RAO-BLACKWELLIZED RESAMPLING PARTICLE FILTER FORREAL-TIME PLAYER TRACKING IN SPORTS

Nicolai v. Hoyningen-Huene, Michael BeetzIntelligent Autonomous Systems Group, Technische Universitat Munchen, Boltzmannstr. 3, D-85748 Garching, Germany

hoyninge, beetz@cs.tum.edu

Keywords: Multi-target tracking, Particle Filter, Rao-Blackwellization, Kalman Filter, Resampling

Abstract: Tracking multiple targets with similiar appearance is a common task in computer vision applications, espe-cially in sports games. We propose a Rao-Blackwellized Resampling Particle Filter (RBRPF) as an imple-mentable real-time continuation of a state-of-the-art multi-target tracking method. Target configurations aretracked by sampling associations and solving single-target tracking problems by Kalman filters. As an ad-vantage of the new method the independence assumption between data associations is relaxed to increasethe robustness in the sports domain. Smart resampling and memoization is introduced to equip the trackingmethod with real-time capabilities in the first place. The probabilistic framework allows for consideration ofappearance models and the fusion of different sensors. We demonstrate its applicability to real world applica-tions by tracking soccer players captured by multiple cameras through occlusions in real-time.

1 INTRODUCTION

Tracking multiple targets is needed in a lot of com-puter vision applications like surveillance or sportsanalysis. The sports domain provides a challeng-ing testbed for concurrent tracking of multiple tar-gets with similar appearance through frequent occlu-sions measured from different views. In team sportsthe complex coordination of movements of differentplayers are crucial to the success of a squad. For auto-mated analysis thereof the correct association of play-ers to movements is equally important as the recogni-tion of the movement itself.

To achieve an automatic extraction of athlete posi-tions during sports games from video streams, besidecamera estimation and player segmentation, a robustand fast multi-target tracking method is needed. Insports games the number of players is usually knownand constant. In contrast the number of observationsfor each player obtained by measurements from sen-sors or segmentation for videos varies; it ranges fromzero in case of occlusion and oversight to several mea-surements in case of hallucination and inaccuracy ofthe player extraction. Players usually differ by ap-pearance from the field to help viewers and referees to

follow the game easily, so the association of playersof one team with their individual name is the biggerproblem.

In this paper we propose a Rao-Blackwellized Re-sampling particle filter (RBRPF) for real-time track-ing of multiple targets. Particles are represented asconfigurations of all players to result in tracking amixture of Gaussians, where the multi-modality iscaused by possible mix-ups of associations and theGaussian refers to the uncertainty of dynamics. Sam-pling of new target configurations is reduced to sam-pling associations and Rao-Blackwellized by usingthe Kalman filter. Taking advantage of the fact that thenumber of probable associations for given player po-sitions and measurements are usually low, the particlefilter focuses on the most likely associations and canavoid unnecessary computations by smart resamplingand memoization. The Bayesian framework allowsthe integration of kinematic and appearance models todetermine the most probable player locations throughocclusions.

Our contributions are the enhancements of a state-of-the-art theoretical multi target tracking method to-wards an implementable real-time algorithm that per-forms well in the demanding sports domain. We relax

the independence assumption of single measurementassociations to suit the original method to the applica-tion domain and achieve more robustness. Further weinvent a smart resampling procedure that allows real-time in the first place and adapts to the complexityof the tracking problem. The proposed memoizationof repeatedly computed results additionally improvesefficiency.

The method is developed as part of the ASPOGA-MO system (Beetz et al., 2006; Beetz et al., 2007),that aims to extract knowledge from broadcasted soc-cer games, and is evaluated by applying it to realsoccer games, showing robust real-time performanceover challenging sequences.

The remainder of this paper is organized as fol-lows. We briefly talk about related work in the nextsection. In section 3 we derive the Rao-BlackwellizedResampling particle filter. Section 4 describes the ex-periments we conducted. We finish in section 5 withour conclusions.

