December 2009
Volume 9, Issue 13
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Research Article  |   December 2009
The spatial scale of perceptual memory in ambiguous figure perception
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Journal of Vision December 2009, Vol.9, 16. doi:10.1167/9.13.16
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      Tomas Knapen, Jan Brascamp, Wendy J. Adams, Erich W. Graf; The spatial scale of perceptual memory in ambiguous figure perception. Journal of Vision 2009;9(13):16. doi: 10.1167/9.13.16.

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Ambiguous visual stimuli highlight the constructive nature of vision: perception alternates between two plausible interpretations of unchanging input. However, when a previously viewed ambiguous stimulus reappears, its earlier perception almost entirely determines the new interpretation; memory disambiguates the input. Here, we investigate the spatial properties of this perceptual memory, taking into account strong anisotropies in percept preference across the visual field. Countering previous findings, we show that perceptual memory is not confined to the location in which it was instilled. Rather, it spreads to noncontiguous regions of the visual field, falling off at larger distances. Furthermore, this spread of perceptual memory takes place in a frame of reference that is tied to the surface of the retina. These results place the neural locus of perceptual memory in retinotopically organized sensory cortical areas, with implications for the wider function of perceptual memory in facilitating stable vision in natural, dynamic environments.

Introduction
When the brain receives ambiguous visual input, it may lapse into a state of perceptual rivalry; different possible interpretations of the visual stimulation strive for dominance (Blake & Logothetis, 2002; see Figure 1A). During continuous presentation of such a stimulus, the competition between the two interpretations leads to a process of ongoing and stochastic perceptual alternation. Each of the interpretations is perceived in turn, with dominance durations that vary unpredictably (Levelt, 1967). When bistable stimuli are shown intermittently rather than continuously, the brain must select a new interpretation at every reoccurrence of the same stimulus. It does so in a process that is qualitatively very different from continuous rivalry and is characterized by highly regular sequences of perception. When seconds-long blank durations are inserted between presentations, the same percept is selected on many consecutive presentations: perceptual stabilization (Leopold, Wilke, Maier, & Logothetis, 2002; Orbach, Ehrlich, & Heath, 1963; Orbach, Zucker, & Olson, 1966). This regularization of perception based on prior experience has been termed “perceptual memory” (Maier, Wilke, Logothetis, & Leopold, 2003; Pearson & Brascamp, 2008) and indicates that the brain uses the outcome of previous computations to augment perceptual decision-making in the selection process that occurs at stimulus onset. If perceptual memory is to assist the visual system in rapid and efficient perceptual decision-making, it should display some degree of spread across spatial locations. In a dynamic world objects move across the retina, and even eye movements intended to refixate an object have limited endpoint accuracy (van Beers, 2007), causing variability in retinal position over time.
Figure 1
 
(A) Two types of stimuli used, binocular rivalry (BR) gratings and structure from motion (SFM) cylinders. (B) Spatial aspects of presentation for Experiment 1. Stimuli were presented alternately at fixation and at one of a number of (12 possible) eccentric locations. (C) Temporal presentation paradigm. (D) Examples of typical percept sequences as reported by individual observers of the (left column) SFM cylinders and (right column) BR gratings. Orange curves show perception at the central location across a session; blue curves show the same for the eccentric locations. The bottom graph of each pair shows raw data, whereas the top graph shows smoothed data (averaged using a Gaussian sliding window with σ = 26 s).
Figure 1
 
(A) Two types of stimuli used, binocular rivalry (BR) gratings and structure from motion (SFM) cylinders. (B) Spatial aspects of presentation for Experiment 1. Stimuli were presented alternately at fixation and at one of a number of (12 possible) eccentric locations. (C) Temporal presentation paradigm. (D) Examples of typical percept sequences as reported by individual observers of the (left column) SFM cylinders and (right column) BR gratings. Orange curves show perception at the central location across a session; blue curves show the same for the eccentric locations. The bottom graph of each pair shows raw data, whereas the top graph shows smoothed data (averaged using a Gaussian sliding window with σ = 26 s).
 
