Representational Momentum Beyond Internalized Physics

Abstract— Prediction of future motion is necessary in order to successfully deal with moving objects. Implicit measures have been used to evaluate the sources of information used in this task. For instance, observers may be asked to localize the final position of a moving target. Judgments have been found to be displaced in the direction of motion (forward displacement), suggesting that observers have internalized a mental analogue of physical momentum. However, more recent studies have shown that forward displacement may not be caused by cognitive mechanisms alone. Rather, predictive mechanisms at the perceptual and motor levels may contribute to the forward error. Supporting the notion that mechanisms of anticipation may be embodied, the forward error was found to depend on the execution of eye and pointing movements. Also, forward displacement depended on the motion type that was presented (smooth vs. jerky or implied), which suggests that attention moves to the next expected target position to facilitate responses to this position.     

Representational momentum and related displacements in spatial memory: A review of the findings

Memory for the final location of a moving target is often displaced in the direction of target motion, and this has been referred to asrepresentational momentum. Characteristics of the target (e.g., velocity, size, direction, and identity), display (e.g., target format, retention interval, and response method), context (landmarks, expectations, and attribution of motion source), and observer (e.g., allocation of attention, eye movements, and psychopathology) that influence the direction and magnitude of displacement are reviewed. Specific conclusions regarding numerous variables that influence displacement (e.g., presence of landmarks or surrounding context), as well as broad-based conclusions regarding displacement in general (e.g., displacement does not reflect objective physical principles, may reflect aspects of naive physics, does not solely reflect eye movements, may involve some modular processing, and reflects high-level processes) are drawn. A possible computational theory of displacement is suggested in which displacement (1) helps bridge the gap between perception and action and (2) plays a critical part in localizing stimuli in the environment.     

线索呈现的时空特性对表征动量的影响

为揭示注意对表征动量的影响机制,我们结合线索提示和表征动量范式,通过两个实验比较高、低相关线索分别在诱导期间与保持间隔呈现对表征动量的影响,结果发现：(1)高相关线索的时间特性主效应不显著,最终位置均发生边缘性的向前偏移。(2)低相关线索呈现在诱导期间时,表征动量显著;呈现在保持间隔时,发生向后偏移。这些表明,随着注意增大,表征动量减小;高相关线索更有利于定位,而低相关线索易受时间特性的影响。研究结果验证表征动量的双加工理论。     

Why eye movements and perceptual factors have to be controlled in studies on "representational momentum"

In order to study memory of the final position of a smoothly moving target, Hubbard (e.g., Hubbard and Bharucha, 1988) presented smooth stimulus motion and used motor responses. In contrast, Freyd (e.g., Freyd and Finke, 1984) presented implied stimulus motion and used the method of constant stimuli. The same forward error was observed in both paradigms. However, the processes underlying the error may be very different. When smooth stimulus motion is followed by smooth pursuit eye movements, the forward error is associated with asynchronous processing of retinal and extraretinal information. In the absence of eye movements, no forward displacement is observed with smooth motion. In contrast, implied motion produces a forward error even without eye movements, suggesting that observers extrapolate the next target step when successive target presentations are far apart. Finally, motor responses produce errors that are not observed with perceptual judgments, indicating that the motor system may compensate for neuronal latencies.     

Comment and Reply Why eye movements and perceptual factors have to be controlled in studies on “representational momentum”

In order to study memory of the final position of a smoothly moving target, Hubbard (e.g., Hubbard & Bharucha, 1988) presented smooth stimulus motion and used motor responses. In contrast, Freyd (e.g., Freyd & Finke, 1984) presented implied stimulus motion and used the method of constant stimuli. The same forward error was observed in both paradigms. However, the processes underlying the error may be very different. When smooth stimulus motion is followed by smooth pursuit eye movements, the forward error is associated with asynchronous processing of retinal and extraretinal information. In the absence of eye movements, no forward displacement is observed with smooth motion. In contrast, implied motion produces a forward error even without eye movements, suggesting that observers extrapolate the next target step when successive target presentations are far apart. Finally, motor responses produce errors that are not observed with perceptual judgments, indicating that the motor system may compensate for neuronal latencies.     