2 RELATED WORK

Multiple-target tracking algorithms can be differenti-ated by their data association methods. Multiple hy-pothesis tracking (MHT) (Bar-Shalom et al., 2001)builds a pruned tree of all possible association se-quences of each measurement with close targets bythe Hungarian algorithm. The assumption of singleassociations and the use of Kalman filtering allowcomputation in polynomial time, but inhibit to handlemultiple or merged associations. Khan, Balch & Del-laert (2006) propose a real-time Rao-BlackwellizedMCMC-based particle filter where associations aresampled by a Markov chain. The Markov chain al-lows also sampling of merged measurement assign-ments but demands computation time that reduces thenumber of particles. In their experiments real-timecould only be provided for a small number of parti-cles (less than 6) i.e. the tracker can cope with threeparallel mix-ups of targets max. Interaction of targetsare modeled as correlations between target positionswhich does not hold for many applications.

The Rao-Blackwellized particle filter approach bySarkka et al. (2004; 2007) samples the associationsdirectly and handles dependencies between them bydata associations priors. The performance of themethod was demonstrated only on synthetic simula-tions without statements about computation time. Ourapproach is an extension of this method to real worldapplications introducing smart resampling and mem-oization that leads to real-time tracking in the firstplace and relaxation of the association independence

assumption.Tracking of soccer players is classified by Li

et al. (2005) in category and identity tracking. Cat-egory tracking extracts trajectories with team affili-ation where in the other case each single player istraced with its identity. Barcelo et al. (2005) andFigueroa et al. (2006) label the measurements bynearest neighbor assignment. In Gedikli et al. (2007)MHT was applied, but Particle filters constitute themostly used method in the literature for categorytracking (i.e. (Yang et al., 2005; A.Dearden & Grau,2006)). Du et al. (2006; 2007) aim on combining lo-cal particle filters to fuse measurements captured fromdifferent views. A MCMC method for team labellingis proposed by Liu et al. (2007) to link observationsof soccer players over time.

Identity tracking is often performed in a sec-ond stage by consistent labelling of the trajectorygraph generated by category tracking. Huang &Hilton (2006) propose an assignment in batch modeby shortest path algorithm, Nillius et al. (2006) solvethe association of the trajectory graph by Bayesiannetwork inference, and Sullivan & Carlsson (2006)combine trajectories of unoccluded players in a graphstructure by clustering. Barcelo et al. (2005) resolvecollisions of nearest neighbor Kalman tracking byconstraints in the trajectory graph. To the best of ourknowledge no real-time identity tracking method forsoccer player that allows multiple measurements andfuses different camera views was proposed in the lit-erature yet.

3 RAO-BLACKWELLIZEDRESAMPLING PARTICLEFILTER

A particle filter for complete player configurationsconstitutes the base of our algorithm. New particlesare predicted by sampling associations of players withcurrent measurements considering dependencies be-tween them. Computation time is spend mostly onthe highly probable configurations and on ambiguousassociations by memoization of precomputed samplesand probabilities. Sampling and weighting is done byusing the Kalman filter for Rao-Blackwellization ofthe particle filter.

3.1 Bayesian View of Tracking

The problem of tracking is to recursively estimate astate xk knowing the evolution of the state sequence

xk = fk (xk−1,vk−1) (1)

from measurements

zk = hk (xk,nk) (2)

where fk is called system or motion model and hk iscalled measurement model, vk−1 and nk denote theprocess and measurement noise, respectively. Thetracked state xk is represented as the configuration ofall player states

xk =

x j,k = N

x

yxy

;mij,k,Vj,k

j = 1, . . . ,T

(3)where x j,k contains the position and velocity of playerj at time k. An individual target sample xi

j,k is as-sumed to be Gaussian with mean mi

j,k and correspond-ing covariance matrix V i

j,k.In a Bayesian framework, the problem of tracking

can be formulated as one of estimating the posteriorprobability density function p(xk|z1:k) for the state xkgiven a sequence of measurements z1:k up to time k.

3.2 Particle Filtering

In Sampling Importance Sampling (SIS) particle fil-tering, the posterior probability density function is ap-proximated by a weighted sum of random samples xi

kalso called particles (Arulampalam, Maskell, Gordon& Clapp, 2002). The weights are normalized suchthat ∑i wi

k = 1:

p(xk|z1:k)≈∑i

wikδ

(xk− xi

k). (4)

We draw samples xik by importance sampling

from a proposal q(.) called an importance density.Doucet (1998) showed that the optimal importancedensity function that minimizes the variance of thetrue weights conditioned on xi

k−1 and zk is

qopt(xk|xi

k−1,zk)

=p(zk|xk,xi

k−1

)p(xk|xi

k−1

)p(zk|xi

k−1

) . (5)

In our case the importance density is the probabil-ity distribution of data associations, while the actualsample is deduced from an association by the use ofKalman filtering.

