Free
Article  |   June 2011
Spatiotemporal averaging of perceived brightness along an apparent motion trajectory
Author Affiliations
Journal of Vision June 2011, Vol.11, 5. doi:10.1167/11.7.5
  • Views
  • PDF
  • Share
  • Tools
    • Alerts
      ×
      This feature is available to authenticated users only.
      Sign In or Create an Account ×
    • Get Citation

      Takehiro Nagai, R. Dirk Beer, Erin A. Krizay, Donald I. A. MacLeod; Spatiotemporal averaging of perceived brightness along an apparent motion trajectory. Journal of Vision 2011;11(7):5. doi: 10.1167/11.7.5.

      Download citation file:


      © ARVO (1962-2015); The Authors (2016-present)

      ×
  • Supplements
Abstract

Objects are critical functional units for many aspects of visual perception and recognition. Many psychophysical experiments support the concept of an “object file” consisting of characteristics attributed to a single object on the basis of successive views of it, but there has been little evidence that object identity influences apparent brightness and color. In this study, we investigated whether the perceptual identification of successive flashed stimuli as views of a single moving object could affect brightness perception. Our target stimulus was composed of eight wedge-shaped sectors. The sectors were presented successively at different inter-flash intervals along an annular trajectory. At inter-flash intervals of around 100 ms, the impression was of a single moving object undergoing long-range apparent motion. By modulating the luminance between successive views, we measured the perception of luminance modulation along the trajectory of this long-range apparent motion. At the inter-flash intervals where the motion perception was strongest, the luminance difference was perceptually underestimated, and forced-choice luminance discrimination thresholds were elevated. Moreover, under such conditions, it became difficult for the observer to correctly associate or “bind” spatial positions and wedge luminances. These results indicate that the different luminances of wedges that were perceived as a single object were averaged along its apparent motion trajectory. The large spatial step size of our stimulus makes it unlikely that the results could be explained by averaging in a low-level mechanism that has a compact spatiotemporal receptive field (such as V1 and V2 neurons); higher level global motion or object mechanisms must be invoked to account for the averaging effect. The luminance averaging and the ambiguity of position–luminance “binding” suggest that the visual system may evade some of the costs of rapidly computing apparent brightness by adopting the assumption that the characteristics of an object are invariant over successive views.

Introduction
Objects are critical functional units for many aspects of visual perception and recognition and play a key role in visual processing. For example, visual attention can be directed not only to interesting spatial locations or visual features but also to interesting objects (Blaser, Pylyshyn, & Holcombe, 2000; Schoenfeld et al., 2003), and objects are important units in determining the dominance in binocular rivalry (Mitchell, Stoner, & Reynolds, 2004). These studies suggest that objects are important functional units in visual information processing. Accordingly, we might reasonably expect that perception may integrate the successive views of what is seen as a single object, and there is evidence of such integration even when the successive views are quite distinct in the retinotopic representation (Shimozaki, Eckstein, & Thomas, 1999). 
In order to update the perceptual representation of objects under changes in the retinal input, information pertaining to successive views of the same object must be collected. The repository for information considered relevant to a particular object has been referred to as an “object file” (Kahneman & Treisman, 1984; Kahneman, Treisman, & Gibbs, 1992). Kahneman et al. (1992) conducted psychophysical experiments about preview benefit in letter identification. In one of their experiments, two squares that contained different letters (preview letters) were presented at different locations framed by boxes (the preview display), and then the letters disappeared. After that, the framing boxes were shown moving to independent locations. Finally, a letter (the target letter) was again presented in either of the two (now displaced) framing boxes. The observer stated what the target letter was after stimulus presentation. Not surprisingly, the response time was longest when the target letter was different from both of the preview letters. More interestingly, when the target letter was the same as either of the preview letters, the response time was shorter when the target letter and the preview letter were linked to the same framing box by the motion than when they were not. This result showed that there was an object-specific preview benefit in letter recognition, because there was a preview benefit despite the spatial position change of the box. To explain this preview benefit, Kahneman et al. invoked the idea of an object file, which is an episodic representation created for each object and which retains features of it. This object file can explain their results as follows. Different object files were created for the two boxes in the preview display and retained the letter information. The target letter identification task benefited from reviewing the contents of the object file when the target letter was the same as the preview letter linked by the motion. However, if the letters were different, the preview and target boxes were seen as distinct objects and a new object file was created; hence, it took a longer time for letter identification. This object file could lead to economy of computational resources. Many studies also have examined the role of the object file on different kinds of recognition tasks (Gordon & Irwin, 2000; Wolfe & Bennett, 1997). 
Could objects affect the low-level sensory attributes such as brightness or color as well as recognition tasks? There have been only a few studies that have investigated this issue. Shimozaki et al. (1999) showed the effects of object identity on apparent luminance with experiments similar to those of Kahneman et al. (1992). In their experiment, two squares with different luminances were presented in a first display, and then the two squares were again presented at different positions shifted to the right or left of the first squares, yielding apparent motion. The observer was asked to judge the luminance difference of the two squares in the second display. In the results, the judgments were biased by the luminance of the squares in the first display. Their results can be interpreted as follows: the luminance information of the squares in the first display was stored in object files, and the judgment of the square luminances in the second display was based not only on the physical information of the current squares but partly on the luminance information retained in the object files. Although their results support the effect of object identity on perceived brightness, they did not quantitatively measure the object reviewing effect on perceived brightness. 
The other phenomenon possibly supporting the effect of object identity on perceived brightness and color is color integration along a motion trajectory (Nishida, Watanabe, Kuriki, & Tokimoto, 2007; Watanabe & Nishida, 2007). In the experiments of Nishida et al. (2007), the color of a moving bar rapidly alternating between two colors was perceptually mixed (e.g., a moving bar with alternation between green and red looked yellow). This demonstrates that different colors are integrated not only in the same retinal location but also along a motion trajectory. It is likely that the same applies to luminance and that lightness and color in a single object are spatiotemporally integrated along the trajectory of motion. 
However, the stimulus of Nishida et al. had only a small gap in both space and time during the successive frames of the color alternation. Their results, therefore, relate to “short-range” apparent motion (Braddick, 1974) and may reflect integration of stimulus energy within the oriented space–time receptive fields of low-level (V1 or V2) directionally selective neurons (Gegenfurtner, Kiper, & Fenstemaker, 1996; Tamura, Sato, Katsuyama, Hata, & Tsumoto, 1996). 
In the current study, our stimulus was made up of wedges or sectors that underwent “long-range” apparent motion as they were presented consecutively in static brief flashes at widely separated positions on a circular trajectory of motion (Figure 1). The spatial steps of the apparent motion were large enough to prevent integration within small spatiotemporal receptive fields. The rotation rate could be varied by manipulating the inter-flash intervals between successive presentations of the wedge. If the inter-flash intervals of wedge presentations were very long, the observer perceived 8 different static wedges, appearing successively (with some suggestion of apparent motion at the moments of transition but no strong impression of progressive rotation); at very short inter-flash intervals, the revolution of the wedge was rapid enough to create the impression that all wedges were simultaneously present, with some flickering. The observer could perceive a single object moving smoothly around the circle only at intermediate inter-flash intervals. Thus, the inter-flash interval could control the strength of object and apparent motion perception. We investigated the effect of object perception on perceived brightness with this stimulus. 
Figure 1
 