线索提示对表征动量的影响

研究结合线索提示和表征动量范式,实验1、2均采用2有无线索(有线索,无线索)×4诱导期间时距(1250ms,1750ms,2250ms,2750ms)混合实验设计,探讨线索呈现的加工阶段和时距对表征动量的影响。实验1恒定保持间隔时距,在不同时距的诱导期间呈现线索,发现线索主效应不显著,但表征动量呈减小趋势;时距主效应不显著。实验2变化诱导时距,在恒定的保持间隔呈现线索,发生向后偏移现象,线索主效应显著;时距主效应不显著。研究结果表明,随着注意的增加,表征动量效应减小;注意时距不显著影响表征动量,而注意阶段显著影响表征动量。研究结果为表征动量的双加工理论提供了实证支持。     

Centripetal force draws the eyes,not memory of the target,toward the center

Many observers believe that a target will continue on a curved trajectory after exiting a spiral tube. Similarly, when observers were asked to localize the final position of a target moving on a circular orbit, displacement of the judged position in the direction of forward motion ("representational momentum") and toward the center of the orbit was observed (cf. T. L. Hubbard, 1996). The present study shows that memory displacement of targets on a circular orbit is affected by eye movements. Forward displacement was larger with ocular pursuit of the target, whereas inward displacement was larger with motionless eyes. The results challenge an account attributing forward and inward displacement to mental analogues of momentum and centripetal force, respectively.     

A matter of design: No representational momentum without predictability

When observers are asked to localize the final position of a moving target, a forward shift of the judged final position is observed. So far, the forward shift has been attributed to the influence of mental continuation of the final target position (representational momentum). However, studies investigating forward displacement have used highly predictable target motion. The direction of target motion and the final target position were often varied between subjects. Thus, observers may have expected the target to travel in a particular direction or vanish at a particular location before a given trial started. In this study, direction of motion and final position were treated as fixed or random factors. The forward shift and the reversal of the shift with time (memory averaging) were absent when both factors were randomized. Thus, the forward shift with implied motion is restricted to repeatedly observed motion sequences that allow for pre-trial motion prediction.     

Colour and spatial cueing in low-prevalence visual search

People are able to judge the current position of occluded moving objects. This operation is known as motion extrapolation. It has previously been suggested that motion extrapolation is independent of the oculomotor system. Here we revisited this question by measuring eye position while participants completed two types of motion extrapolation task. In one task, a moving visual target travelled rightwards, disappeared, then reappeared further along its trajectory. Participants discriminated correct reappearance times from incorrect (too early or too late) with a two-alternative forced-choice button press. In the second task, the target travelled rightwards behind a visible, rectangular occluder, and participants pressed a button at the time when they judged it should reappear. In both tasks, performance was significantly different under fixation as compared to free eye movement conditions. When eye movements were permitted, eye movements during occlusion were related to participants' judgements. Finally, even when participants were required to fixate, small changes in eye position around fixation (<2°) were influenced by occluded target motion. These results all indicate that overlapping systems control eye movements and judgements on motion extrapolation tasks. This has implications for understanding the mechanism underlying motion extrapolation.     

Do common systems control eye movements and motion extrapolation?

People are able to judge the current position of occluded moving objects. This operation is known as motion extrapolation. It has previously been suggested that motion extrapolation is independent of the oculomotor system. Here we revisited this question by measuring eye position while participants completed two types of motion extrapolation task. In one task, a moving visual target travelled rightwards, disappeared, then reappeared further along its trajectory. Participants discriminated correct reappearance times from incorrect (too early or too late) with a two-alternative forced-choice button press. In the second task, the target travelled rightwards behind a visible, rectangular occluder, and participants pressed a button at the time when they judged it should reappear. In both tasks, performance was significantly different under fixation as compared to free eye movement conditions. When eye movements were permitted, eye movements during occlusion were related to participants' judgements. Finally, even when participants were required to fixate, small changes in eye position around fixation (<2°) were influenced by occluded target motion. These results all indicate that overlapping systems control eye movements and judgements on motion extrapolation tasks. This has implications for understanding the mechanism underlying motion extrapolation.     

