Since the introduction of particle filtering for object tracking, a lot of improvements have been suggested. However, the definition of the observation likelihood.
Influence of The Observation Likelihood Function on Particle Filtering Performance in Tracking Applications Jeroen Lichtenauer, Marcel Reinders, Emile Hendriks Information and Communication Theory Group, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands {J.F.Lichtenauer, M.J.T.Reinders, E.A.Hendriks}@EWI.TUDelft.nl
Abstract Since the introduction of particle filtering for object tracking, a lot of improvements have been suggested. However, the definition of the observation likelihood function, needed for determining the particle weights, has received little attention. Because particle weights determine how the particles are re-sampled, the likelihood function has a strong influence on the tracking performance. We show experimental results for three different tracking tasks for different parameter values of the assumed observation model. The results show a large influence of the model parameters on the tracking performance. Optimizing the likelihood function can give significant tracking improvement. Different optimal parameter settings are observed for the three different tracking tasks. Consequently, when performing multiple tasks a tradeoff must be made for the parameter setting. In practical situations where robust tracking must be achieved with a limited amount of particles, the true observation probability is not always the optimal likelihood function.
1. Introduction Visual object tracking has a very broad area of applications. It can be used for instance in automated surveillance or gesture recognition systems. In these applications speed is often a very important factor. Recently, the rapid increase of computer power has facilitated more practical use of particle filtering, also known as sequential importance (re-)sampling (SIS/SIR) or sequential Monte Carlo (SMC) methods [1,2,3,4]. These methods produce much better tracking performance than, previously often used, Kalman filtering.
In SIR, a weighted set of hypothesized samples of the possible object state, called ‘particles’, are tracked simultaneously. At time t this set consists of N object states xt(1),…,xt(N) and their associated weights ʌt(1),…, ʌt(N). The particle set is a discrete approximation of the posterior distribution of the real object state given the observations up to time t: p(xt|z0:t). At the next time step, the particles are re-sampled according to their weights. This is to decrease the number of lowweighted particles and to increase the ones with more ‘potential’. For SIR to be successful a large number of samples N is needed for two reasons: 1) to get a good approximation of p(xt|z0:t) and 2) to be able to recover from object loss and to find multiple instances if more than one object is visible. However, the size of N has a direct relation with the computational cost and should be kept as low as possible. To increase the efficiency of particle filtering for small N, many improvements have been suggested. For instance, hierarchical methods [5,6] where a course to fine approach is used to find the real mode(s) of the object(s) without getting stuck in local optima. Other methods involve more sophisticated re-sampling and/or prediction [7,8]. However, not much research has been performed on improving the observation model, or likelihood function p(z|x), which is necessary to calculate the particle weights from the observed image. Often no details are given on how the observation model of a particle filtering algorithm is determined. In [9] an optimization method is proposed that is used to optimize the likelihood function with respect to the effective sample size (ESS) and the mean square error (MSE) of the estimated object state. In [10] the observation model parameters are estimated from observations by simplified approximate maximum likelihood (AML) estimation, which is explained in [11].
Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition (FGR’04) 0-7695-2122-3/04 $ 20.00 © 2004 IEEE
The likelihood function determines the re-sampling behavior of the particle filter algorithm and is expected to have influence on the tracking performance. Therefore, in this paper, we present experimental results providing more insight into the influence of the likelihood function on the tracking performance. We distinguish between three tracking tasks: 1) the ability to track a single object moving unpredictably, 2) the ability to track multiple objects simultaneously, and 3) the ability to retrieve the object after tracking loss. We do not regard tracking precision because in visual tracking it is often more important not to lose the object than to have a precise state estimate. For this evaluation we use the CONDENSATION algorithm [3] because it is widely used for comparison and its performance is primarily based on efficient resampling. In the supplementary information [12] we have additional information about the experimental setup as well as additional experiments.
2. Observation model The observation model that we assume here is given by: § [α ]2 · ¸ , ε
