- Research Article
- Open Access

# Combined Data Association and Evolving Particle Filter for Tracking of Multiple Articulated Objects

- Harish Bhaskar
^{1}Email author and - Lyudmila Mihaylova
^{2}

**2011**:642532

https://doi.org/10.1155/2011/642532

© Harish Bhaskar and Lyudmila Mihaylova. 2011

**Received:**1 May 2010**Accepted:**14 January 2011**Published:**10 February 2011

## Abstract

This paper proposes an approach for tracking multiple articulated targets using a combined data association and evolving population particle filter. A visual target is represented as a pictorial structure using a collection of parts together with a model of their geometry. Tracking multiple targets in video involves an iterative alternating scheme of selecting valid measurements belonging to a target from a clutter or other measurements that all fall within a validation gate. An algorithm with extended likelihood probabilistic data association and evolving groups of populations of particles representing a multiple-part distribution is designed. Variety in the particles is introduced using constrained genetic operators both in the sampling and resampling steps. We explore the effect of various model parameters on system performance and show that the proposed model achieves better accuracy than other widely used methods on standard datasets.

## Keywords

- Root Mean Square Error
- Markov Chain Monte Carlo
- Particle Filter
- Data Association
- Markov Chain Monte Carlo Method

## 1. Introduction

Tracking articulated targets is a central problem in computer vision, with applications including robotics and surveillance. The problem of multiple articulated target tracking (MATT) deals with tracking a variable number of targets, each consisting of the same number of different constituent body parts, given noisy measurements at every instant of time from a dynamic scene, and simultaneously maintaining correct target identities irrespective of any visual perturbations [1–4]. However, these tasks are complicated by the nonrigid variation within the general class of objects that we wish to track (e.g., people, animals, etc.), appearance variations of targets, and the presence of occlusions. Different methods have been proposed in the literature to cope with these challenges, for example, [2, 5–7]. The pictorial structure approach proposed in [6] is an appealing approach for people modelling in view its simplicity and generality. A different, limb-based structure model is developed in [5], particularly suited for the detection and tracking of multiple people in crowded scenes.

The problem of MATT can be divided into the subproblems of estimation and data association. A popular approach to solving this estimation problem is to build linearised filters such as the extended Kalman filter (EKF) [8], under a Gaussian noise assumption. Consequently, sufficient statistics from such linearised filters are used for data association. However, with nonlinear models in the state equation and non-Gaussian noise assumption, such linearised models often lead to inaccurate solutions or even face divergence. The sequential Monte Carlo (SMC) methods, such as the particle filters (PFs) [9] have proven their potential for the estimation of nonlinear systems, with non-Gaussian noise assumption and multimodal distributions.

In this paper, we propose an approach combining evolving population particle filtering with extended likelihood data association for MATT applications. To account for the uncertainty in the origin of the measurement, the extended likelihood data association method [10] incorporates local attribute information of measurements weighted by probabilistic data association (PDA) for correctly identifying the measurement from the target as against the clutter. On the other hand, the evolving population particle filter, provides iterative convergence of groups of particles through a specified kernel by introducing variety in the population using constrained genetic operators in both the sampling and resampling steps.

One of the main novelties of the method is that it conveniently integrates data association into evolving population particle filtering, thus allowing particles to regenerate both in sampling and resampling steps by simultaneously disregarding particle measurement that account for clutter within a specified validation gate. Our results suggest that the proposed integrated approach can considerably improve performance when compared individually to a Markov chain Monte Carlo (MCMC) combined data association technique or a generic particle filter (*non-MCMC filter*). Second, the geometrical constraints imposed by the picture structure representing the target are intrinsically modeled into the particle regeneration process through *constrained* genetic operations. Furthermore, some of the system parameters (such as the size of the validation gate) are learned from the data rather than specified by hand.

The remaining part of the paper is organised in the following way. Section 2 makes an overview of related works. Section 3 presents the proposed approach for multiple articulated object tracking. Results are given in Section 4. Finally, conclusions are summarised in Section 5.

## 2. Related Work

MATT is a highly challenging area of research within computer vision and tracking communities. The high degree of freedom of multiple articulated regions together with the interdependencies between them and with other targets requires efficient techniques able to cope effectively with the dynamic changes of the objects. In general, motion tracking of articulated objects in video consists of two distinct steps: *detection* and *tracking*. During the detection process, we aim to segment the human objects and their constituent body parts from the frames of the video sequences. In tracking, we are spatially locating these detected regions in time. A number of techniques have been proposed for the detection and tracking phases [2, 11–13]. In our paper, we assume a standard procedure applied for the detection step and propose a novel tracking methodology.