3.3 Sampling new Configurations

For known associations between measurements zk andplayers of the sample xi

k−1 the new sampled con-figuration is Gaussian and can be evaluated analyti-cally as an optimal fusion between measurements and

predicted player positions. The Kalman filter pro-vides the method to find the Gaussian that equals bothprobabilities in the numerator of equation 5 and thusmaximizes their product. The sampling problem re-duces therefor to sample associations between mea-surements and the predicted player configuration andsolving multiple single target tracking problems byKalman filtering. The analytical sampling part formsthe Rao-Blackwellization of the particle filter. Tosupply an optimal solution the Kalman filter assumesstate and measurement noise to be zero-mean, whiteGaussian and the measurement as well as the motionmodel to be linear. If the last assumption does nothold an extended or unscented Kalman filter could beapplied for a suboptimal solution. Following this ap-proach the posterior probability density function ofconfigurations form a mixture of Gaussians, wherethe multi-modality originates from ambiguities in theassociations.

3.3.1 Predicting by System Model

We can sample from p(x′k|xi

k−1

)analytically by the

Kalman prediction step according to the system dy-namics of eq. 1. Each player state is predicted in-dependently using the discretized Wiener velocitymodel A∆t (Bar-Shalom, Li & Kirubarajan, 2001) fortime difference ∆t between k−1 and k as a linear mo-tion model:

m′j,k =

x′j,ky′j,kx′j,ky′j,k

=

1 0 ∆t 00 1 0 ∆t0 0 1 00 0 0 1

xij,k−1

yij,k−1

xij,k−1

yij,k−1

(6)

The covariance matrix evolves to

V ′k = A∆tVk−1AT

∆t +

∆t3

3 0 ∆t2

2 00 ∆t3

3 0 ∆t2

2∆t2

2 0 ∆t 00 ∆t2

2 0 ∆t

q (7)

with power spectral density q as a constant factor.

3.3.2 Sampling Associations

We introduce associations

Jk : {1, . . . , |zk|} →℘({1, . . . ,T}) (8)

as mappings from all measurements at time k to a(possibly empty) subset of all targets. We denoteJk as the inverse mapping from targets to their as-signed observations for convenience. The space ofdata associations equals the finite and discrete set ofall possible associations of measurements to targets

containing 2|zk|×T elements. If we restrict the dataassociations Jk to assign a measurement to one tar-get max, the number of possible associations reduceto (T +1)|zk|. We can further reduce this number tomin(T,|zk|)

∑i=0

(min(T, |zk|)

i

)max(T, |zk|)min(T,|zk|)−i if we

prohibit multiple measurements per target, also calledexclusion principle (MacCormick & Blake, 1999).Enumerating this set and solving each single targettracking problem is still intractable even for a smallnumber of targets and measurements. Fortunatelyonly a few associations have high probability, but tosample them efficiently, we have to assume the associ-ations for single measurements to be independently orthe dependency between them to be determined fast.

Individual independent associations If we look atsampling an individual association for measurementz∈ zk, we can enumerate all possible assignments eas-ily as z can be clutter viz. a false alarm or assigned toone of the players. Thus the importance distributionπ(z) for an association of a specific measurement zcan be evaluated by normalizing the probabilities π(z)for each possible association.

Clutter measurements are assumed to be indepen-dent from player positions and uniformly distributedin the measurement space with volume M

π∅(z) = p(Jk(z) = ∅|zk)∼1M

. (9)

The probability for a data association between targett and an observation z is up to a constant factor:

πt(z) = p(t ∈ Jk(z)|zk,x′k

)∼ papp (t ∈ Jk(z))N

(z;Hzm′

t,k,HTz V ′

t,kHz +Rz

)(10)

with measurement model Hz =(

1 0 0 00 1 0 0

)and Rz as measurement noise covariance.papp (t ∈ Jk(z)) denotes the propability of an as-sociation based on the appearance model only, whichis independent from player and measurement posi-tions. The Gaussian in the second part refers to theprobability of the association by the kinematic model.We included the appearance model in difference to(Sarkka et al., 2007) to allow a realistic influenceof additional information from segmentation besidespatial data only.

