Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> The paper presents an analysis of a nonlinear filtering problem corresponding to tracking of an extended target whose shape is modelled by an ellipse. The measurements of target extent are assumed to be available in addition to the usual positional measurements. Using Cramer-Rao bounds we establish the best achievable error performance for this highly nonlinear problem. The theoretical bounds are used to examine the performance as a function of measurement accuracy, observer-target geometry and prior knowledge of shape parameters. Finally an extended Kalman filter (KF) and an unscented KF are developed for this application and their performance (consistency and RMS error) are examined. <s> BIB001 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> Abstract In order to gain a detailed understanding of cell signalling and regulation processes, live cell imaging is often used. Such signalling can involve the nuclear-cytoplasmic translocation of signalling molecules, and to follow this, it is necessary to mark the cell and nuclear boundaries in an image sequence in individual cells. For complex processes, with both rapid cell motion and nuclear translocation, it is extremely time-consuming to mark such cell boundaries manually. The particle filter (PF) is a Monte Carlo method based on sequential importance sampling. It is robust to clutter and the occlusion of targets in object tracking. The active contour (AC) method is based on a deformable model and is capable of capturing minor cell shape variations, although a good initialisation is often required. Prior information from a particle filter provides a reasonable initialisation for the active contour method and prevents it from being trapped in local minima. Combining these two methods (PF-AC) thus makes it possible to track complex cellular processes automatically. The combined method is used to study the important NF-κB signalling pathway. Comparable results to those obtained manually by a biologist are obtained using the hyphenated approach, but in a small fraction of the time. <s> BIB002 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> This correspondence addresses the problem of tracking extended objects, such as ships or a convoy of vehicles moving in urban environment. Two Monte Carlo techniques for extended object tracking are proposed: an interacting multiple model data augmentation (IMM-DA) algorithm and a modified version of the mixture Kalman filter (MKF) of Chen and Liu , called the mixture Kalman filter modified (MKFm). The data augmentation (DA) technique with finite mixtures estimates the object extent parameters, whereas an interacting multiple model (IMM) filter estimates the kinematic states (position and speed) of the manoeuvring object. Next, the system model is formulated in a partially conditional dynamic linear (PCDL) form. This affords us to propose two latent indicator variables characterizing, respectively, the motion mode and object size. Then, an MKFm is developed with the PCDL model. The IMM-DA and the MKFm performance is compared with a combined IMM-particle filter (IMM-PF) algorithm with respect to accuracy and computational complexity. The most accurate parameter estimates are obtained by the DA algorithm, followed by the MKFm and PF. <s> BIB003 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> In algorithms for tracking and sensor data fusion the targets to be observed are usually considered as point source objects; i.e., compared with the sensor resolution their extension is neglected. Due to the increasing resolution capabilities of modern sensors, however, this assumption is often no longer valid as different scattering centers of an object can cause distinct detections when passing the signal processing chain. Examples of extended targets are found in short-range applications (littoral surveillance, autonomous weapons, or robotics). A collectively moving target group can also be considered as an extended target. This point of view is the more appropriate, the smaller the mutual distances between the individual targets are. Due to the resulting data association and resolution conflicts any attempt of tracking the individual objects within the group seems to be no longer reasonable. With simulated sensor data produced by a partly unresolvable aircraft formation the addressed phenomena are illustrated and an approximate Bayesian solution to the resulting tracking problem is proposed. Ellipsoidal object extensions are modeled by random matrices, which are treated as additional state variables to be estimated or tracked. We expect that the resulting tracking algorithms are also relevant for tracking large, collectively moving target swarms. <s> BIB004 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> Contour tracking for a single source emission is addressed in this paper. This problem is solved by estimating the contour boundary positions using a set of particle filters. The use of Sequential Monte Carlo techniques enables the tracking to performed when the measurements are noisy and the tracking results also includes the estimation uncertainly. The proposed technique is illustrated for a SCIPUFF generated single emission scenario and simulation experiments showed the successful tracking throughout the tracking period. <s> BIB005 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Due to limited sensor resolution capabilities, group targets (i. e., a number of closely spaced targets moving in a coordinated fashion) may show a similar detection pattern as extended objects, namely a varying number