Tracking in recent years is often considered as a dynamic system estimation problem [14]. A number of different techniques have been proposed [15] in the past to estimate the variables of such dynamic systems. Some of the important methods include the Kalman filter [16], and unscented Kalman filter [17]. These methods assume that the posterior probability density of the system model is Gaussian. This assumption is more often restrictive and does not always suit different applications. In order to cope with the nonlinearity, extended techniques such as unscented Kalman filter [18], extended Kalman filter [19], approximation grid filter, and particle filters [17, 20] have been recommended. A particle filter approximates the posterior state probability density using a set of particles and propagating these particles over time with appropriate weighting coefficients often produces efficient tracking. Particle filters are robust to nonlinear, non-Gaussian systems with multi-modal distributions. However, even with a large population of particles, there may be no or little number of particles near the actual correct state. The second main drawback of particle filter methods is degeneracy. The problem of degeneracy refers to some particles having negligible weight as against the weight being concentrated on few others. Resampling techniques are employed to tackle degeneracy issues but sometimes when applied improperly can lead to sample impoverishment [21].

Population-based methods [22–24] are techniques that generate a collection of samples in parallel as against single independent or dependent samples. We can conveniently categorize these population-based methods into (a) MCMC type of methods and (b) methods based on importance sampling and resampling ideas. While MCMC methods are directed by theoretical convergence based on iterations, sampling/resampling techniques rely on processing a number of samples in parallel and sequential Monte. The population MCMC methods apply population moves that exchange variables between population members in order to generate the new target density. An example of a population move is the exchange move that swaps information between chains in a population. Similar types of moves are realised in the genetic algorithms, with the crossover, mutation, and exchange steps. In contrast, the sequential Monte Carlo methods [25] were constructed to sample from a sequence of related target distributions, using resampling techniques on the samples from previous target density. Commonly used resampling techniques include multinomial resampling [26], residual resampling technique [25], and stratified resampling [25].

One of the other main issues of MATT applications is the presence of multiple parts of the body and multiple targets that share similar feature characteristics, thus leading to uncertainty in the origin of measurements. Data association (DA) methods [27, 28] are used for correctly identifying the measurement that originated from the target from clutter of other multiple noisy measurements. It is assumed that the clutter is a model of false detections whose statistical properties are significantly different from those of the targets. Data association is of crucial importance to our problem because of the requirement to relate each measurement to the correct body part of the correct object of interest. There has been extensive studies in data association [10, 27, 29–36]. Most methods are restricted by assumptions on the number of targets, statistical properties of observations, and number of possible measurements.

In order to tackle the problem of MATT, it is important to combine estimation techniques and data association so that robust tracking is possible.

## 3. The Combined Data Association with Evolving Population Particle Filter for Multiple Articulated Object Tracking

where, is the dynamic model of state evolution and is the likelihood of any measurement given the state .

- (1)
initialisation: using pictorial structure type models as in [7], we localise all the targets along with the configuration of their parts,

- (2)for iterations ,
- (a)
evolve particles using

*constrained*genetic operators as in EPMCMC filter, - (b)
the expected likelihood data association provides an efficient solution for data association of each object into the particle weights of the EPMCMC filter.

- (a)

In the following sections, we describe the two steps in detail before outlining how they are integrated within the proposed framework.

### 3.1. EPMCMC Filter

The EPMCMC filter algorithm proceeds in three distinct steps. The first step involves initialising the populations of particles from their respective proposal distributions. Let , represent the population of particles for target (each particle is a configuration vector containing the position and speed of the body parts for the target) at time instant . So, during initialisation: , where is the distribution of particles around the initial localisation of different body parts of target . During initialisation, we also evaluate the initial weights of particles and normalise the weights to get .

*same*population belonging to the

*same*part of the target are combined iteratively using steps of crossover, mutation, or exchange. This approach introduces variety in particles by regenerating a unique and good population. Here, we also recalculate weights of particles in each population using a relevant likelihood metric and normalise them. An illustration of the genetic moves involved in the EPMCMC filter is presented in Figure 1.

In the sampling step, we perform global evolution of particles, that is, iteratively evolving particles from *different* populations belonging to *different* parts of the target using the steps of crossover, mutation, or exchange. However, the main difference from local evolution of particles is that in the global evolution we enforce geometrical constraints into the evolution, process. These geometrical constraints are derived from the pictorial structure model of the target and are based on the neighbourhood structure of every part of the target. When subjecting the particles to evolution using genetic operators, we allow particles of one part to be influenced by only the particles of its neighbours. For example, when performing the crossover operation, between two particles
and
, we crossover chromosomes only based on the neighbourhood relationships that parts share with each other. That is, we restrict crossovers between the arms of one particle to the legs of the other and encourage crossovers between arms of one part together with the torso of the other, as these are neighbouring regions of the elastic pictorial structure model.

