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Multiple Trajectory Tracking - Scholarpedia

Multiple Trajectory Tracking

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Srimant Tripathy and Christina J. Howard (2012), Scholarpedia, 7(4):11287. doi:10.4249/scholarpedia.11287 revision #124467 [link to/cite this article]
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Curator: Srimant Tripathy

Multiple Trajectory Tracking (MTT) refers to the human ability to report the properties of the trajectories of moving objects when observers are required to monitor several objects that are in motion at the same time. Performing well in the MTT task requires monitoring the current status of the moving objects as well as their previous history and involves attention and memory.


The General Problem of Tracking

In a game of football the players have to keep track of their teammates, opponents and the ball at the same time. The fact that humans are capable of playing this game well (among others) indicates that the human visual system possesses the ability to track several objects simultaneously. This ability to track multiple moving items has been the focus of much recent research.

Tracking, for purposes of this review, refers to the ability of humans to monitor properties of moving objects. Multiple object tracking refers to the task of monitoring properties of several moving objects at the same time. This ability to track multiple items simultaneously was first demonstrated by Pylyshyn and Storm (1988) using the paradigm called Multiple Object Tracking (MOT). Since this original paper a number of studies have used this paradigm to replicate and extend the original finding (e.g. Pylyshyn, 1989, 2000, 2001; Scholl, Pylyshyn & Feldman, 2001). In addition, several newer paradigms have been introduced to investigate the human ability to track multiple moving items. These include:

  • Multiple Identity Tracking (MIT – Oksama & Hyona, 2004, 2008),
  • Multiple Object Permanence Tracking (MOPT – Saiki, 2003a, 2003b) and
  • Multiple Trajectory Tracking (MTT – Shooner, Tripathy, Bedell & Öğmen, 2010)

Each of the above paradigms addresses the general problem of tracking properties of multiple moving objects. To distinguish the general problem of tracking addressed by the above paradigms from MOT, the specific paradigm of tracking introduced by Pylyshyn & Storm (1988), we refer to the General Multiple Object Tracking problem as GMOT. While the different studies of tracking have attempted to explain results obtained with individual tracking paradigms, a coherent effort that integrates the results across the different paradigms and thus addresses the problem of GMOT has been lacking. This review investigates the contribution of one paradigm, MTT, to the GMOT problem.

The Multiple Trajectory Tracking Paradigm

Figure 1: Schematic of typical MTT stimuli, with one trajectory deviating (left panel) and three trajectories deviating (right panel). The dotted lines represent trajectories of moving dots. Adapted from Tripathy & Barrett, 2004, Figures 4a and 5a, with permission from ARVO.

The term Multiple Trajectory Tracking (MTT) was introduced by Shooner et al. (2010). The paradigm itself was introduced earlier, briefly in Tripathy and Barrett (2003) and in a more elaborate form by Tripathy and Barrett (2004). The basic paradigm is illustrated in Figure 1.

The stimulus consists of a small number of dots moving left-to-right along random orientations following linear trajectories. All the dots reach the vertical midline of the screen (indicated by the vertical markers in Figure 1) at the same instant, exactly halfway through the trajectories. At the midline, one or more dots deviate in their direction(s) of motion (in Figure 1(left panel)one dot deviates and in Figure 1(right panel) all three dots deviate). On any trial the “target” dot or dots deviate together, either all clockwise (CW) or all counter-clockwise (CCW), by the same angle. The observer is required to report the perceived direction of deviation, CW or CCW. The proportion of trials on which the direction of deviation is correctly identified is the measure of performance. From these proportions, deviation-thresholds were estimated in some studies, or the effective numbers of tracked trajectories were estimated in others.