Here we investigate the extent to which perceptual memory spreads across spatial locations. We investigate the perception of an ambiguous stimulus presented at various successive retinal locations, measuring correlations between consecutive perceptual reports at different locations (i.e., a tendency for consecutive perceptual reports at different locations to be the same). The experiments were designed specifically to distinguish the effects of perceptual memory from those of percept bias—the tendency for observers to experience a particular perceptual interpretation on the majority of presentations of a given ambiguous stimulus, regardless of prior perception (Carter & Cavanagh, 2007). These perceptual biases vary and may indeed be entirely opposite, from one retinal location to the next, even within the same observer. This means that consecutive responses to an ambiguous stimulus presented at two different locations in alternation will usually be correlated, regardless of the contents of perceptual memory: a positive correlation if the biases at the two locations are similar, or a negative correlation if they are opposed. This effect of bias may have influenced prior investigations into the spatial spread of perceptual memory in which two retinal locations were stimulated in alternation (Chen & He, 2004; see Discussion section). Here we modified our experiments and analyses to circumvent such an influence in our results. 
We employed two highly dissimilar types of ambiguous stimuli for our experiments. In separate sessions we used (1) binocular rivalry between gratings (BR), where conflicting interpretations correspond to the two incompatible patterns that are projected to the two eyes, and (2) structure-from-motion (SFM), where conflict arises from the ambiguous depth ordering of a rotating transparent cylinder projected orthographically, resulting in percepts of either a rightward or a leftward rotating cylinder ( Figure 1A). Observers reported their visual percept (grating tilted right/left, or front face of cylinder moving rightward/leftward) on each presentation of a bistable stimulus. 
Methods
Distinguishing perceptual memory from bias
As in other studies of perceptual memory we used an intermittent presentation regime where the same ambiguous stimulus is presented repeatedly. As noted in the Introduction section, a main challenge in studying the spatial spread of perceptual memory is distinguishing this factor from retinally local percept biases (Carter & Cavanagh, 2007). While biases cannot be eliminated altogether from experiments such as these, we designed our experiments and analyses in a way that would allow us to separate those effects due to bias from the effects of perceptual memory itself. To that end, we presented our stimuli alternately at a central fixation location and one of twelve locations situated on an imaginary ring around fixation (Figure 1B). The duration of individual stimulus presentations, as well as that of the blank intervals separating presentations, was 1 s (Figure 1C) such that the central, recurring position was stimulated every 4 s for 1 s. Such steady and relatively fast intermittent presentation, over a period of time (about 10 min or longer) is known to cause a slow perceptual alternation cycle, where one percept dominates for many presentations, before a switch to the other percept (Brascamp, Pearson, Blake, & van den Berg, 2009). That is, bias is likely to influence the initial dominant percept of a session rather than the perceptual alternation cycle that subsequently develops (Figure S1 in Brascamp et al., 2008). In our design, each of the peripheral locations was stimulated only once every 48 s. Such a long separation between presentations precludes the evolution of a slow perceptual alternation cycle locally within each of the peripheral locations (Brascamp et al., 2009). This design paved the way for our main analysis, which investigated the extent to which perception at the peripheral “test” locations would become entrained with the alternating perceptual dominance episodes at the central location. Specifically, we assessed perception at the peripheral locations conditional on the immediately preceding percept at the central location. While percept biases can, and do, influence the predominance of either percept at a given location, they cannot affect how this predominance varies with a preceding perception at another location. To distinguish nonlocal perceptual memory from percept bias, therefore, we centered our analyses on such conditional probabilities. 
Presentation paradigm
Observers were seated in a darkened room and viewed binocular rivalry (BR) or bistable rotating cylinder (structure from motion, SFM) stimuli via a stereoscope with a viewing distance of 57 cm. The screen's resolution was 1600 × 1200, 75 Hz refresh, subtending 20 degrees in width when viewed through the stereoscope. In a single session, which lasted 20–35 min depending on the experiment (30 for the first experiment, 20 for the second, 35 for the third, and 25 for the fourth), observers were presented with one of the two types of bistable stimulus. Stimuli were presented in an on–off fashion for the entire session, with no interruptions other than the blank periods between presentations (see Figure 1). Both stimulus presentation durations and blank screen durations were 1 s and observers reported their dominant percept for each stimulus presentation using key presses. Ambiguous stimuli do not always give rise to a crisp percept of one of the two competing interpretations. Observers sometimes report mixtures, such as a combination of both eyes' images in binocular rivalry (Yang, Rose, & Blake, 1992), or two convex shells instead of a full cylinder in the case of SFM (Hol, Koene, & van Ee, 2003). For that reason, we instructed our observers to always choose the strongest percept, i.e., the dominant one, even if perception was mixed. In our first experiment every odd presentation was at fixation, and every even presentation was at one of twelve eccentric locations located on an imaginary ring surrounding fixation, with these locations being visited in random order throughout a session. Thus, a steady stream of presentations at fixation, 3 s apart, was interleaved with “test” presentations at the eccentric locations while observers maintained fixation. Separated radially by 30° from one another, the eccentric stimulus locations did not overlap with the stimulus area for central, fixated presentation. This first experiment was followed by three additional experiments that were identical in stimulus timing and dimensions, which also involved alternating presentations at a recurring position and at “test” positions that were visited in random order. These additional experiments differed in other aspects such as the spatial arrangement of stimulus locations and the fixation instructions as described in detail below. In Experiments 1 through 4, the number of observers for the bistable cylinder was 8, 6, 6, and 6, respectively, and the number for binocular rivalry was 6, 5, 7, and 6, respectively. Three authors participated in all experiments. 
Binocular rivalry stimuli
Binocular rivalry stimuli were grayscale sinusoidal gratings of full contrast and 3 cycles per degree, displayed in a circular aperture subtending 0.9 degrees of visual angle. Background luminance was 1.7 cd/m 2 and peak stimulus luminance was 70 cd/m 2. During peripheral presentation in Experiment 1, the distance from the center of the stimulus to fixation was 1.35 deg. In Experiments 2 and 4, the distances of test stimuli from fixation were 0.7 and 1.35 deg. In Experiment 3, the distance of the center of the recurring stimulus to fixation was 1.0 deg. 
Rotating cylinder stimuli
