Visual Tracking by Continuous Density Propagation in Sequential Bayesian Filtering Framework

Particle filter (PF) is a method dedicated to posterior density estimations using weighted samples whose elements are called particles. In particular, this approach can be applied to object tracking in video sequences in complex situations and, in this paper, we focus on articulated object tracking, i.e., objects that can be decomposed as a set of subparts. One of PF's crucial step is a resampling step in which particles are resampled to avoid degeneracy problems. In this paper, we propose to exploit mathematical properties of articulated objects to swap conditionally independent subparts of the particles in order to generate new particle sets. We then introduce a new resampling method called Combinatorial Resampling that resamples over the particle set resulting from all the "admissible" swappings, the so-called combinatorial set. In essence, combinatorial resampling (CR) is quite similar to the combination of a crossover operator and a usual resampling, but there exists a fundamental difference between CR and the use of crossover operators: we prove that CR is sound, i.e., in a Bayesian framework, it is guaranteed to represent without any bias the posterior densities of the states over time. By construction, the particle sets produced by CR better represent the density to estimate over the whole state space than the original set and, therefore, CR produces higher quality samples. Unfortunately, the combinatorial set is generally of an exponential size and, therefore, to be scalable, we show how it can be implicitly constructed and resampled from, thus resulting in both an efficient and effective resampling scheme. Finally, through experimentations both on challenging synthetic and real video sequences, we also show that our resampling method outperforms all classical resampling methods both in terms of the quality of its results and in terms of computation times.

The particle filter has attracted considerable attention in visual tracking due to its relaxation of the linear and Gaussian restrictions in the state space model. It is thus more flexible than the Kalman filter. However, the conventional particle filter uses system transition as the proposal distribution, leading to poor sampling efficiency and poor performance in visual tracking. It is not a trivial task to design satisfactory proposal distributions for the particle filter. In this paper, we introduce an improved particle filtering framework into visual tracking, which combines the unscented Kalman filter and the auxiliary particle filter. The efficient unscented auxiliary particle filter (UAPF) uses the unscented transformation to predict one-step ahead likelihood and produces more reasonable proposal distributions, thus reducing the number of particles required and substantially improving the tracking performance. Experiments on real video sequences demonstrate that the UAPF is computationally efficient and outperforms the conventional particle filter and the auxiliary particle filter.KeywordsParticle FilterImportance SamplingObservation ModelVisual TrackingUnscented Kalman FilterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Particle filtering, also known as Sequential Monte Carlo methods (SMC), is a sophisticated model estimation techniques based on simulation. Particle filtering has important applications in location, tracking and other fields. It indicates probability using particle set and can be used in any space-state model. Its core idea is to extract a random state from the posterior probability express the distribution. In general, particle filtering is a process which uses a set of stochastic sample propagating in space-state to approximate probability density function and to replace integral operation with mean value of a sample to obtain minimum state variance distribution. It solves the restriction that nonlinear filtering should match Gaussian distribution, expresses a wider range of distribution than Gaussian distribution and has a strong ability to model the nonlinear characteristic of variance parameter. This paper introduces the application of particle filtering in visual tracking. Finally, it puts forward some improved algorithms to revise the inherent deficiencies existing in particle filtering.

For state estimation problem, particle filter is generally used to construct the posterior probability density function by a set of particles, which is regarded as a solution to state estimation. Many techniques have been developed to improve performance of particle filter, at the cost of largely increased computational burden for each particle. In this paper, we propose a post-resampling based particle filter. The modified particle filter is capable of accurately representing the posterior probability density function through properly sampling particles. We applied the proposed particle filter to the classic bearings-only tracking problem. Simulation results showed that our modified particle filter had superior performance and reasonably computational cost, compared with the general approaches. It may provide a promising alternative to the existent particle filters.

Firefly algorithm (FA) based particle filter method for visual tracking

Particle filters perform the nonlinear estimation and have been proven to be a powerful tool in solving visual tracking problems. However, the problem of sample impoverishment is still a drawback of particle filter. To solve this problem, a bat-inspired particle filter is proposed in this work. The particles in the particle filter are optimized using a new biologically inspired optimization algorithm, namely bat algorithm before re-sampling. The meaningful particles are increased and they can approximate the true state of the target more accurately. Experiments on visual tracking show that the proposed algorithm outperforms the standard particle filter and it can track targets accurately and robustly in various challenging conditions.

Appearance change of moving targets is a challenging problem in visual tracking. In this paper, we present a novel visual object tracking algorithm based on the observation dependent hidden Markov model (OD-HMM) framework. The observation dependency is computed by structure complexity coefficients (SCC) which is defined to predict the target appearance change. Unlike conventional methods addressing the appearance change problem by investigating different online appearance models, we handle this problem by addressing the fundamental reason of motion -related appearance change during visual tracking. Based on the analysis of motion-related appearance change, we investigate the relationship between the structure of the object surface and the appearance stability. The appearance of complex structural regions is easier to change compared with that of smooth structural regions with object moving. Based on this, we define SCC to predict the appearance stability of moving objects. Different from the standard HMM-based tracking algorithms where observations between different frames are assumed to be independent, we consider the observation dependency between consecutive frames with the information provided by SCC. Moreover , we present a novel outlier removing method in appearance model updating which helps to avoid error accumulation. Experimental results on challenging video sequences demonstrate that the proposed visual tracking algorithm with OD-HMM and SCC achieves better performance than existing related tracking algorithms.