Comparison of MTT with other GMOT Paradigms

Some differences between MTT and other GMOT paradigms are listed below:

  1. In MTT all stimulus dots are potential “targets” since the observer does not know which of the dots will deviate in their direction of motion. In contrast, in MOT for example, the targets are identified at the start of the trial.
  2. Good performance in the MTT task requires that the first as well as the second halves of the trajectories be remembered and compared in order to detect deviations. In contrast good performance in other GMOT paradigms typically involves monitoring the instantaneous state of the stimulus, for example, which of the objects on the screen at any instant are the targets. Thus, other GMOT paradigms are less heavily dependent on memory compared to MTT.
  3. In MTT the dots move along linear trajectories and each trajectory has at most one deviation. This results in fewer degrees of freedom with regard to modelling human performance using computers (e.g. Ma & Huang, 2009).
  4. Most tracking paradigms do not take precision into account when estimating capacity and the responses that observers are required to make typically involve judgements of identity (target/distractor). In MTT the measure of interest is the precision with which direction of motion or deviations in directions of motion can be detected.

Findings from MTT Studies

Interactions between precision and tracking capacity.

Most studies of GMOT have viewed capacity as an absolute measure that is independent of precision; the obvious trade-off between precision and capacity has largely been ignored. MTT provides the opportunity to measure the interaction between precision and capacity. If the angle of deviation in MTT is small, the observer is required to track the trajectories more precisely and the capacity for effective tracking drops; conversely, the greater the angle of deviation, the larger the capacity for effective tracking (e.g. Tripathy, Narasimhan & Barrett, 2007). The following are some of the insights on capacity that are obtained from MTT.

When tracking capacity is measured using a threshold paradigm of MTT, only one trajectory can be tracked effectively (Tripathy & Barrett, 2004).

Figure 2: Sample MTT stimulus used (left panel) and deviation thresholds as a function of set-size (right panel). Adapted from Tripathy & Barrett, 2004, Figure 5, with permission from ARVO.

The stimulus was the basic MTT stimulus described earlier. Only one of the T trajectories deviated. The angle of deviation was varied from trial to trial using a Method of Constant Stimuli. The resulting psychometric function was plotted of the proportion of CCW responses for deviation direction identification versus the angle of deviation. From this, thresholds for detecting deviations were estimated. These are plotted in Figure 2 as a function of the number of trajectories in the stimulus. Increasing the number of trajectories from one (the deviating trajectory alone) to two results in a dramatic increase in thresholds, clearly indicating that only one trajectory can be tracked with precision when the deviations in the trajectories are close to their detection thresholds.

When tracking capacity is measured using MTT tasks with large trajectory deviations, several trajectories can be tracked simultaneously and effectively (Tripathy, Narasimhan & Barrett, 2007).

Figure 3: Sample MTT stimulus used (left panel) and effective number of trajectories tracked as a function of the number of deviating trajectories, with number of trajectories and deviation angles as parameters (right panel). Adapted from Tripathy, Narasimhan & Barrett, 2007, Figures 2a and 8, with permission from ARVO.

The stimulus used was the basic MTT stimulus described earlier. The number of deviating trajectories (D) was varied, as was the total number of trajectories presented (T). On any trial the D deviating trajectories all deviated in the same direction (say CW) with the same magnitude. The magnitude of deviation in a block of trials was fixed at 19, 38, or 76°. In Figure 3(left panel), T = 10, D = 3 and the CCW deviations have a magnitude of 76°. The proportion of trials on which the direction of deviation was correctly identified was converted into the effective number of tracked trajectories, by comparing with a limited-capacity hypothetical observer (LCHO) that attends and tracks A of the T trajectories perfectly and ignores the remaining (T-A) trajectories. The effective number of trajectories tracked, plotted in Figure 3(right panel) as a function of D, was largely uninfluenced by both D and T, but varied systematically with the magnitude of the deviation in the trajectories. The effective number of tracked trajectories was about four when the angle of deviation was 76° and was about one when the angle of deviation was 19°. These results demonstrate that the capacity for tracking changes in direction of motion is severely influenced by the precision demanded by the task.

A direct test of the interaction between precision and tracking capacity (Shooner, Tripathy, Bedell & Öğmen, 2010).