Orthographic projections of rotating cylinders made up of two hundred 1.5′ dots subtended 0.8 deg. Dot luminance was 70 cd/m 2, and the cylinders were rotated 0.36 times per second. Background luminance was 0.0 cd/m 2. During peripheral presentation in Experiment 1, the distance from the center of the stimulus to fixation was 2.0 deg. In Experiments 2 and 4, the distances of test stimuli from fixation were 1.0 and 2.0 deg. In Experiment 3, the distance of the center of the recurring stimulus to fixation was 1.41 deg. 
Gaze position recordings
Gaze position was recorded during a separate SFM experiment for 2 observers using an Eyelink1000 infrared gaze tracker sampling at 1 kHz, using both infrared and corneal reflection. The spatial arrangement of the bistable cylinder stimuli, the screen dimensions, and the viewing distance were identical to those used in Experiment 1, with the exception that no stereoscope was used. Long-term drift was removed from the gaze position data by using the fixation periods of every odd trial (when only a fixation cross was presented) as drift correction, and position data were then binned to reveal gaze density plots as shown in Figure 3
Control experiment for reliable reports
To gauge the reliability of perceptual reports, four observers (two authors and two naive) performed a control experiment, which used the same stimuli and procedure as Experiment 1, other than two key differences. First, on a total of 5% (randomly selected) of all stimulus presentations, we showed an unambiguous stimulus rather than an ambiguous one, to objectively test our observers' accuracy. For BR, these catch trials consisted of one of the two gratings presented monocularly, without any stimulus in the other eye. For SFM we added binocular disparity to our cylinders, thus disambiguating their rotation directions. The control experiment also differed from Experiment 1 in the observers' task. Observers now had a dual task of reporting, on each presentation, both the dominant percept and whether this percept was exclusive or not (i.e., whether any sign of the alternative interpretation was visible). A high degree of nonexclusivity might raise concern regarding the reliability with which observers reported their dominant percept in our experiments. However, the control experiment indicated that our main experiments were reliable. In summary, the responses to disambiguated stimuli (catch trials) indicated that observers had no trouble reporting what they saw: responses were correct on 98% and 91% of the catch trials for BR and SFM, respectively. The exclusivity reports indicated that perception was exclusive on 98% of all presentations for SFM, but on only 38% of all presentations for BR. This relatively high occurrence of nonexclusivity for BR is consistent with previous literature, which has reported nonexclusivity at a broad range of stimulus settings (Brascamp, van Ee, Noest, Jacobs, & van den Berg, 2007; Hollins & Hudnell, 1980; O'Shea, A J Sims, & Govan, 1997; Yang et al., 1992), and particularly at the onset of a newly appearing BR stimulus (Burke, Alais, & Wenderoth, 2000; Liu, Tyler, & Schor, 1992; Wolfe, 1983). Reassuringly, the outcome of our experiments is essentially the same for BR (which involves much nonexclusivity) and for SFM (which hardly involves any nonexclusivity), indicating that nonexclusivity does not have an important influence on our results, and that our observers were, therefore, able to accurately report a dominant percept, even when aware of the alternative interpretation. 
Results
Experiment 1: Nonlocal perceptual memory
Figure 1D shows typical percept sequences for Experiment 1, for two different observers for each stimulus. Perception is indicated on the y-axes versus time on the x-axes. The orange curves indicate perception on consecutive presentations at the central, recurring location, whereas the blue curves denote perception at the twelve eccentric test locations, averaged across all twelve locations. For each observer/stimulus combination, we show two plots: a lower one showing the raw percept sequences and an upper one showing the same data but smoothed using a sliding window. As expected (see Methods section), many sessions were characterized by alternations between minute-long periods during which one percept was experienced on the great majority of presentations at the central location, and similar periods during which the alternative percept predominated (most obvious in the smoothed data; orange). Overall, this led to a proportion of percept repetitions from one central presentation to the next of 80%, and a relative lack of bias at the central location (the percept that was predominant at the central location for each individual observer was experienced on 67% and 68% (SFM and BR, respectively) of all central presentations). The blue curves, showing perception combined across all twelve peripheral locations, do not show such clear alternation cycles. As discussed in the Methods section, this relative absence of a slow alternation cycle at the peripheral locations is expected, given locally varying percept biases (Carter & Cavanagh, 2007) and the long separation between consecutive presentations at individual eccentric locations (almost a minute on average). Our objective was to investigate whether perceptual memory at the central location (orange curves in Figure 1D) spreads to eccentric locations (blue curves in Figure 1D) or, in other words, whether perception at the eccentric “test” locations would become entrained by the perceptual alternations at fixation. Such an entrainment is apparent in the data from individual sessions shown in Figure 1D. That is, although the eccentric locations (blue curves) show less ordered perception than the central location (orange curves), the two curves (blue and orange) within each plot are clearly not independent. To quantify the relationship between percepts at the recurring, central location and perception at the eccentric, test locations, we separated observer responses at the eccentric locations based on the immediately preceding percept at fixation. If central perceptual memory does not influence visual conflict resolution at peripheral locations, the probability of a rightward response at a peripheral location should be exactly the same whether it follows a left percept at fixation or follows a right percept at fixation. We denote these conditional probabilities of a peripheral rightward percept as P(RtestRcenter) and P(RtestLcenter). Note that we arbitrarily chose to depict probabilities of reporting rightward perception, and that probabilities of reporting leftward perception simply equal 1 minus the probabilities shown. 
If perceptual memory is local such that perceptual stabilization does not extend to peripheral stimulus positions, we should find that P( RtestRcenter) = P( RtestLcenter). The data depicted in Figure 2 show that this is clearly not the case. The left and right columns of this figure show the same analyses for SFM (left) and BR (right). In our discussion of this figure, we will focus on the SFM results, but BR results are similar in all respects. In Figure 2A, SFM data are collapsed across all eccentric stimulus positions and depict the probability of a rightward percept during eccentric stimulation, conditional on the preceding percept at the central location. The red and yellow bars represent P( RtestRcenter) and P( RtestLcenter), respectively, averaged across observers. The probability of perceiving rightward at a test location is significantly higher following a central rightward percept than following a central leftward percept (paired t-tests: t7 = 4.30, p < 0.002 and t5 = 2.76, p < 0.02, cylinder and binocular rivalry, respectively). The dashed lines in this figure depict individual observers' data, demonstrating the nonlocal nature of perceptual memory within each individual observer. A further control experiment confirmed that these results are not influenced by eye movements, as observers were able to refrain from making saccades to eccentric target locations ( Figure 3).
Figure 2
 