Importance density Utilizing the independence ofsingle associations the importance density for a sam-pled state x j

k can be computed as a product over prob-abilities of assignments for each single measurement

Figure 1: Association of a and m1 increases the probabilityof b and m2 being associated.

that are given by the normalized importance distribu-tion π of equations 9 and 10.

q(xk|xi

k−1,zk)

= ∏zk

π (11)

Relaxation of Independence In the underlyingmethod by Sarkka et al., the measurements are pro-cessed one at a time in sequential fashion based onthe independence assumption of associations of indi-vidual measurements. This assumption does not al-ways hold, the order of associations often do matter.This can be best exemplified by figure 1 assuming thatmeasurements can be assigned to one target at max: Iftarget a is assigned to measurement m1, the probabil-ity of the association of m2 and target b increases.

Sarkka et al. did not consider this problemat all but proposed the use of an data associationprior. We follow this solution instead of establish-ing an additional Markov Chain as proposed by Khanet al. (2006) in favor of computational efficiency butchange the procedure slightly to improve robustnessagainst violation of the mentioned assumption. Togenerate new particles x j

k including the whole playerconfiguration, we repeatedly sample an ordering onthe measurements of one sweep uniformly at random,reducing the relevance of the ordering and the induceddependencies on the tracking result. With the ran-domly sampled ordering we draw an association foreach measurement with the normalized importancedistribution π(z) one at a time. If a target was associ-ated, it is excluded from further associations with thesingle detection probability psd and the importancedistribution is renormalized. If the mentioned exclu-sion principle holds i.e. targets can be assigned to onemeasurement at max, psd should be set to one.

Determination of State from Associations Forsampled associations Jk the predicted player positionsx′k can be updated individually by Kalman update withtheir observations

xij,k = x′j,k +V ′

j,kHT (HV ′

kHT +R)−1 (

Jk( j)−Hx′j,k),

(12)

with H denoting the linear measurement model (2) asHz stacked |Jk ( j) | times and R as diagonal matrix ofmeasurement covariances of observations Jk ( j).

3.4 Weighting

For a good performance of the particle filter the com-putation of the weights of each sampled state is cru-cial. To approximate p(xk|z1:k) correctly the weightswi

k have to be defined recursively as

wik ∝ wi

k−1p(zk|xi

k

)p(xi

k|xik−1

)q(xi

k|xik−1,zk

) . (13)

The denominator was already computed in the sam-pling phase and was depicted in equation 11. Thelikelihood of the measurements given the sampledstate xi

k with known associations and the likelihood ofxi

k given the former state xik−1 and the dynamics can

be computed for each player and measurement sepa-rately. The measurement likelihood can be computedanalogously to eq. 10 but substituting x′k by xi

k and V ′k

by V ik , respectively:

p(zk|xi

k)

= ∏z/∈Ji

k

π∅(z)∏j

p(

Jik(x

ij,k)|xi

j,k

). (14)

The likelihood of the new sample according to themotion model can be computed by reusing the alreadypredicted state x′k of eq. 6

p(xi

k|xik−1

)= ∏

jN

(mi

j,k;m′j,k,V

ij,k +V ′

j,k

). (15)

3.5 Resampling

SIS particle filters suffer from the so called degener-acy phenomenon, where only a small amount of allparticles have not negligible weights. This impliesthat most of the computation time will be spent onparticles that contribute only marginally to the ap-proximation of the posterior probability density func-tion of equation 4. To reduce the degeneracy problemresampling has been proposed to eliminate particleswith small weights and clone the others according totheir weights. We include the resampling step by sam-pling wi

k−1×Nmax associations for particle xik−1. Par-

ticles with larger weights will therefor allocate moreparticles in the next time step, while particles withsmall weights are dropped.

Sampling several times from the same particle thenumber of distinct sampled particles will approach thenumber of ambiguities in the associations because aspecific assignment leads to the same sampled con-figuration. Due to their discreteness there are usuallyonly a small number of distinct probable associations.

This allows a chance for noticeable improvement incomputation time by smart memoization. Cachingand testing sampled associations for equality can savecomputation time considering not only the update togenerate a new state of equation 12 but also the pre-diction in the next particle filtering step in equation6.