In these experiments the stimuli consisted of discs that moved along straight lines in random directions, only deviating if they bounced off the edge of the screen. Observers used the mouse to report the perceived final direction of motion of the discs. A probability density function (pdf) was fitted to the errors in the reported direction and the standard deviation of this pdf was estimated and was plotted as a function of the number of discs. The standard deviation increases rapidly with the number of discs that are to be tracked, indicating a loss of precision in representing the direction of motion when more trajectories have to be tracked (also see Horowitz & Cohen, 2010).

Interactions of precision and capacity in other GMOT paradigms.

Howard and Holcombe (2008, Experiment 3) found a gradual decrease in positional precision as the number of discs to be tracked was increased. This experiment involved stimuli similar to those used in typical MOT tasks, but with discs moving within individual cages. On each trial observers reported the end point of the trajectory in the cued cage.

Horowitz and Cohen (2010) had observers report direction of motion in stimuli similar to that of Shooner et al. (2010) described above, but their stimuli also included distractors, as in the traditional MOT studies. They reported a loss of precision with increase of set-size for the targets. Distracters were represented with much lower precision than targets.

Iordanescu, Grabowecky and Suzuki (2009) reported that the precision for localising targets in a MOT-like task was dynamically adjusted during tracking; within a trial, crowded targets were localised more precisely than uncrowded targets. Targets ‘in danger of being lost’ were allocated more attention, but this result is also consistent with more precise encoding of locations when other objects nearby provide a frame of reference.

Alvarez and Franconeri (2007) varied speed in an MOT task and found that for very high speeds few objects could be tracked, whereas for very slow speeds as many as eight objects could be tracked. Based on this they proposed that tracking resources are flexibly allocated among the tracked objects. Franconeri et al. (2008) found that performance was constrained not by the speed of the moving objects per se, but by the enhanced crowding that results from targets approaching other objects more frequently when the objects move with greater speed, with a greater probability for confusion of identities (see also: Shim, Alvarez & Jiang, 2008; Bettencourt & Somers, 2008). However, this view is questioned in Holcombe and Chen (in press).

Involvement of sensory memory in MTT:

Sperling (1960) showed that the visual system has access to visual stimuli for a few hundred milliseconds after they have been physically extinguished because of the persistence of these stimuli in “sensory” or “iconic” memory. Studies described below investigate the role of sensory memory in determining performance in MTT as well as other forms of GMOT.

Figure 4: Sample MTT stimulus with target changing colour at the midline (left panel) and the corresponding deviation thresholds as a function of set-size (right panel). Adapted from Narasimhan, Tripathy & Barrett, 2009, Figure 3, with permission from Elsevier.

Narasimhan, Tripathy and Barrett (2009) proposed that sensory memory made an important contribution to tracking in MTT. Their experiments used the basic MTT stimulus, but the single deviating dot was clearly identified during the second half of each trial. This was done either by having the deviating dot change colour at the time of deviation (as in Figure 4(left panel)) or by having all dots apart from the one deviating dot disappear during the second half of each trial. Surprisingly, in spite of the deviating trajectory being clearly identified during the second half of the trial, observers performed poorly as the number of trajectories in the stimulus increased. Figure 4(right panel) shows deviation thresholds as a function of set-size for three observers.

The effect of set-size observed above indicates that visual memory is a probable limiting factor in MTT. Observers are unable to recall the first half of the deviating trajectory in order to determine the direction of deviation, possibly because of the decay of earlier traces of the trajectories.

Figure 5: Deviation thresholds of two observers, as a function of delay introduced at the midline, with the number of trajectories as a parameter. Adapted from Narasimhan, Tripathy & Barrett, 2009, Figure 6, with permission from Elsevier.

Presenting stimuli similar to the moving dots above, but with a delay introduced between the first and second half of each trial should result in greater decay of the early half of the trajectory and result in much larger thresholds. The magnitude of the delay needed for threshold to be elevated is an indication of the nature of visual memory that is involved in MTT, decay of sensory memory typically occurs in a few hundred milliseconds (Sperling, 1960). As seen in Figure 5(right panel), for three-trajectory stimuli, thresholds were elevated by a factor of 4 with the introduction of delays as short as 400 ms. These results implicate sensory memory in the MTT task.