Illusory motion and representational momentum

When a moving target vanishes abruptly, participants judge its final position as being ahead of its actual final position, in the direction of motion (representational momentum; Freyd & Finke, 1984). In the present study, we presented illusory motion and examined whether or not forward displacement was affected by the perceived direction and speed of the target. Experiments 1A and 1B showed that an illusory direction of movement of a target was perceived, and Experiment 2 showed that an illusory speed of a moving target was observed. However, neither the direction nor the magnitude of forward displacement was affected by these illusions. Therefore, it was suggested that the mechanism underlying forward displacement (or some extrapolation processing) uses different motion signals than does the perceptual mechanism.     

Adaptation in the constancy of visual direction measured by a one-trial method

Adaptation to field displacement during head movements in the direction with the head rotation and in the direction against it was produced under otherwise identical conditions and compared; the field displacement rate was also varied. A rapid training procedure was used, and a novel one-trial test was employed that could measure the adaptation well enough to compare the effects of various training conditions. The one-trial test measured the magnitude of one of the manifestations of adaptation, the apparent displacement of a stationary target during head movements. This apparent horizontal target displacement was transformed into an oblique one by having the head movements that brought forth the apparent target displacement simultaneously cause an objective vertical target displacement. The slant of the resultant apparent motion path varied with the magnitude of the apparent horizontal target displacement. It was measured by having S reproduce its slant angle. It was found that adaptation to field displacement in the direction with the head rotation was consistently greater than adaptation to the opposite displacement conditions. An explanation for this result is offered.     

The role of perception in the mislocalization of the final position of a moving target

The judged final position of a moving stimulus has been suggested to be shifted in the direction of motion because of mental extrapolation (representational momentum). However, a perceptual explanation is possible: The eyes overshoot the final position of the target, and because of a foveal bias, the judged position is shifted in the direction of motion. To test this hypothesis, the authors replicated previous studies, but instead of having participants indicate where the target vanished, the authors probed participants' perceptual focus by presenting probe stimuli close to the vanishing point. Identification of probes in the direction of target motion was more accurate immediately after target offset than it was with a delay. Another experiment demonstrated that judgments of the final position of a moving target are affected by whether the eyes maintain fixation or follow the target. The results are more consistent with a perceptual explanation than with a memory account.     

Localization of moving sound

The final position of a moving sound source usually appears to be displaced in the direction of motion. We tested the hypothesis that this phenomenon, termed auditory representational momentum, is already emerging during, not merely after, the period of motion. For this purpose, we investigated the localization of a moving sound at different points in time. In a dark anechoic environment, an acoustic target moved along the frontal horizontal plane. In the initial, middle, or final phase of the motion trajectory, subjects received a tactile stimulus and determined the current position of the moving target at the moment of the stimulus by performing either relative-judgment or pointing tasks. Generally, in the initial phase of the auditory motion, the position was perceived to be displaced in the direction of motion, but this forward displacement disappeared in the further course of the motion. When the motion stimulus had ceased, however, its final position was again shifted in the direction of motion. The latter result suggests that representational momentum in spatial hearing is a phenomenon specific to the final point of motion. Mental extrapolation of past trajectory information is discussed as a potential source of this perceptual displacement.     

Distractor interference during smooth pursuit eye movements

When 2 targets for pursuit eye movements move in different directions, the eye velocity follows the vector average (S. G. Lisberger & V. P. Ferrera, 1997). The present study investigates the mechanisms of target selection when observers are instructed to follow a predefined horizontal target and to ignore a moving distractor stimulus. Results show that at 140 ms after distractor onset, horizontal eye velocity is decreased by about 25%. Vertical eye velocity increases or decreases by 1 degrees /s in the direction opposite from the distractor. This deviation varies in size with distractor direction, velocity, and contrast. The effect was present during the initiation and steady-state tracking phase of pursuit but only when the observer had prior information about target motion. Neither vector averaging nor winner-take-all models could predict the response to a moving to-be-ignored distractor during steady-state tracking of a predefined target. The contributions of perceptual mislocalization and spatial attention to the vertical deviation in pursuit are discussed.     