After resampling the weights are usually reset towk = 1/Nmax to reflect the equal probability of all par-ticles. In our case we count the times nJk the sameassociation Jk was sampled for a specific particle andprovide only one single particle for the next filteringstep having the weight set to wk = nJk/Nmax. Then theweights are recursively updated as in equation 13 andnormalized at the end of the filtering step. The actualnumber of particles can therefor vary between 1 andNmax using more particles in situations with high as-sociation ambiguities. This smart resampling reducesthe computation time and allows real time in the firstplace.

3.6 Estimate of the state

An estimate of the player positions at time k i.e. of thestate xk can be found by either selecting the particlewith maximum weight or by clustering the particlesand taking the weighted mean of the most probablecluster. Calculating the weighted mean of all parti-cles should not be considered here because it can leadto the so called ghost phenomenon for multi-modaldistributions i.e. it leads to a state estimated as themean of two modes that is known to be wrong.

3.7 Implementation

The complete algorithm is depicted in figure 2 fol-lowing the derivation of the former section. The indi-vidual importance distributions π as well as π and theKalman prediction and updates are cached for reuse inthe next sampling iteration to improve efficiency. Theimportance distribution, all probabilities and weightsare calculated in log-space to avoid numerical prob-lems.

4 EXPERIMENTAL RESULTS

The proposed tracking method is evaluated as partof the ASPOGAMO system (Beetz et al., 2006; Beetzet al., 2007), that aims to extract knowledge frombroadcasted soccer games. ASPOGAMO is able to trackmultiple dynamic pan-tilt-zoom cameras and segmentthe soccer players and referee by a combination of

[{xi

k,wik}Nk

i=1

]= RBRPF

[{xi

k−1,wik−1

}Nk−1

i=1 ,zk

]Nk = 0FOR i = 1 : Nk−1Predict x′k as in 6C = ∅FOR j = 1 :

(wi

k−1×Nmax)

Sample an association Jk:τ = {1, . . . ,T}Init Jk : ∀p ∈ τ.Jk(p) = ∅Reorder measurements zk randomlyFOR l = 1 : |zk|Compute π() as in 9 and 10π = normalized π

Draw association for lth measurementwith player p ∈ τ by π

Jk(p) = Jk(p)∪{l}IF random(0,1) < psd: τ = τ \ p andrenormalize π

END FOR

IF Jk not in CNk = Nk +1nJk = 1Compute xNk

k by Kalman update if not donepreviously as in 12wNk

k = 1Nmax

Update wNkk as in 13

C = C∪{Jk}

ELSEnJk = nJk +1wk = wk

nJknJk−1

END IF

END FOR

END FORCalculate total weight: t = ∑

Nkj=1 w j

kFOR j = 1 : NkNormalize: w j

k = t−1w jk

END FOR

Figure 2: Algorithm for one iteration of the proposed Rao-Blackwellized Resampling particle filter.

variance filter and color templates. Segmentation in-fluences the tracking process as the Kalman filterssmooth assigned measurements, quality evaluation ofthe used method can be found in (Beetz et al., 2007).However segmentation by background subtraction forstatic cameras is usually of higher quality. Digitalvideos captured by two dynamic cameras with a framerate of 25Hz provide the basic raw material. Track-ing results in both camera perspectives are depictedin figures 3 and 4 and are presented quantitatively intable 2. The extracted players spatial measurementsof each camera are fused by the proposed tracking al-

gorithm as different measurement sweeps with sametime stamps.

Player positions have been measured in metersand were initialized manually in the image with co-variance V0 = 2I4, initial velocity was set to zero. Thefactor for the kinematic process noise q = 0.0008 isderived from maximal human speed. The probabilityof multiple observations for the same target was ob-tained experimentally to psd = 0.92. A confusion ma-trix between different categories was used as a sim-ple appearance model papp and is depicted in table4. The measurement space is determined by the num-ber of pixels in each camera frame and evaluates toM = 720×576. We used Nmax = 50 particles to trackall of the 22 players and the referee.