Figure 6: Precision for reporting direction of motion as a function of cue delay for two observers. Adapted from Shooner, Tripathy, Bedell & Öğmen, 2010, Figure 3, with permission from ARVO.

A more direct demonstration of the involvement of sensory memory in tracking was presented in Shooner et al. (2010). According to Sperling (1960) the typical signatures of sensory memory are: persistence of less than a second, and a performance-advantage for single/partial report (i.e. report for one randomly selected item, or a subset of randomly selected items from those in the stimulus; SR or PR) over full report (i.e. report for all items in the stimulus; FR). Both of these were observed in the findings of Shooner et al. (2010) illustrated in summary in Figure 6 and Figure 7.

As described earlier, Shooner et al. (2010) used a direction report paradigm. To investigate the persistence of the memory involved, a delay was introduced between the termination of motion and the cueing of the disc, the direction of motion of which was to be reported. As shown in Figure 6, performance dropped rapidly with increasing delay and in less than one second asymptoted to a level that was significantly greater than chance-level. This demonstrated a significant sensory memory contribution to tracking performance as well as a contribution from visual short-term memory.

Figure 7: Performance for direction of motion under single and full reporting conditions. Also shown is the drop in performance for items reported later. Adapted from Shooner, Tripathy, Bedell & Öğmen, 2010, Figure 4, with permission from ARVO.

The SR advantage illustrated in Figure 7 confirms the involvement of sensory memory in tracking.

Uni- v multi-focal attentional systems in MTT:

Studies of GMOT have generally favoured explanations based on multi-focal attentional systems (e.g. Cavanagh & Alvarez, 2005). Arguments against the single-focus explanation that are based on the speed of attention need to be re-evaluated to take into account the involvement of sensory memory. Moving objects leave traces in sensory memory that persist for several hundred milliseconds (Narasimhan et al., 2009; Shooner et al., 2010). A single-focus attentional system with access to sensory memory does not need to update the registered positions of tracked objects every few video frames, but needs to update the registered positions at least once within the duration that object-traces persist in sensory memory. Thus, if the persistence of sensory memory was 400ms and 4 trajectories were being tracked, then 100ms are available for processing each trajectory cyclically to determine if a deviation has occurred since the trajectory was last accessed. When deviations are large (say 76°), this (hypothetical) duration of 100ms may be adequate and all four trajectories may be accurately tracked, yielding an effective number of tracked trajectories that is approximately four. When the deviations are small (say 19°), detecting deviations within the 100ms time-window might be challenging for the attentional system, leading to deviations that are undetected and a reduction in the number of trajectories that are effectively tracked. An interesting additional possibility was raised by Howard and Holcombe (2010) who showed that large changes in direction of motion may attract attention during an unrelated task. This may have facilitated deviation detection in MTT tasks when the deviations were relatively large.

If tracking involves an attentional system that processes each trajectory cyclically and if an unsynchronised event occurs on one of these trajectories, we would expect random delays between when the event occurs and when it is attended. For example, if one of the trajectories undergoes a deviation at an instant when it is unattended, then we would expect this trajectory to be misperceived because of the delay in detecting the deviation. In fact, Tripathy and Barrett (2003) reported gross misperceptions in the trajectories of objects when trying to track more than one trajectory. These misperceptions are enhanced if the deviation occurs in the observer's blind spot, or behind an occluder at the eccentricity of the blind spot, since the blind spot or occluder delays the directing of attention to the deviation (Tripathy & Barrett, 2006). These distortions are of a much smaller magnitude if only a single trajectory is present in the stimulus (Nieman, Sheth & Shimojo, 2010, Yilmaz, Tripathy & Öğmen, submitted), but can be amplified by asking observers to perform a secondary task that is attentionally demanding (Yilmaz, Tripathy & Öğmen, submitted).

