x

x

(a)

1

0

tminus1

t

X2

10

X1

x

x

(b)

tminus1

t

1

0

X2

10

X1

x

x

(c)










2is kept













119889 (119909 119909) =

1

119899

119899

sum

119894=1

1003817100381710038171003817119909119894minus 119909119894

1003817100381710038171003817 (4)






PSO119873 = 20 120593

1 1205932= 20

120596max = 20 120596min =



119890+ 119891119904




HeadLUL

LLL

RUL

RLL

RUA

RLA

TOR

LUA

LLA











Algorithm



partitioning(S-HP)





50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)


H-SPH-HPGlobal-PSO

(a)


H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)






6 Conclusion




(a)


(b)


(c)







Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




























Mussi et al (2010) [46] HP 11 PSO 32



constrainedPSO

31













latencytolerant

parallel PSO26




RAPSOAPSO 26




Table 1 Continued

























1

1

0

0

X2

X1

t

tminus1

x

x

(a)

1

0

tminus1

t

X2

10

X1

x

x

(b)

tminus1

t

1

0

X2

10

X1

x

x

(c)










2is kept













119889 (119909 119909) =

1

119899

119899

sum

119894=1

1003817100381710038171003817119909119894minus 119909119894

1003817100381710038171003817 (4)






PSO119873 = 20 120593

1 1205932= 20

120596max = 20 120596min =



119890+ 119891119904




HeadLUL

LLL

RUL

RLL

RUA

RLA

TOR

LUA

LLA











Algorithm



partitioning(S-HP)





50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)


H-SPH-HPGlobal-PSO

(a)


H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)






6 Conclusion




(a)


(b)


(c)







Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table 1 Continued

























1

1

0

0

X2

X1

t

tminus1

x

x

(a)

1

0

tminus1

t

X2

10

X1

x

x

(b)

tminus1

t

1

0

X2

10

X1

x

x

(c)










2is kept













119889 (119909 119909) =

1

119899

119899

sum

119894=1

1003817100381710038171003817119909119894minus 119909119894

1003817100381710038171003817 (4)






PSO119873 = 20 120593

1 1205932= 20

120596max = 20 120596min =



119890+ 119891119904




HeadLUL

LLL

RUL

RLL

RUA

RLA

TOR

LUA

LLA











Algorithm



partitioning(S-HP)





50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)


H-SPH-HPGlobal-PSO

(a)


H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)






6 Conclusion




(a)


(b)


(c)







Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1

1

0

0

X2

X1

t

tminus1

x

x

(a)

1

0

tminus1

t

X2

10

X1

x

x

(b)

tminus1

t

1

0

X2

10

X1

x

x

(c)










2is kept













119889 (119909 119909) =

1

119899

119899

sum

119894=1

1003817100381710038171003817119909119894minus 119909119894

1003817100381710038171003817 (4)






PSO119873 = 20 120593

1 1205932= 20

120596max = 20 120596min =



119890+ 119891119904




HeadLUL

LLL

RUL

RLL

RUA

RLA

TOR

LUA

LLA











Algorithm



partitioning(S-HP)





50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)


H-SPH-HPGlobal-PSO

(a)


H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)






6 Conclusion




(a)


(b)


(c)







Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












2is kept













119889 (119909 119909) =

1

119899

119899

sum

119894=1

1003817100381710038171003817119909119894minus 119909119894

1003817100381710038171003817 (4)






PSO119873 = 20 120593

1 1205932= 20

120596max = 20 120596min =



119890+ 119891119904




HeadLUL

LLL

RUL

RLL

RUA

RLA

TOR

LUA

LLA











Algorithm



partitioning(S-HP)





50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)


H-SPH-HPGlobal-PSO

(a)


H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)






6 Conclusion




(a)


(b)


(c)







Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












PSO119873 = 20 120593

1 1205932= 20

120596max = 20 120596min =



119890+ 119891119904




HeadLUL

LLL

RUL

RLL

RUA

RLA

TOR

LUA

LLA











Algorithm



partitioning(S-HP)





50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)


H-SPH-HPGlobal-PSO

(a)


H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)






6 Conclusion




(a)


(b)


(c)







Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










50 100 1500

20

40

60

80

100

120

Frame index

Erro

r (m

m)


H-SPH-HPGlobal-PSO

(a)


H-SPH-HPGlobal-PSO

0

20

40

60

80

100

Erro

r (m

m)


(b)






6 Conclusion




(a)


(b)


(c)







Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











(a)


(b)


(c)







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









review article a review on particle swarm optimization...

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