In recent years, particle filters have emerged as a useful tool that enables the application of Bayesian reasoning to problems requiring dynamic state estimation. The efficiency and accuracy of these type of filters are highly dependent on an appropriate propagation of the particles in time. In this paper we present a new method to improve the propagation step of the regular particle filter. Using results from the theory of importance sampling, our method adaptively propagates the set of samples without adding a significant computational load to the normal operation of the filter. Compared to existing techniques, our approach introduces two important enhancements: 1) An adaptive method to improve the propagation function, 2) A mechanism to identify when the use of adaptation is beneficial. We show the advantages of our method by applying the resulting filter to the visual tracking of targets in a real video sequence.

One of the main difficulties in visual tracking is to take into account appearance changes (not only of the target but also of or due to the scene, illumination for example). The use of a Bayesian framework is very flexible and has proven to be very efficient in visual tracking. Moreover, color or greylevel histograms allow to track an objet with a low computational cost. The recently proposed color-based trackers integrated in a probabilistic framework are efficient for a given application (face tracking for example) but can not be generalized easily, due to the initialization and the adjustment of the different tracker parameters that are dependent on the input sequence. This paper presents a method based on color integrated in a particle filter that allows to cope with some of the usual problems of visual tracking (occlusions, target appearance changes, changes in resolution or in illumination) and to adapt easily to different applications (tracking of structures in aerial imagery as well as football players). The novelty of the tracker is its ability to automatically regulate all the parameters needed for tracking, which makes it flexible and easily usable for different applications.

We present a scheme for vehicle detection and tracking in video. The proposed method effectively combines statistical knowledge about the class of vehicles with motion information. The unknown distribution of the image patterns of vehicles is approximately modeled using higher-order statistical information derived from sample images. Statistical information about the background is learnt the fly. A motion detector identifies regions of activity. The classifier uses a higher-order statistical closeness measure to determine which of the objects actually correspond to moving vehicles. The tracking module uses position co-ordinates and difference measurement values for correspondence. Results on real video sequences are given.

Parameter estimation of time-varying non-Gaussian autoregressive processes can be a highly nonlinear problem. The problem gets even more difficult if the functional form of the time variation of the process parameters is unknown. In this paper, we address parameter estimation of such processes by particle filtering, where posterior densities are approximated by sets of samples (particles) and particle weights. These sets are updated as new measurements become available using the principle of sequential importance sampling. From the samples and their weights we can compute a wide variety of estimates of the unknowns. In absence of exact modeling of the time variation of the process parameters, we exploit the concept of forgetting factors so that recent measurements affect current estimates more than older measurements. We investigate the performance of the proposed approach on autoregressive processes whose parameters change abruptly at unknown instants and with driving noises, which are Gaussian mixtures or Laplacian processes.

Intelligent Trigonometric Particle Filter for visual tracking

The interacting multiple model (IMM) algorithm is a widely accepted state estimation scheme for solving maneuvering target tracking problems, which are generally nonlinear. During the IMM filtering process, serious errors can arise when a Gaussian mixture of posterior probability density functions is approximated by a single Gaussian. Particle filters (PFs) are effective in dealing with nonlinearity and non-Gaussianity. This work considers an IMM algorithm that includes a constant velocity model, a constant acceleration model and a 3D turning rate (3DTR) model for tracking three-dimensional (3D) target motion, using various combinations of nonlinear filters. In existing literature on combining IMM and particle filtering techniques to tackle difficult target maneuvers, a PF is usually used in every model In comparison, simulation results show that by using a computationally economical PF in the 3DTR model and Kalman filters in the remaining models, superior performance can be achieved with significant reduction in computational costs.

Residual and stratified branching particle filters

It is essential to update the model with reflecting observation or inspection data for reliability estimation of existing structures. Authors proposed updated reliability analysis by using Particle Filter. We discuss how to apply the proposed method through numerical examples on reinforced concrete structures after verification of the method with hypothetical linear Gaussian problem. Reinforced concrete structures in a marine environment deteriorate with time due to chloride-induced corrosion of reinforcing bars. In the case of existing structures, it is essential to monitor the current condition such as chloride-induced corrosion and to reflect it to rational maintenance with consideration of the uncertainty. In this context, updated reliability estimation of a structure provides useful information for the rational decision. Accuracy estimation is also one of the important issues when Monte Carlo approach such as Particle Filter is adopted. Especially Particle Filter approach has a problem known as degeneracy. Effective sample size is introduced to predict the covariance of variance of limit state exceeding probabilities calculated by Particle Filter. Its validity is shown by the numerical experiments.