Experiment 1. (Left) SFM. (Right) BR. (A, D) Data averaged across eccentric location. After a rightward percept at fixation, the probability of a rightward percept in the periphery increases (red) compared to perception after leftward percepts at fixation (yellow). Individual observer data depicted with dashed lines, error bars depict ±1 SEM. (B, E) Polar plots depicting response patterns for six separate observers. Radial angle indicates test location; radius indicates p (rightward) at those locations after perceiving rightward (red) or leftward (yellow) at the fixation location, or irrespective of perception at the recurring location (black). Polar plots of all observers can be downloaded from pdf. (C, F) Probability of a rightward peripheral percept after a rightward central percept ( P( RtestRcenter)) against the probability of a rightward peripheral percept after a leftward central percept ( P( RtestLcenter)). Data for all positions and all observers plotted separately, the red shaded line is a grand moving average with bin width of 20. Different shades of green signify different observers. The diagonal histogram shows the same data collapsed onto the stabilization/destabilization axis, with the arrow denoting the average over locations and observers.
Figure 2
 
Experiment 1. (Left) SFM. (Right) BR. (A, D) Data averaged across eccentric location. After a rightward percept at fixation, the probability of a rightward percept in the periphery increases (red) compared to perception after leftward percepts at fixation (yellow). Individual observer data depicted with dashed lines, error bars depict ±1 SEM. (B, E) Polar plots depicting response patterns for six separate observers. Radial angle indicates test location; radius indicates p (rightward) at those locations after perceiving rightward (red) or leftward (yellow) at the fixation location, or irrespective of perception at the recurring location (black). Polar plots of all observers can be downloaded from pdf. (C, F) Probability of a rightward peripheral percept after a rightward central percept ( P( RtestRcenter)) against the probability of a rightward peripheral percept after a leftward central percept ( P( RtestLcenter)). Data for all positions and all observers plotted separately, the red shaded line is a grand moving average with bin width of 20. Different shades of green signify different observers. The diagonal histogram shows the same data collapsed onto the stabilization/destabilization axis, with the arrow denoting the average over locations and observers.
Figure 3
 
Gaze control experiment. Observers were instructed to fixate each stimulus as it appeared on the screen (bottom row), or to maintain fixation at the centrally displayed fixation mark (top row). The red squares indicate the size of the stimulus in these experiments. Gaze density plots clearly show that observers were well able to maintain fixation at the central fixation point, even when the stimulus was presented at a peripheral position (right column).
Figure 3
 
Gaze control experiment. Observers were instructed to fixate each stimulus as it appeared on the screen (bottom row), or to maintain fixation at the centrally displayed fixation mark (top row). The red squares indicate the size of the stimulus in these experiments. Gaze density plots clearly show that observers were well able to maintain fixation at the central fixation point, even when the stimulus was presented at a peripheral position (right column).
 