Localization of moving sound

The final position of a moving sound source usually appears to be displaced in the direction of motion. We tested the hypothesis that this phenomenon, termed auditory representational momentum, is already emerging during, not merely after, the period of motion. For this purpose, we investigated the localization of a moving sound at different points in time. In a dark anechoic environment, an acoustic target moved along the frontal horizontal plane. In the initial, middle, or final phase of the motion trajectory, subjects received a tactile stimulus and determined the current position of the moving target at the moment of the stimulus by performing either relative-judgment or pointing tasks. Generally, in the initial phase of the auditory motion, the position was perceived to be displaced in the direction of motion, but this forward displacement disappeared in the further course of the motion. When the motion stimulus had ceased, however, its final position was again shifted in the direction of motion. The latter result suggests that representational momentum in spatial hearing is a phenomenon specific to the final point of motion. Mental extrapolation of past trajectory information is discussed as a potential source of this perceptual displacement.     

Representational momentum contributes to motion induced mislocalization of stationary objects

The influence of a moving target on memory for the location of a briefly presented stationary object was examined. When the stationary object was aligned with the final portion of the moving target's trajectory, memory for the location of the stationary object was displaced forward (i.e., in the direction of motion of the moving target); the magnitude of forward displacement increased with increases in the velocity of the moving target, decreased with increases in the distance of the stationary object from the final location of the moving target, and increased and then decreased with increases in retention interval. It is suggested that forward displacement in memory for a stationary object aligned with the final portion of a moving target's trajectory reflects an influence of representational momentum of the moving target on memory for the location of the stationary object. Implications of the data for theories of representational momentum and motion induced mislocalization are discussed.     

Overt is no better than covert when rehearsing visuo-spatial information in working memory

In the present study, we examined whether eye movements facilitate retention of visuo-spatial information in working memory. In two experiments, participants memorised the sequence of the spatial locations of six digits across a retention interval. In some conditions, participants were free to move their eyes during the retention interval, but in others they either were required to remain fixated or were instructed to move their eyes exclusively to a selection of the memorised locations. Memory performance was no better when participants were free to move their eyes during the memory interval than when they fixated a single location. Furthermore, the results demonstrated a primacy effect in the eye movement behaviour that corresponded with the memory performance. We conclude that overt eye movements do not provide a benefit over covert attention for rehearsing visuo-spatial information in working memory.     

Cognitive representation of linear motion: Possible direction and gravity effects in judged displacement

The judged vanishing point of a target undergoing apparent motion in a horizontal, vertical, or oblique direction was examined. In Experiment 1, subjects indicated the vanishing point by positioning a crosshair. Judged vanishing point was displaced forward in the direction of motion, with the magnitude of displacement being largest for horizontal motion, intermediate for oblique motion, and smallest for vertical motion. In addition, the magnitude of displacement increased with faster apparent velocities. In Experiment 2, subjects judged whether a stationary probe presented after the moving target vanished was at the same location where the moving target vanished. Probes were located along the axis of motion, and probes located beyond the vanishing point evidenced a higher probability of a same response than did probes behind the vanishing point. In Experiment 3, subjects judged whether a stationary probe presented after the moving target vanished was located on a straight-line extension of the path of motion of the moving target. Probes below the path of motion evidenced a higher probability of a same response than did probes above the path of motion for horizontal and ascending oblique motion; probes above the path of motion evidenced a higher probability for a same response than did probes below the path of motion for descending oblique motion. Overall, the pattern of results suggests that the magnitude of displacement increases as proximity to a horizontal axis increases, and that in some conditions there may be a component analogous to a gravitational influence incorporated into the mental representation.     

The role of action plans and other cognitive factors in motion extrapolation: A modelling study

When observers are asked to remember the final location of an object undergoing apparent or implied motion, a forward displacement is observed. The magnitude of this form of motion extrapolation is known to depend on various factors including stimulus attributes, action plans, and other cognitive cues. Here we present a modelling approach that aims at bridging different existing theories of displacement within a single theoretical framework. A network model consisting of interacting excitatory and inhibitory cell populations coding for stimulus attributes like position or orientation is used to study the response to motion displays. The intrinsic network dynamics can be modulated by additional information sources representing action plans directed at the moving target or cognitive cues such as prior knowledge about the trajectory. These factors decide the extent to which the dynamic representation overshoots the final position. The model predictions are quantitatively compared with the experimental findings. The results are discussed in relation to theoretical ideas about processing principles underlying motion extrapolation and a comparison with neurophysiological findings linked to movement prediction is made.