of detections whose spread is determined by both the statistical sensor errors as well as the physical extension of the group or extended object. Different tracking approaches treating these situations have been proposed where physical extension is represented by a random symmetric positive definite matrix. This paper discusses some results that should give deeper insight into behavior and performance analysis of these approaches. Further improvements are presented. <s> BIB006 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> With the wide application of Green Fluorescent Proteins (GFP) in the study of live cells, there is a surging need for computer-aided analysis on the huge amount of image sequence data acquired by the advanced microscopy devices. In this paper, a framework based on Sequential Monte Carlo (SMC) is proposed for multiple interacting object tracking. The distribution of the dimension varying joint state is sampled efficiently by a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm with a novel height swap move. Experimental results were performed on synthetic and real confocal microscopy image sequences. <s> BIB007 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> In this paper, we present a fully automatic approach to multiple human detection and tracking in high density crowds in the presence of extreme occlusion. Human detection and tracking in high density crowds is an unsolved problem. Standard preprocessing techniques such as background modeling fail when most of the scene is in motion. We integrate human detection and tracking into a single framework, and introduce a confirmation-by-classification method to estimate confidence in a tracked trajectory, track humans through occlusions, and eliminate false positive detections. We use a Viola and Jones AdaBoost cascade classifier for detection, a particle filter for tracking, and color histograms for appearance modeling. An experimental evaluation shows that our approach is capable of tracking humans in high density crowds despite occlusions. <s> BIB008 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> In this paper, a novel approach for tracking extended objects is presented. The target object is modeled as a circular disc such that the center and extent of the target object can be estimated. At each time step, a finite set of position measurements that are corrupted with stochastic noise may be available. Each position measurement stems from an unknown measurement source on the extended object. In contrast to existing approaches, no statistical assumptions about the distribution of the measurement sources on the extended object are made. As a consequence, it is necessary to deal with stochastic and set-valued uncertainties. For this purpose, a novel combined stochastic and set-theoretic estimator that employs random hyperboloids to express the uncertainties about the true circular disc is derived. <s> BIB009 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> In many tracking applications, the extent of the target object is neglected and it is assumed that the received measurements stem from a point source. However, modern sensors are able to supply several measurements from different scattering centers on the target object due to their high-resolution capability. As a consequence, it becomes necessary to incorporate the target extent into the estimation procedure. This paper introduces a new method for tracking the smallest enclosing rectangle of an extended object with an unknown shape. At each time step, a finite set of noisy position measurements that stem from arbitrary, unknown measurement sources on the target surface may be available. In contrast to common approaches, the presented approach does not have to make any statistical assumptions on the measurement sources. <s> BIB010 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> In this paper, we address the problem of detection and tracking of multiple contaminant clouds. We develop a stochastic extension of the Gaussian puff model to characterize evolution of the average atmospheric pollutant concentration. To perform the sequential inference on this difficult problem, we propose a Markov Chain Monte Carlo (MCMC)-based Particle algorithm. Numerical simulations illustrate the ability of the algorithm to detect and track multiple contaminant clouds. <s> BIB011 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> In extended target tracking, targets potentially produce more than one measurement per time step. Multiple extended targets are therefore usually hard to track, due to the resulting complex data association. The main contribution of this paper is the implementation of a Probability Hypothesis Density (PHD) filter for tracking of multiple extended targets. A general modification of the PHD filter to handle extended targets has been presented recently by Mahler, and the novelty in this work lies in the realisation of a Gaussian mixture PHD filter for extended targets. Furthermore, we propose a method to easily partition the measurements into a number of subsets, each of which is supposed to contain measurements that all stem from the same source. The method is illustrated in simulation examples, and the advantage of the implemented extended target PHD filter is shown in a comparison with a standard PHD filter. <s> BIB012 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> Poisson point processes (PPP's) are very useful theoretical models for diverse applications. One of those is multi-target tracking of an unknown number of targets, leading to the intensity filter (iFilter) as a