Figure 2B depicts data for three individuals, also for the SFM stimuli, but now not collapsed across eccentric locations. In these polar plots, the polar angle (the “time” on the clock face) indicates the location of an eccentric stimulus. The radius at a given angle denotes the probability of perceiving rightward at that particular test location; from “no rightward perception” indicated by a point in the origin to “only rightward perception” indicated by a maximal radius value of 1 or R. The black line indicates the probability of perceiving “rightward,” independent of the prior percept. The red and yellow curves, in contrast, indicate perception at the eccentric locations, separated depending on the preceding foveal percept. Plotting data for individual observers and locations in this way reveals the effects of both percept bias and perceptual memory: Chance probability of 0.5 (indicated by the gray dashed line) would be observed if both percepts dominated equally at a given location, deviations of the black line (the unconditional “rightward” probability, regardless of prior perception) from this chance perception of 0.5 are perceptual biases. Figure 2B shows that biases indeed exist and differ across locations within the same subject as well as across subjects. These idiosyncratic bias patterns were highly stable across sessions and did not correlate between BR and SFM stimuli. The modulatory influence of perceptual memory, on top of percept bias, is shown by the deviations of the colored curves, from the black line. The red and yellow curves indicate perception at the eccentric locations, separated depending on the preceding foveal percept. These curves show that spatial spread of perceptual memory occurs irrespective of these bias patterns, as the yellow curve (denoting P( R testL center) is inside the black one, whereas the red one (denoting P( R testR center)) runs outside of it. 
Nonlocal perceptual memory occurs in spite of individual biases. However, these biases play an important role in measuring nonlocal perceptual memory; stabilization effects have to be strong to overcome pronounced biases, becoming undetectable when bias reaches ceiling at a value of 0 or 1. This relationship is highlighted in the scatterplot of Figure 2C. Here P( R testR center) is plotted against P( R testL center) for all eccentric stimulus positions and observers. The diagonal dashed line indicates the line of no effect of central stabilization on eccentric perception. Points above this line signify a nonlocal perceptual memory where perception of the central stimulus predicts perception of the subsequent peripheral stimulus. The red moving average line in the scatterplot shows the greatest deflection from the (no effect) diagonal at halfway. Thus, the greatest effect of foveal perceptual memory on surrounding perception is observed when there is relatively little bias. The points near the bottom and top end of this graph, however, show only a modest effect of foveal perceptual memory, as these correspond to situations where extreme biases almost entirely determine peripheral perception. 
The overall effect of nonlocal perceptual memory is underscored by the frequency histogram in the top right corner of Figure 2C, which summarizes the scatterplot data across bias. Observations to the left on this axis indicate a spread of foveal stabilization to the eccentric locations. In agreement with our previous analyses, the mean of the distribution (black dashed arrow) lies to the left of center, indicating a significant transfer of perceptual memory across visual space ( p < 10 −7 for both BR ( df = 72) and SFM ( df = 96) when pooled across observers). 
Experiment 2: Spatial extent of nonlocal perceptual memory
One possible underlying mechanism for this nonlocal perceptual memory is that it is a high-level process involving cortical areas known to be involved in working memory tasks. This might be evidenced by a memory that applies a decision bias globally across the visual field, where the resolution of visual conflict at the fovea biases the system to make the same decision across the visual field. Another possibility is that perceptual memory is a low-level sensory process, whereby it spreads across the visual field but diminishes with distance from the stabilized position, due to the limited extent of the neuronal receptive fields involved. To distinguish between these two hypotheses, we modified the presentation paradigm of Experiment 1. Rather than on a virtual circle like in Experiment 1, eccentric test presentations were now placed on a virtual plus sign, centered on fixation (see Figure 4A). Each line included four test positions, two on each side of fixation. Similar to Experiment 1, stimulus presentation at a peripheral location was interleaved with presentation at fixation. This novel spatial arrangement allowed us to probe the falloff of perceptual memory with distance along the horizontal and vertical meridians of the visual field. In Figure 2, we quantified perceptual memory by plotting the probability of perceiving rightward tilt/rotation, both conditional on the preceding central percept being rightward, and conditional on the preceding central percept being leftward tilt/rotation. From Figure 4 onward, we quantify stabilization as the difference between these two conditional probabilities. Any nonzero value of this “stabilization” measure signifies nonlocal perceptual memory, uncontaminated by bias. Ceiling or floor effects occur when the bias for a given observer at a given location is so strong that he/she experiences only one percept at that location, regardless of prior percept history. Such effects can lead to an underestimation of the strength of perceptual memory (the “stabilization” value will lie closer to 0 than would otherwise be expected) but cannot introduce spurious perceptual memory effects (“stabilization” cannot be lifted away from 0 due to these ceiling or floor effects). These strong bias effects are demonstrated by points in the bottom left and top right corners of the ROC-type curves of Figures 2C and 2F. Using this measure of stabilization, Figure 4A clearly shows that perceptual memory spreads nonuniformly across the visual field, being strongest at the recurrent stabilization position and dropping off with increasing distance from this position.
Figure 4
 