In addition, we evaluate the likelihood of each particle based on how well the image data supports the proposed hypothesized candidate parts. We map this support as the weighted summation of two subsequent terms: the first one indicates the goodness of fit of the part with the image data, and the second one measures the goodness of fit of pairs of candidate parts as connected in the pictorial structure model.

The proposed EPMCMC filter is given in Algorithm 1, the population MCMC move is presented in Algorithm 2, and the details for each step of the genetic algorithm (crossover, mutation, and exchange) are given in the next subsection.

**Algorithm 1:**The proposed evolving population Markov chain Monte Carlo filter.

- (1)
Initialisation: at generate initial samples and their respective weights .

- (2)Sampling
- (i)
For .

- (ii)
For each sample .

Draw , where is the th sample at th time instant and is a known transition prior at time

instant .

- (iii)
Move the populations of samples by , using the genetic transition kernel according to

crossover, mutation or exchange steps as described below.

- (iv)
Evaluate weights from the likelihood as presented in the next subsection and normalise the weights

to obtain .

- (i)
- (3)Resampling
- (i)If , where the is measured as and is some threshold.
- (a)For iterations
- (a1)
Resample using one of the standard resampling techniques such as residual resampling.

- (a2)
Perform population MCMC based moves to samples as mentioned in Section 3.1.1.

- (a3)
Recompute the weights and normalise the weights to obtain .

- (a1)
- (b)
End

- (a)
- (ii)
Increment the time instant .

- (iii)
Iterate steps (2). and (3).

- (i)

**Algorithm 2:**Population MCMC moves.

- (1)Initialisation
- (i)
Select resampled particles from each population , where .

- (i)
- (2)
Iterate steps (2) and (3).

- (3)
- (a)
Mutation

Perform Mutation as illustrated in Section 3.1.3.

- (b)
CrossOver or Exchange Move Perform CrossOver or Exchange moves as illustrated in Section 3.1.2 or Section 3.1.4, respectively. Accept the move based on the Metropolis-Hastings rule, for example, from the probability as described in Section 3.1.4.

- (a)

#### 3.1.1. Resample Moves

In the resample move step, equally weighted particles are chosen, and population MCMC is applied. We summarise the population MCMC algorithm as shown in Algorithm 2.

#### 3.1.2. Crossver

- (i)
draw a uniform random number for every component , and if , then perform crossover,

- (ii)
(ii)estimate a crossover point based on a uniform random integer between 1 and the length of the component ,

- (iii)

where and refers to the length of the samples and , respectively.

Here, is the likelihood function for the th offspring, is the likelihood function of the th offspring and and are the weights at th time instant, for the th and th offspring, respectively.

Hence, in the case of the crossover, where there are paired particles with the same weight, we marginalise one of them and express the weights as a function of the proposal PDF of the other PDF.

#### 3.1.3. Mutation

- (i)
draw a uniform random number for every component , and if , then perform mutation,

- (ii)
(ii)estimate a mutation point based on a uniform random integer between 1 and length of the component ,

- (iii)
flip the mutation point .

where, is a uniform random number. During mutation, samples that undergo mutation are mutually independent. Therefore, the updated proposal distribution at time is a factor of the proposal distribution at the previous iteration .

#### 3.1.4. Exchange

The genetic transition kernel combines the effectiveness of samples between various populations to create more efficient groups of samples.

### 3.2. Expected Likelihood Probabilistic Data Association (ELPDA)

Since the state vector for target consists of the states for all body parts , a data association problem needs to be resolved. In our work, we adopt the expected likelihood data association method from [10]. For the set of available measurements, we assume that one of the measurements originates from the target, and the rest are due to spurious clutter. In the case of tracking the pictorial structure of the human target, colour histograms are used for matching and the corresponding measurement equation is highly nonlinear. The data association problem is considered with respect to the whole pictorial structure (the whole graph) representing the target, for example, with respect to .

We adapt the weights of particles in the move step of the EPMCMC filter specified in Section 3.1.

where is the detection probability, is the probability mass function of the number of incorrect measurements, refers to the probability that a target is detected and its measurements fall within the gate, and is the measurement error covariance matrix.

where .