There is no ground truth for broadcasted soccergames because players can be tracked only visuallyand camera parameters are unknown. We abandon topresent a spatial error as this is influenced mainly bycamera estimation and segmentation. Instead we triedto find a error measure that is related with the numberof false associations. A failure was counted when theprojected player position differed from the real playerin the image by more than 10 pixels for longer than 3frames. In this case the tracker was reset in the failedplayer positions and run again on the rest of the se-quence. We tracked both camera views separately andalso ran the same sequence fusing the measurementsof both perspectives. Because the broadcasted high-angle camera shows only a part of the field and is pan-ning and zooming fast, in average only 9.9 players arevisible (with standard deviation of 3.2). We splittedthe number of failures into association errors and as-signing emerging players (second number) to be com-parable with the other results. The second row of ta-ble 2 shows the number of frames that were trackedin the according experiment. The computation timewas taken for one update step, where all experimentshave been conducted on a 2.2 GHz Dual-core PC. Wethink the actual needed time is more significant thanthe theoretical complexity of the algorithm since theinput data do not scale but stay in fixed boundaries(number of players is 22, number of measurementsusually lower than 200). The last row depicts the av-erage number of particles and the corresponding stan-dard deviation. Table 2 clearly evidences the real-timetracking ability of the proposed method with low fail-ure rate for single cameras. Fusion of different cam-eras reduces the occurrence of occlusions and there-with failure rate and number of particles even further.

The fourth experiment states a challenging se-quence including several fouls and header duelswhere kinematic and appearance model have oftenbeen to weak to differentiate between players causing

Italy France Referee

Italy 0.6 0.1 0.3France 0.1 0.8 0.1Referee 0.3 0.1 0.6

Table 1: Confusion matrix between different categories.

Game Frames Fail Time(ms) Particles

Tactical 1262 13 23.3± 4 43.5±10Highangle 1262 7+54 8.5± 5 12.1±12

Fused 1262 11 30.2±20 33.3±16Fused II 3202 98 33.4±18 34.1±14

Table 2: Tracking performance on the final of the world cup2006.

a higher number of failures. The amount of measure-ments (lower for the highangle view) correlates obvi-ously with the number of particles and the computa-tion time demonstrating the adaptiveness of the pro-posed method to the complexity of the tracking prob-lem. Also we observed assignment errors if segmen-tation could not extract a specific player for longerthan 20 frames (e.g. fouled player on the ground).

We also implemented the method as proposed byKhan et al. (2006) and tested it on the World Cupfinal. We encountered problems of two kind: lowvariance in sparse particles and misleading interactionhandling. The real-time requirement allowed only asmall number of particles (6 in our case) which hada low variance because the Markov chain convergedto very similar associations. This misled the trackerto remember the most probable configuration onlywhich often did not equal the true positions. Inter-actions are handled by dependencies in the positionsvia symmetric entries in the configuration covariancematrix. This modeling is inappropriate for interact-ing soccer players, where e.g. the player on the ballshows contrary motion to his competitor. Both draw-backs resulted in poor tracking performance for theinspected soccer game sequences.

5 CONCLUSIONS

In this article we have proposed a real-time multipletarget tracking method based on Rao-BlackwellizedResampling particle filtering for tracking soccerplayer identities. We presented the necessary exten-sions of an so far only theoretically evaluated state-of-the-art multi-target tracking method to handle real

Figure 3: Tactical camera view of the World Cup final 2006.

Figure 4: Identity tracking of soccer players in the broad-casted highangle camera view of the World Cup final 2006.

tracking problems being as challenging as in thesports domain. The first extension comprises the pro-cessing of measurements of one sweep instead of oneat a time to relax the independence assumption of as-sociations. Secondly, smart resampling and memoiza-tion was introduced to equip the tracking method withreal-time capabilities. Experimental results demon-strate robustness and real-time performance of thedeveloped method in challenging soccer game se-quences including increased achievements by fusionof measurements from different cameras. A compari-son with another recent multi-target tracking methodexplains the supremacy of our approach for the soc-cer domain. For future research we plan to examinemore complex appearance models for automatic reini-tialization of the identities especially regarding broad-casted single view sports videos.

ACKNOWLEDGEMENTS

This work was partially funded by the German Re-search Foundation DFG.

ReferencesA.Dearden, Y. & Grau, O. (2006). Tracking football player

movment from a single moving camera using particlefilters. In European Conf. on Visual Media Production(CVMP 2006).

Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp,T. (2002). A tutorial on particle filters for on-line nonlinear/non-gaussian bayesian tracking. IEEETrans. on Signal Processing, 50(2).