(A) Right: Schematic for Experiment 2; recurring presentation was at fixation, and eight test locations were used, four on the horizontal meridian (blue) and four on the vertical meridian (red). Left: 3D figures illustrate the spatial extent of stabilization. Stabilization is quantified as the chance of a rightward percept after a rightward percept at the recurring location minus the chance of a rightward percept after a leftward percept at the recurring location, or P( R testR center) − P( R testL center). Positive values indicate stabilization, zero indicates no effect, and negative values indicate destabilization. This measure compensates for effects of bias at any position in the visual field. Perceptual memory, as indexed by stabilization on the z-axis, falls off with distance from fixation. Values are averages across observers, error bars on each point indicate ±1 SEM. (B) Spatial spread is greater for SFM than for BR, as indicated by these Bezier curves connecting the means across subjects and directions for the sampled eccentricities. Vertical arrows indicate the point at which the fit reaches half its maximum. Standard errors are smaller than line width, arrows indicate the eccentricity at which the spline function reaches half its maximum.
Figure 4
 
(A) Right: Schematic for Experiment 2; recurring presentation was at fixation, and eight test locations were used, four on the horizontal meridian (blue) and four on the vertical meridian (red). Left: 3D figures illustrate the spatial extent of stabilization. Stabilization is quantified as the chance of a rightward percept after a rightward percept at the recurring location minus the chance of a rightward percept after a leftward percept at the recurring location, or P( R testR center) − P( R testL center). Positive values indicate stabilization, zero indicates no effect, and negative values indicate destabilization. This measure compensates for effects of bias at any position in the visual field. Perceptual memory, as indexed by stabilization on the z-axis, falls off with distance from fixation. Values are averages across observers, error bars on each point indicate ±1 SEM. (B) Spatial spread is greater for SFM than for BR, as indicated by these Bezier curves connecting the means across subjects and directions for the sampled eccentricities. Vertical arrows indicate the point at which the fit reaches half its maximum. Standard errors are smaller than line width, arrows indicate the eccentricity at which the spline function reaches half its maximum.
 
Experiment 3: The spread of peripheral perceptual memory
An alternative interpretation of the results of Experiment 2 is that perceptual memory decreases into the periphery, rather than dropping off with distance from the stabilized position per se. To investigate this possible confound of visual eccentricity and distance to the position at which perceptual memory is instilled, we conducted an extra experiment. In this experiment, we presented the recurring stimulus in the upper right visual quadrant, and “test” stimuli in an arrangement of two straight lines, downward and leftward from the point of recurring stimulus presentation (see Figure 5A). Thus, we tested (1) whether the strength of stabilization is the same as it was in the fovea and (2) the drop-off from this more eccentric recurrent location. The data, shown in Figure 5, indicate that perceptual memory in the periphery (orange markers in Figures 5B and 5C at approximately 70–80%) is as strong as it is at fixation (compare with Figure 4, where values are also in that range). Furthermore, the decay of peripheral memory corresponds closely with the falloff of foveally instigated perceptual memory ( Figure 4). As in the previous experiment, the memory for the bistable cylinder spreads further than binocular rivalry memory.
Figure 5
 
Experiment 3. (A) Relative positions of stimulus presentation and fixations, and stabilization data in screen coordinates. Stabilization is quantified as before (see Figure 4 legend). The layout of the stimulus presentations in Experiment 3. (B) Results for binocular rivalry, averaged across 6 observers. (C) Results for bistable cylinder, averaged across 7 observers.
Figure 5
 
Experiment 3. (A) Relative positions of stimulus presentation and fixations, and stabilization data in screen coordinates. Stabilization is quantified as before (see Figure 4 legend). The layout of the stimulus presentations in Experiment 3. (B) Results for binocular rivalry, averaged across 6 observers. (C) Results for bistable cylinder, averaged across 7 observers.
 
Experiment 4: Spatiotopic/retinotopic perceptual memory
Having determined that perceptual memory is nonlocal yet limited in its spatial extent, we now ask, what coordinate frame does this memory operate within? In other words, does stabilization occur in lower, retinotopic areas of the brain or higher level areas representing space as referenced to the surrounding world or the head? In a final experiment, we used changes in gaze position to investigate whether transfer of perceptual memory occurs according to retinal coordinates or, alternatively, relative to exogenous spatial locations, irrespective of retinal location. 
The stimulation sequence again consisted of interleaved test presentations at eccentric locations and recurring presentations at the central location. Test stimuli could occur at four different locations, two above and two below fixation ( Figure 6A). On half of the trials, observers were prompted, after the central stimulus disappeared, to shift their gaze to a new location before the test was presented. On those saccade trials, which were randomly chosen during a session, there were different potential test locations than on no-saccade trials. These different test locations were shifted, relative to the four original test locations, to match the shift in fixation. Thus, in retinal coordinates these test locations were exactly aligned with test locations around the original fixation position. A retinotopic implementation of perceptual memory would therefore predict identical patterns for tests around the stabilization fixation position and test around the novel fixation position. In spatiotopic coordinates, however, a test location right next to the new fixation location could be far away from the previous fixation location, where perceptual memory had been built up ( Figure 6A, top). Following the disappearance of a test stimulus, fixation always returned to the original position. Thus, the recurring central stimulus always appeared in the same location both spatiotopically and retinotopically.
Figure 6
 
