Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Future trends <s> Culham, Jody C., Stephan A. Brandt, Patrick Cavanagh, Nancy G. Kanwisher, Anders M. Dale, and Roger B. H. Tootell. Cortical fMRI activation produced by attentive tracking of moving targets. J. Neurophysiol. 80: 2657–2670, 1998. Attention can be used to keep track of moving items, particularly when there are multiple targets of interest that cannot all be followed with eye movements. Functional magnetic resonance imaging (fMRI) was used to investigate cortical regions involved in attentive tracking. Cortical flattening techniques facilitated within-subject comparisons of activation produced by attentive tracking, visual motion, discrete attention shifts, and eye movements. In the main task, subjects viewed a display of nine green “bouncing balls” and used attention to mentally track a subset of them while fixating. At the start of each attentive-tracking condition, several target balls (e.g., 3/9) turned red for 2 s and then reverted to green. Subjects then used attention to keep track of the previously indicated targets, which were otherwise indistinguishable from the nontargets. Attentive-tracking conditions alternated with passive viewing of the same display when no targets had been indicated. Subjects were pretested with an eye-movement monitor to ensure they could perform the task accurately while fixating. For seven subjects, functional activation was superimposed on each individual's cortically unfolded surface. Comparisons between attentive tracking and passive viewing revealed bilateral activation in parietal cortex (intraparietal sulcus, postcentral sulcus, superior parietal lobule, and precuneus), frontal cortex (frontal eye fields and precentral sulcus), and the MT complex (including motion-selective areas MT and MST). Attentional enhancement was absent in early visual areas and weak in the MT complex. However, in parietal and frontal areas, the signal change produced by the moving stimuli was more than doubled when items were tracked attentively. Comparisons between attentive tracking and attention shifting revealed essentially identical activation patterns that differed only in the magnitude of activation. This suggests that parietal cortex is involved not only in discrete shifts of attention between objects at different spatial locations but also in continuous “attentional pursuit” of moving objects. Attentive-tracking activation patterns were also similar, though not identical, to those produced by eye movements. Taken together, these results suggest that attentive tracking is mediated by a network of areas that includes parietal and frontal regions responsible for attention shifts and eye movements and the MT complex, thought to be responsible for motion perception. These results are consistent with theoretical models of attentive tracking as an attentional process that assigns spatial tags to targets and registers changes in their position, generating a high-level percept of apparent motion. <s> BIB001 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Future trends <s> Visual attention allows an observer to select certain visual information for specialized processing. Selection is readily apparent in ‘tracking’ tasks where even with the eyes fixed, observers can track a target as it moves among identical distractor items1. In such a case, a target is distinguished by its spatial trajectory. Here we show that one can keep track of a stationary item solely on the basis of its changing appearance—specified by its trajectory along colour, orientation, and spatial frequency dimensions—even when a distractor shares the same spatial location. This ability to track through feature space bears directly on competing theories of attention, that is, on whether attention can select locations in space2,3,4, features such as colour or shape5,6,7, or particular visual objects composed of constellations of visual features. Our results affirm, consistent with a growing body of psychophysical8,9,10,11,12,13 and neurophysiological14,15,16 evidence, that attention can indeed select specific visual objects. Furthermore, feature-space tracking extends the definition of visual object17 to include not only items with well defined spatio-temporal trajectories18, but also those with well defined featuro-temporal trajectories. <s> BIB002 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Future trends <s> In recent years particle filters have been applied to a variety of state estimation problems. A particle filter is a sequential Monte Carlo Bayesian estimator of the posterior density of the state using weighted particles. The efficiency and accuracy of the filter depend mostly on the number of particles used in the estimation and on the propagation function used to re-allocate weights to these particles at each iteration. If the imprecision, i.e. bias and noise, in the available information is high, the number of particles needs to be very large in order to obtain good performances. This may give rise to complexity problems for a real-time implementation. This kind of imprecision can easily be represented by interval data if the maximum error is known. Handling interval data is a new approach successfully applied to different real applications. In this paper, we propose an extension of the particle filter algorithm able to handle interval data and using interval analysis and constraint satisfaction techniques. In standard particle filtering, particles are punctual states associated with weights whose likelihoods are defined by a statistical model of the observation error. In the box particle filter, particles are boxes associated with weights whose likelihood is defined by a bounded model of the observation error. Experiments using actual data for global localization of a vehicle show the usefulness and the efficiency of the