Thus the precision-capacity interactions, the persistence of sensory memory and the perceived distortions in trajectories collectively suggest that the attentional systems that are engaged in MTT belong to the single-focus variety (Tripathy, Öğmen & Narasimhan, 2011).

Mechanisms of tracking in MTT

The basic components of the mechanisms involved in MTT-like tasks may be as follows:

  • A high capacity (“parallel”) sensory memory stage that briefly stores traces of moving objects for a few hundred milliseconds (Narasimhan et al., 2009; Shooner et al., 2010; see also Treisman, Russell & Green, 1975; Demkiw & Michaels, 1976; Burr, 1980; Chen, Bedell & Öğmen, 1995; Blake, Cepeda & Hiris, 1997; Geisler, 1999; Edwards & Crane, 2007; Tong, Aydin & Bedell, 2007).
  • A lower capacity visual short-term memory (VSTM) that stores motion information (and possibly other object features/attributes) for durations as long as several seconds (Shooner et al., 2010).
  • An attentional system that cyclically updates registered information for tracked trajectories with a cycle-time that is less than the persistence of the sensory memory (Narasimhan et al., 2009; Tripathy et al., 2011).

Ma and Huang (2009) successfully modelled a variety of MTT data using a Bayesian observer that is constrained by stimulus uncertainty that increases with the number of items to be tracked. They argued against a fixed capacity for tracking that had been proposed for more traditional tracking paradigms.

The loss of tracking abilities in MOT with aging has been well documented (Trick, Perl & Sethi, 2005; Sekuler, McLaughlin & Yotsumoto, 2008). Kennedy, Tripathy & Barrett (2009) looked at the effects of age on MTT in subjects aged from 18 to 62 years and found that between the ages of 30-60 years, the effective numbers of tracked trajectories during MTT dropped by about 20% with each decade of aging. This very sharp drop in performance is not explained by a drop in visual acuity because:

  • visual acuity does not drop so steeply with age, and
  • amblyopes who had much reduced visual acuity in their amblyopic eye showed tracking deficits in their affected eye that were small and comparable to deficits in tracking normally seen in an adult over a decade of aging (Levi & Tripathy, 2006; Tripathy & Levi, 2008; Kennedy et al., 2009).

The drop in performance with aging probably reflects increased stimulus uncertainty (i.e. increased loss of precision), possibly as a consequence of either an increase in the time needed to process each trajectory, or a decrease in the persistence of sensory memory.

Implications of MTT for GMOT

Interactions between precision and tracking capacity.

The capacity of tracking is not fixed but varies with task difficulty. This can be seen in MTT as discussed above (Tripathy et al., 2007) as well as in several other MTT-like and MOT-like tasks (Alvarez & Franconeri, 2007; Howard & Holcombe, 2008; Bettencourt & Somers, 2008; Franconeri et al., 2008; Shim et al., 2008; Iordanescu et al., 2009; Shooner et al., 2010; Horowitz & Cohen, 2010; Howard, Masom & Holcombe, 2011). Thus the precision-capacity interaction appears to be a general feature of the GMOT problem.

Involvement of sensory memory.

Apart from Narasimhan et al. (2009) and Shooner et al. (2010) we are not aware of any studies that have tried to systematically evaluate the contribution of sensory memory to tracking. There are several reasons for believing that these sensory-memory findings can be generalised to the GMOT problem.

First, a variety of experiments have demonstrated the involvement of sensory memory in both static tasks as well as motion tasks. These experiments have introduced terms such as iconic storage, motion streaks, motion persistence, motion deblurring, etc. into the vocabulary of vision science (e.g. Sperling, 1960; Burr, 1980; Chen, Bedell & Öğmen, 1995; Geisler, 1999). These studies demonstrate apparently universal use of sensory memory as a temporary buffer for visual stimuli. Given the availability of this buffered information, it is reasonable to expect that the tracking system will use this information when it would be advantageous. Whether the attentional system has a single focus or is multi-focal, its tracking performance could be enhanced by the use of a high-capacity visual buffer.