generalization of the probability hypothesis density (PHD) filter. This article develops a sequential Monte Carlo (SMC) implementation of the iFilter. In theory it was shown that the iFilter can estimate a clutter model from the measurements and thus does not need it as a-priori knowledge, like the PHD filter does. Our studies show that this property holds not only in simulations but also in real world applications. In addition it can be shown, that the performance of the PHD filter decreases substantially if the a-priori knowledge of the clutter intensity is chosen incorrectly. <s> BIB013 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> Tracking algorithms are traditionally based on either a variational approach or a Bayesian one. In the variational case, a cost function is established between two consecutive frames and minimized by standard optimization algorithms. In the Bayesian case, a stochastic motion model is used to maintain temporal consistency. Among the Bayesian methods we focus on the particle filter, which is especially suited for handling multimodal distributions. In this paper, we present a novel approach to fuse both methodologies in a single tracker where the importance sampling of the particle filter is given implicitly by the optimization algorithm of the variational method. Our technique is capable of outlying nuclei and tracking the lineage of biological cells using different motion models for mitotic and non-mitotic stages of the life of a cell. We validate its ability to track the lineage of HeLa cells in fluorescence microscopy. <s> BIB014 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> Summary This paper describes a novel software algorithm, called constrained Sequential Monte Carlo (SMC) clusters, for tracking a large collection of individual cells from intra-vital two-photon microscopy image sequences. We show how our method and software tool, implemented in python, is useful for quantifying the motility of T and B lymphocytes involved in an immune response vs lymphocytes under non immune conditions. We describe the theory behind our algorithm and briefly discuss the architecture of our software. Finally, we demonstrate both the functionality and utility of software by applying it to two practical examples from videos displaying lymphocyte motility in B cell zones (follicles) and T cell zones of lymph nodes. <s> BIB015 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> Multiple object tracking (MOT) is a very challenging task yet of fundamental importance for many practical applications. In this paper, we focus on the problem of tracking multiple players in sports video which is even more difficult due to the abrupt movements of players and their complex interactions. To handle the difficulties in this problem, we present a new MOT algorithm which contributes both in the observation modeling level and in the tracking strategy level. For the observation modeling, we develop a progressive observation modeling process that is able to provide strong tracking observations and greatly facilitate the tracking task. For the tracking strategy, we propose a dual-mode two-way Bayesian inference approach which dynamically switches between an offline general model and an online dedicated model to deal with single isolated object tracking and multiple occluded object tracking integrally by forward filtering and backward smoothing. Extensive experiments on different kinds of sports videos, including football, basketball, as well as hockey, demonstrate the effectiveness and efficiency of the proposed method. <s> BIB016 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> Extended objects are characterised with multiple measurements originated from ifferent locations of the object surface. This paper presents a novel Sequential Monte Carlo (SMC) approach for extended object tracking in the presence of clutter. The problem is formulated for general nonlinear problems. The main contribution of this work is in the derivation of the likelihood function for nonlinear measurement functions, with sets of measurements belonging to a bounded region. Simulation results are presented when the object is surrounded by a circular region. Accurate estimation results are presented both for the object kinematic state and object extent. <s> BIB017 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> This paper proposes a technique for motion estimation of groups of targets based on evolving graph networks. The main novelty over alternative group tracking techniques stems from learning the network structure for the groups. Each node of the graph corresponds to a target within the group. The uncertainty of the group structure is estimated jointly with the group target states. New group structure evolving models are proposed for automatic graph structure initialization, incorporation of new nodes, unexisting nodes removal, and the edge update. Both the state and the graph structure are updated based on range and bearing measurements. This evolving graph model is propagated combined with a sequential Monte Carlo framework able to cope with measurement origin uncertainty. The effectiveness of the proposed approach is illustrated over scenarios for group motion estimation in urban environments. Results with challenging scenarios with merging, splitting, and crossing of groups are presented with high estimation accuracy. The performance of the algorithm is also evaluated and shown on real ground moving target indicator (GMTI) radar data and in the presence of data origin uncertainty. <s> BIB018 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s>  <s> This paper is about tracking an extended object or a group target, which gives rise to a varying number of measurements from different measurement sources. For this purpose, the shape of the target is tracked in addition to its kinematics. The target extent is modeled with a new approach called Random Hypersurface Model (RHM) that assumes varying measurement sources to lie on scaled versions of the shape boundaries. In this paper, a star-convex RHM is introduced for tracking star-convex shape approximations of targets. Bayesian inference for star-convex RHMs is performed by means of a Gaussian-assumed state estimator allowing for an efficient recursive closed-form measurement update. Simulations demonstrate the performance of this approach for typical extended object and group tracking scenarios. <s> BIB019