proposed approach. <s> BIB003 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Future trends <s> We present a novel framework for identifying and tracking dominant agents in groups. Our proposed approach relies on a causality detection scheme that is capable of ranking agents with respect to their contribution in shaping the system's collective behaviour based exclusively on the agents' observed trajectories. Further, the reasoning paradigm is made robust to multiple emissions and clutter by employing a class of recently introduced Markov chain Monte Carlo-based group tracking methods. Examples are provided that demonstrate the strong potential of the proposed scheme in identifying actual leaders in swarms of interacting agents and moving crowds. <s> BIB004 </s> Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking <s> Future trends <s> This work presents sequential Bayesian detection and estimation methods for nonlinear dynamic stochastic systems using measurements affected by three sources of uncertainty: stochastic, set-theoretic and data association uncertainty. Following Mahler's framework for information fusion, the paper develops the optimal Bayes filter for this problem in the form of the Bernoulli filter for interval measurements. Two numerical implementations of the optimal filter are developed. The first is the Bernoulli particle filter (PF), which turns out to require a large number of particles in order to achieve a satisfactory performance. For the sake of reduction in the number of particles, the paper also develops an implementation based on box particles, referred to as the Bernoulli Box-PF. A box particle is a random sample that occupies a small and controllable rectangular region of nonzero volume in the target state space. Manipulation of boxes utilizes the methods of interval analysis. The two implementations are compared numerically and found to perform remarkably well: the target is reliably detected and the posterior probability density function of the target state is estimated accurately. The Bernoulli Box-PF, however, when designed carefully, is computationally more efficient. <s> BIB005
We consider five potential future avenues which are based on synthesizing results from different fields: • A promising avenue is the combination of SMC methods with compressed sensing   and sparse representations  for online group and extended object tracking, with sensor scheduling and model determination. Models for objects with and without interactions can lead to different proposal distributions in the SMC and MCMC methods. These can be combined with the sparse data representation and bring novel techniques. • Interval particle filtering and extensions to high dimensions: The recently emerged box particle filtering approach BIB003 BIB005   relies on the concept of a box particle, which occupies a small and controllable rectangular region having a non-zero volume in the state space. Key advantages of the box particle filter (Box-PF) against the standard PF are in its reduced computational complexity and its suitability for solving high dimensional problems such as those emerging in tracking of groups of hundreds of targets. The Box-PF has a potential to solve group and extended object tracking problems with reduced computational complexity. • Selective/attentive tracking and perception: Future tracking systems would have to cope with possibly a large number of moving objects, each of which is prone to produce more than a single measurement. The raw data from the scene would potentially be acquired simultaneously from many sensors. This amounts to massive data sets that would have to be processed efficiently. One direction for alleviating this problem relies on selective attention -a concept from neuropsychology and cognitive sciences BIB002 . Selective attention has long been studied in psychological research BIB001 and cognitive sciences BIB002 . This refers to the ability of a human observer to selectively track a specific visual information in puzzling scenarios. Selective attention comes into being via the identification of myriad traits, many of which are abstract and are extracted as part of cognitive and perceptual processes. Such particularities account for behavioral characteristics, motion as well as other visual and spatial features (e.g., color, shape deformations, trajectories). The application of selective attention to tracking of information (not necessarily visual) is referred to as selective or attentive tracking BIB001 . SMC and MCMC methods have the potential of handling severe nonlinearities and complex dynamic network structures, which make them adequate for carrying out inference in selective tracking paradigms. In a recent study it has been shown how an MCMC-based scheme is capable of identifying and tracking dominant agents in highly complex scenarios involving many moving objects BIB004 . Causal networks can model interrelations between moving agents and then be used for identifying those agents which are prominent in shaping the collective group behavior. This information can be further used for selectively track only a small, however dominant, part of the object population. SMC samplers  could also provide better proposal distributions, especially between the interacting objects of groups. • Intentionality prediction: Having the perceptual capabilities described above allows predicting the intentionality of either individual entities or the whole group. • Joint decision making and tracking: Traditional inference schemes decouple these two tasks, namely, decision making and tracking. A performance gain is expected by integrating decision variables into tracking systems. Here one can consider integrated Bayesian decision making on the identity of the objects being tracked, including cost functions expressing the relative importance of different error types.