Experiment 4. (A) Orange lines depict the amount of perceptual memory at locations sampled around the position of stabilization, blue lines show the data sampled at positions around the novel fixation location. The gray dashed line shows the prediction (monotonically extrapolated) if perceptual memory effects spread according to spatiotopic location. (B) Same data as in (A) but aligned in retinal coordinates. (C) SFM data.
Figure 6
 
Experiment 4. (A) Orange lines depict the amount of perceptual memory at locations sampled around the position of stabilization, blue lines show the data sampled at positions around the novel fixation location. The gray dashed line shows the prediction (monotonically extrapolated) if perceptual memory effects spread according to spatiotopic location. (B) Same data as in (A) but aligned in retinal coordinates. (C) SFM data.
 
For BR, the data at the novel fixation location (blue lines) clearly deviate from the spatiotopic prediction, which is indicated in Figure 6A by the gray dashed continuation of the orange line. This is especially clear when we replot our data in retinotopic coordinates ( Figure 6B). The shapes of the curves for original and novel fixation positions are almost identical apart from a small nonsignificant decrement in effect size after relocated fixation, which may relate to a detrimental effect of the saccadic transient on stabilization (Ross & Ma-Wyatt, 2004). Figure 6C shows a very similar outcome for SFM, again demonstrating an almost perfect overlap in retinotopic but not spatiotopic coordinates. These data thus support an implementation of perceptual memory in retinotopically organized cortical areas. 
Discussion
We have demonstrated that perceptual memory has a nonlocal component, influencing retinal locations not stimulated by the original stimulus. This influence spans distances of up to about two degrees of visual angle close to the fovea but falls off with distance. Furthermore, the effects are determined by retinal location, rather than being specific to locations in external space. Moreover, the rate of falloff with distance is different for binocular rivalry than for structure from motion. 
A previous study of the spatial extent of perceptual memory (Chen & He, 2004) concluded that perceptual memory is “retinotopically specific and local,” which appears at odds with our findings. However, the data from the two papers are not in conflict, for two reasons. Chen and He (2004) investigated perception of an ambiguous stimulus (either BR or SFM) presented alternately to two different retinal locations. They examined the probability that perception would switch across two consecutive presentations at different retinal locations, using as a baseline the same probability for consecutive presentations within a single location. This method suffers from influences of perceptual bias, both because the within-location baseline overestimates the strength of local perceptual memory (the number of switches is reduced by bias at the baseline location), and because the across-location probability depends, in part, on bias differences between the two locations that are stimulated (cf. Figure 2). Indeed, an influence of bias in suggested by the fact that the probability of percept switching across two locations is around 80% in most of the conditions in Chen and He's (2004) study (their Figures 2 and 3), where 50% would be expected if the two locations stimulated in alternation were not biased (with values below 50% being indicative of either nonlocal perceptual memory or similar biases at the two locations, and values above 50% being indicative of opposing biases at the two locations). In addition to a potential role of bias, we are aware that the stimuli used by Chen and He (2004) lay further apart (2.8 degrees and 4 degrees center-to-center distance for BR and SFM, respectively) than our recurring stimulus and the test stimuli (1.35 and 2 degrees maximum for the two types of stimuli, respectively). Given the falloff of perceptual memory effects with distance (Figures 5 and 6), it is well possible that stimuli at the distances used by Chen and He (2004) do not show perceptual memory interactions even after correcting for bias effects. 
The occurrence of strong, observer-specific patterns of percept preference across the visual field, known to occur for binocular rivalry (Carter & Cavanagh, 2007) and now replicated for binocular rivalry and newly demonstrated with bistable cylinders, is striking, and we may speculate as to its origins. An interesting possibility, requiring further study, is that these patterns may reflect spatial anisotropies at low levels of visual cortex. These anisotropies could, for instance, stem from the random sampling that the retinal cone array provides (Chui, Song, & Burns, 2008; Roorda & Williams, 1999), and vascular scotomas (Adams & Horton, 2003). This uneven sampling would then propagate upward from the retina to visual cortex (Ringach, 2007), where it could influence perceptual decision-making. Whatever the origin of the bias patterns found in our experiments, their existence testifies to the sensitivity of the binary choice that the brain is forced to make at the onset of an ambiguous visual stimulus (Noest, van Ee, Nijs, & van Wezel, 2007) as ongoing rivalry exhibits much weaker effects of these biases (Carter & Cavanagh, 2007). 