In recent years there has been an increasing interest in tracking a number of objects moving in a coordinated and interacting fashion. There are many fields in which such situations are frequently encountered: video surveillance, sport events, biomedicine, neuroscience, meteorology, situation awareness and search rescue operations, to mention but a few. Although individual objects in the group can exhibit independent movement at a certain level, overall the group moves as one whole, synchronously with respect to the individual entities and avoiding collisions. Terminology. Groups are structured objects, formations of entities moving in a coordinated manner, whose number varies over time because targets can enter a scene, or disappear at random times. The groups can split, merge, can be relatively near to each other or move independently of each other. What is typical for group formations is that they maintain certain patterns of motion. Some typical examples are: formations of aircrafts and ships, respectively, for air traffic control, sea, harbor or land surveillance BIB006 BIB013 , flocks of bird migration trajectories for ecological purposes, tracking groups of cells BIB014 BIB015 BIB007 BIB002 (for in vitro purposes, stem cells, cardiovascular treatment and other medical diagnostics), a group of robots (for industrial tasks), a group of football players BIB016 in sport videos, convoys of vehicles and groups of pedestrians for traffic management BIB008 . Within this broad range of problems, one can distinguish two main classes: (1) tracking of multiple groups with only a few components per group, which is called small groups tracking, and (2) groups with a relatively large number of constituents whose individual members cannot be easily distinguished, termed large groups. Large groups are also often referred as to crowds or clusters. A related but distinct is the problem of tracking extended objects, such as a cyclist and maritime vessels BIB003 . Extended objects cannot be considered as points but instead have a spatial extent characterizing their size or volume BIB004 . They are usually modeled with simple geometrical shapes which are typically circles BIB017 , ellipses BIB001 , rectangles BIB009 BIB010 BIB018  BIB012 , closed contours or arbitrary shapes such as star-convex contours BIB019 . Other examples are tracking a cloud BIB005 BIB011 of radio-active materials and a human face or hand in video  . Human body limb tracking is also often referred to extended target tracking. Challenges and differences. The challenges in solving the task for groups with a small number of components differ from those of groups with a large number of components. In small groups it is possible to model the interactions and interrelationships between the components within a group. The difficulties with groups of hundreds or thousands of objects (such as pedestrians and riots in video surveillance and radar based tracking of hundreds of aircraft) are mainly due to two reasons: (1) the individual objects cannot be distinguished/identified within the group, (2) the information and features extracted by the sensors are not sufficient to track those objects. Hence, one considers the aggregated motion of the whole group. In small groups one can estimate the states of each particular object and parameters characterizing the size or volume of the group. In large groups by contrast, one typically considers the group as a geometric shape and its centre coordinates. Similarities. Both groups of objects and extended objects give rise to a large, varying number of measurements and require a flexible framework able to deal with all these challenges. Although the methods for solving these two kinds of problems vary, there is a common approach in which both extended and large group of targets are seen as the same problem. The large group or extended object is surrounded with a shape (e.g. a circle) and the center and extent of this shape are sequentially computed based on the incoming data. Consequently, in this paper, the choice is made to classify the existing works in the literature into methods dealing with small groups and method dealing with large groups and for extended objects. This classification of extended/group objects is according to whether: (1) the group/extended object is rigid and unchanging in shape/size, (2) whether individual entities can be tracked dynamically and interact with one another. Examples of non-rigid extended objects are radioactive clouds. They can be spawn and also disappear. The group tracking and non-rigid extended object tracking lead to dynamic state and varying parameter estimation. Rigid extended targets such as submarines, ships, have fixed shapes and fixed size. This leads to dynamic state and static parameter estimation.