Second, Howard and Holcombe (2008) found that position reports were consistent with the presence of a serial component even for tracking fewer than four targets. In this context, sensory memory could represent the parallel component and the focus of attention the serial component of the tracking process.

Uni- v multi-focal attentional systems.

A case for multi-focal attention based explanation for tracking has been repeatedly made in the tracking literature (e.g. Howe, Cohen, Pinto & Horowitz, 2010). But the topic has always remained controversial (e.g. Cavanagh & Alvarez, 2005; Jans, Peters & De Weerd, 2010a, 2010b; Cave, Bush & Taylor, 2010). A criticism of many of the studies advocating multi-focal attention is that these studies have not addressed the possible role of sensory memory, which could cause a single-focus attentional system to appear, under casual inspection, to be multi-focal. Here we list some of the evidence in support of a serial component in the attentional mechanisms involved in GMOT tasks:

  1. In MOT, as the number of targets is increased, the error rate increases slightly, and response latency increases more substantially. These increases were attributed to a ‘limited resource’ parallel process but are also explained, perhaps more parsimoniously, by sensory memory working in conjunction with a serial attentional process (Pylyshyn & Storm, 1988).
  2. When tracking colour-switches behind occluders in the MOPT task, performance drops rapidly as the number of targets is increased, a result that is consistent with a serial component in this form of tracking (Saiki, 2002).
  3. A wide range of GMOT tasks yield a decrease in tracking performance when task difficulty is increased, which is consistent with a serial algorithm for tracking multiple objects. Examples of this drop in performance are seen when dot speed is increased in MOPT (Saiki, 2002; 2003a, 2003b), or in MOT (Alvarez & Franconeri, 2007), or in MIT (Oksama & Hyona, 2008), or when dot separation is reduced (Franconeri, Lin, Pylyshyn, Fisher & Enns, 2008; Shim et al, 2008).
  4. The most systematic investigation into the involvement of a serial process in tracking is found in Oksama and Hyona (2004; 2008). Their MIT paradigm showed deterioration in performance when the number or speed of the targets was increased, or the familiarity of the targets was decreased, as predicted by their MOMIT.
  5. In an MOT task Howard and Holcombe (2008; also see Howard, Masom & Holcombe, 2011) showed that when observers attempted to report the final positions of targets, reports were more similar to previous than to final target positions i.e. reports exhibited perceptual lag. They observed a systematic increase in perceptual lag with increase in the number of targets. Lags were also longer on occasions when observers were less likely to be sure of their responses and shorter when observers were more likely to be sure of their responses. This pattern of lags is consistent with the presence of a serial element to tracking whereby processing switches to some extent between targets.
  6. A study involving size discrimination and duration discrimination over multiple target items reported large set-size effects, causing the authors to conclude that under, some circumstances, “estimates of size or duration require the serial examination of individual display items” (Morgan, Giora & Solomon, 2008). The MTT studies suggest that estimations of other stimulus attributes, such as direction of motion or changes in direction of motion, may require serial examination.


MTT studies show that the mechanisms of tracking involve sensory memory and a low capacity attentional system, possibly even a single focus attentional system. These studies show that the capacity of these mechanisms is related to the desired tracking precision. It is proposed, based on parsimony and evidence from other tracking paradigms, that similar tracking mechanism may be involved in GMOT. The role of sensory memory needs to be carefully considered in any tracking task before a judgement can be made about the single- or multi-focal nature of attention involved.


Constructive suggestions and comments from Prof. Haluk Öğmen and Drs. Brendan Barrett, Alex Holcombe and Sathyasri Narasimhan are gratefully acknowledged.


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Internal Links

Howard Eichenbaum (2008). Memory, Scholarpedia, 3(3):1747.

Steven J. Luck (2007). Visual short-term memory, Scholarpedia, 2(6):3328.

Zenon Pylyshyn (2007). Multiple object tracking, Scholarpedia, 2(10):3326.

Lawrence M. Ward (2008). Attention, Scholarpedia, 3(10):1538.

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