## 4. Results

In this section, we perform systematic experiments evaluating (1) the accuracy of our proposed EPMCMC + ELPDA method with the EPMCMC + PDA algorithm and with a generic particle filter framework with a joint probabilistic data association (JPDA PF) proposed in [37, 38] and (2) the influence of the system parameters on the model including the geometric constraints, number of parts being tracked, the radius of the validation gate. We demonstrate our results on videos containing human targets, where the pictorial structure of the target is modeled as a graphical model of the parts of the body. The transition prior is assumed to be a constant velocity model [8] applied jointly with the pictorial structure for each target. The pictorial structure is represented as rectangles for each body part, and the state vector consists of the position and speed for the centre of each body part. To evaluate the performance of the models, we compute the *root mean square error distance* (RMSE) between the estimated center point of every part and its manually labeled counterpart. The results are presented in the form of a cumulative RMSE for all the targets in the video.

### 4.1. Multiple People Tracking

Tabular description of the chosen video clips (B2-Browse2, BWW1-BrowseWhileWhalking1, FC-Fight Chase, FR1-FightRunway1, LB-LeftBag, LBx-LeftBox, MC-MeetCrowd, MWS-MeetWalkSplit, MWT1-MeetWalkTogether1, RFF-RestFallenFloor, WBS1-Walk and ByShop1) and comparison of combined RMSE between EPMCMC + ELPDA model (Proposed), EPMCMC + PDA model (Baseline) and RMSE of *Torso alone* in generic particle filter framework (JPDA PF).

Video | Frames | Targets | Occlude | Clutter | Proposed | Baseline | JPDAPF | Time |
---|---|---|---|---|---|---|---|---|

B2 | 173 | 1 | No | 0 | 1.1821 | 2.0413 | 0.9648 | 3187 |

198 | 1 | Self | 0 | 1.6669 | 2.3425 | 1.1578 | 3276 | |

BWW1 | 361 | 1 | Self | 1 | 2.1638 | 2.6804 | 1.5673 | 3106 |

FC | 129 | 1 | No | 0 | 0.5187 | 0.9835 | 0.2784 | 3016 |

178 | 2 | Yes | 0 | 2.7861 | 4.0076 | 3.1279 | 3127 | |

FR1 | 199 | 2 | Yes | 0 | 2.7883 | 3.9801 | 1.4531 | 3229 |

LB | 201 | 3 | Self | 0 | 3.4412 | 7.6359 | 5.8763 | 3663 |

401 | 3 | Partial | 1 | 3.6567 | 8.0015 | 5.1455 | 3841 | |

208 | 1 | No | 0 | 1.4009 | 2.2156 | 1.0151 | 2923 | |

146 | 1 | Self | 0 | 1.9768 | 3.8970 | 2.1412 | 3312 | |

LBx | 373 | 2 | Partial | 0 | 2.8990 | 5.7682 | 4.2349 | 3401 |

370 | 1 | Yes | 1 | 2.5238 | 3.3532 | 2.0451 | 3198 | |

MC | 282 | 4 | Partial | 0 | 3.8982 | 6.4235 | 6.7347 | 3789 |

MWS | 301 | 2 | Partial | 1 | 2.0679 | 4.2176 | 3.9567 | 3128 |

MWT1 | 323 | 2 | Partial | 0 | 2.5003 | 3.9134 | 2.2734 | 3215 |

RFF | 388 | 1 | Self | 0 | 2.3027 | 4.5231 | 1.7235 | 3309 |

WBS1 | 876 | 5 | Yes | 0 | 3.5694 | 9.2722 | 7.0163 | 4789 |

### 4.2. Comparison of Proposed with Related Techniques

### 4.3. Effect of Changing System Parameters

### 4.4. Failure Modes

## 5. Conclusion

We have proposed an innovative method for combining extended likelihood data association with evolving population particle filtering for robust and accurate multiple target tracking. The evolving population filter introduces variety in the population of particles by combining them in both the sampling and resampling steps using constrained genetic operations. The extended likelihood data association filters those measurements that belong to the target from a clutter of other noisy measurements analysed within the validation gate. System parameters such the radius of validation gate are reestimated during each iteration, rather than fixed empirically, resulting in a model that outperforms similar recent methods on standard datasets.

## Declarations

### Acknowledgments

The authors acknowledge the support of UK MOD Data and Information Fusion Defence Technology Centre under the Tracking Cluster Project no. DIFDTC/CSIPC1/02. The authors would also like to sincerely thank Professor Simon Godsill for his useful advices and discussions on sequential population Monte Carlo methods. They acknowledge the support from the (European Community's) Seventh Framework Programme (FP7/2007–2013) under Grant no. 238710 (Monte Carlo-based Innovative Management and Processing for an Unrivalled Leap in Sensor Exploitation).

## Authors’ Affiliations

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