Bar-Shalom, Y., Li, X.-R., & Kirubarajan, T. (2001). Esti-mation with Applications to Tracking and Navigation.Wiley Interscience.

Barcelo, L., Binefa, X., & Kender, J. R. (2005). Robustmethods and representations for soccer player track-ing and collision resolution. In Proc. of Intl. Conf.on Image and Video Retrieval (CIVR 2005), (pp. 237–246).

Beetz, M., Bandouch, J., Gedikli, S., von Hoyningen-Huene, N., Kirchlechner, B., & Maldonado, A.(2006). Camera-based observation of football gamesfor analyzing multi-agent activities. In Proc. of Intl.Joint Conf. on Autonomous Agents and MultiagentSystems (AAMAS).

Beetz, M., Gedikli, S., Bandouch, J., Kirchlechner, B., vonHoyningen-Huene, N., & Perzylo, A. (2007). Visu-ally tracking football games based on tv broadcasts.In Proc. of Intl. Joint Conf. on Artificial Intelligence(IJCAI).

Doucet, A. (1998). On sequential Monte Carlo methods forBayesian filtering. Technical report, Dept. End., Univ.Cambridge, UK.

Du, W., Hayet, J.-B., Piater, J., & Verly, J. (2006). Col-laborative multi-camera tracking of athletes in teamsports. In Workshop on Computer Vision Based Anal-ysis in Sport Environments (CVBASE), (pp. 2–13).

Du, W. & Piater, J. H. (2007). Multi-camera People Track-ing by Collaborative Particle Filters and PrincipalAxis-Based Integration. In Asian Conference on Com-puter Vision, number 4843 in LNCS, (pp. 365–374).Springer.

Figueroa, P. J., Leite, N. J., & Barros, R. M. L. (2006).Tracking soccer players aiming their kinematical mo-tion analysis. Computer Vision and Image Under-standing, 101(2), 122–135.

Gedikli, S., Bandouch, J., von Hoyningen-Huene, N.,Kirchlechner, B., & Beetz, M. (2007). An AdaptiveVision System for Tracking Soccer Players from Vari-able Camera Settings. In Proc. of Intl. Conf. on Com-puter Vision Systems (ICVS).

Huang, P. & Hilton, A. (2006). Football player tracking forvideo annotation. In European Conf. on Visual MediaProduction.

Khan, Z., Balch, T., & Dellaert, F. (2006). Mcmc data asso-ciation and sparse factorization updating for real timemultitarget tracking with merged and multiple mea-surements. IEEE Trans. on Pattern Analysis and Ma-chine Intelligence, 28(12), 1960–1972.

Li, Y., Dore, A., & Orwell, J. (2005). Evaluating the per-formance of systems for tracking football players andball. In IEEE Intl. Conf. on Advanced Video and Sig-nal Based Surveillance.

Liu, J., Tong, X., Li, W., Wang, T., Zhang, Y., Wang, H.,Yang, B., Sun, L., & Yang, S. (2007). Automaticplayer detection, labeling and tracking in broadcastsoccer video. In British Machine Vision Conference.

MacCormick, J. & Blake, A. (1999). A probabilistic exclu-sion principle for tracking multiple objects. In Proc.of Intl. Conf. on Computer Vision (ICCV), (pp. 572–578).

Nillius, P., Sullivan, J., & Carlsson, S. (2006). Multi-targettracking - linking identities using bayesian networkinference. In Proc. of Computer Vision and PatternRecognition, (pp. 2187–2194).

Sarkka, S., Vehtari, A., & Lampinen, J. (2004). Rao-blackwellized monte carlo data association for mul-tiple target tracking. In Proc. of Intl Conf. on Infor-mation Fusion, volume 7, Stockholm.

Sarkka, S., Vehtari, A., & Lampinen, J. (2007). Rao-blackwellized particle filter for multiple target track-ing. Information Fusion Journal, 8(1), 2–15.

Sullivan, J. & Carlsson, S. (2006). Tracking and labellingof interacting multiple targets. In Proc. of EuropeanConf. on Computer Vision, (pp. 619–632).

Yang, C., Duraiswami, R., & Davis, L. (2005). Fast mul-tiple object tracking via a hierarchical particle filter.In Proc. of Intl. Conf. on Computer Vision, volume 1,(pp. 212–219).