Our eye movement recordings of Figure 4 indicate that fixation was sufficiently accurate to exclude any retinal overlap between the recurring stimulus and the test stimuli of Experiment 1 ( Figure 2), as well as between the recurring stimulus and the outermost test stimuli of the remaining experiments ( Figures 46), which were all located at 2 degrees of the recurring stimulus (center to center). However, we cannot exclude some degree of retinal overlap in Experiments 2 through 4 ( Figures 46) between the recurring stimulus and the innermost test stimuli. This means that, quantitatively, the estimated slope of the falloff of perceptual memory with distance, shown in Figures 46, might be somewhat shallower than if fixation were perfect, amounting to a potential overestimation of the degree of retinal spread. This does not, however, affect any of our main conclusions: that perceptual memory influences retinal locations noncontiguous with the location where it was elicited ( Figures 2, 4, 5, and 6) yet does fall off with distance ( Figures 46); that this falloff occurs in a retinal reference frame ( Figure 6); and that it is steeper for binocular rivalry than for structure from motion ( Figures 4B and 5). 
Our results demonstrate a perceptual memory that spreads outside the locus where it arose, but with a distinct falloff as distance increases. One can envision how such a memory system could facilitate perceptual function. During our visual explorations of the world, we actively and continually use eye movements to foveate particular items of interest (Buswell, 1935; Najemnik & Geisler, 2005). When freely examining a scene, human observers' fixation positions show very strong clustering. This repeated sampling of the same scene elements is influenced by task demand (Yarbus, 1961) and draws on low-level visual saliency, which forms a strong and relatively stable guide of eye movements within a scene (Itti & Koch, 2001). Thus, typical fixation patterns show clustering within areas and the inherent endpoint variability of directed eye movements contributes to spread within these clusters (van Beers, 2007). Given this pattern of visual exploration behavior, there is a clear potential benefit from a retinotopically organized system that transfers information from previously stimulated retinal locations to the immediate vicinity. The system characterized in the present work would be ideally suited to fulfill such a function. 
Our results provide strong evidence that perceptual memory of ambiguous stimuli draws on mechanisms in lower visual cortex. Whereas a higher level, global type of memory might be expected to apply uniformly to the entire visual field, the falloff of memory with retinal distance that we demonstrate suggests a substrate in retinotopically organized lower visual areas. Particularly striking in this respect is the observed difference in spatial dispersion of perceptual memory between binocular rivalry and bistable cylinders, despite using identical stimulus sizes for both types of stimuli. If we think of perceptual memory as a sensory phenomenon, this difference can be associated with differences in the sensory neural circuitry involved in mediating perceptual conflict resolution within both stimuli. For binocular rivalry, conflict resolution has been proposed to occur at a low cortical level (near the point of binocular convergence in V1). Although not undisputed (Leopold & Logothetis, 1996; Logothetis, Leopold, & Sheinberg, 1996), this idea is supported by data from fMRI (Lee, Blake, & Heeger, 2004; Polonsky, Blake, Braun, & Heeger, 2000; Tong & Engel, 2001) and psychophysics (Wilson, Blake, & Lee, 2001). A recently formulated compromise states that rivalry occurs at multiple levels simultaneously (Tong, Meng, & Blake, 2006). For bistable cylinders, the neural correlate of perceptual conflict resolution is thought to be at a higher, extrastriate, level in the visual hierarchy that is involved in the appreciation of structure from motion, such as the medial temporal area (MT; Brouwer & van Ee, 2007; Parker & Krug, 2003). The large difference in spatial dispersion of perceptual memory observed here fits with known differences between receptive field sizes in, for example, V1 and the medial temporal area (MT; Born & Bradley, 2005). 
An involvement of lower visual areas in perceptual stabilization is consistent with various previous results (Chen & He, 2004; Pearson & Brascamp, 2008). For instance, it corresponds well with the facts that multiple distinct bistable stimuli will elicit multiple independent memory traces when interleaved with one another (Maier et al., 2003), and that perceptual memory appears to be highly specific for stimulus properties such as orientation, color and in the case of binocular rivalry, eye-of-origin information (Pearson & Clifford, 2004). Other lines of evidence have pointed to a more high-level kind of memory, such as an interaction between perceptual memory and attention (Kanai & Verstraten, 2006), and the implication of higher level frontal areas in an fMRI study of perceptual memory (Sterzer & Rees, 2008). However, the present results provide evidence in favor of a low-level sensory account, by demonstrating properties of perceptual memory that are readily reconciled with known properties of lower level, but not higher level, cortical areas. 
Acknowledgments
This work was supported by a Worldwide Universities Network Fellowship to TK and JB. EWG was supported by BBSRC Grant Number BB/E012698/1. 
Commercial relationships: none. 
Corresponding author: Tomas Knapen. 
Email: tknapen@gmail.com. 
Address: Laboratoire Psychologie de la Perception, Université Paris Descartes, Paris, France. 
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