Stimulus used in our experiments. The 8 wedges were not presented simultaneously in the main experiments but were presented in rotation with a range of inter-flash intervals.
Figure 1
 
Stimulus used in our experiments. The 8 wedges were not presented simultaneously in the main experiments but were presented in rotation with a range of inter-flash intervals.
Experiment 1: Matching
We first examined the effects of object or apparent motion perception on the brightness perceived when the wedge became successively light and dark as it “moved” around the circle. As we have noted, it is possible that the visual system tends to average feature values over successive views of the same object in the interests of perceptual stability. Any such assumption of object constancy would lead to a perceptual regression toward constant brightness and to underestimation of real luminance differences among the successively presented wedges. 
Methods
Apparatus
The stimulus was presented on a CRT monitor (Iiyama Vision Master Pro 514, 100 Hz) controlled by a Cambridge Research System VSG2/3 and a PC with Windows XP. We calibrated the gamma characteristics of the CRT monitor with a computer-interfaced photometer (UDT Instruments UDT S370) and the spectral properties with a Photo Research PR650 spectroradiometer. The observers viewed the screen at a distance of 57 cm except for observer MN, who viewed it from 85 cm, but the head of the observer was not strictly fixed during the experiment. The observer was required to fixate a center cross on the screen during a trial, though the eye movements were not monitored. 
Observers
Two observers from the authors and 2 naive observers participated in Experiment 1. All of them had normal acuity or corrected normal acuity and normal color vision. 
Stimulus
The stimulus is shown in Figure 1. It consisted of 8 wedges presented counterclockwise in sequence on a black (0.7 cd/m2) background. The wedge was a sector from a centrally fixated annulus with an inner radius of 5.9 deg and an outer radius of 12.7 deg for most observers (57-cm viewing distance) but scaled down by 2/3 at MN's greater viewing distance. The center angle of the wedges was 28 deg. For brightness matching, a circular reference disk of adjustable luminance with a radius of 2.9 deg appeared at the center of the screen. There was a fixation cross (73.3 cd/m2, 0.4 deg) at the center of the screen. 
The wedge was flashed for only one 10-ms video frame at a time at each of its positions, and the inter-flash interval between these successively flashed views varied over trials. The stimulus was expected to appear as unrelated flashes at different positions when the inter-flash interval was very long and as 8 wedges existing simultaneously when the inter-flash interval was very short. On the other hand, when the interval was moderate, the stimulus appeared as a single wedge moving along the circular trajectory. We used 4 inter-flash intervals: 0, 30, 150, and 630 ms. These inter-flash intervals correspond to motion velocities of 100, 25, 6.25, and 1.56 jumps/s, respectively, or 12.5, 3.1, 0.8, and 0.2 revolutions/s, respectively. This range of intervals used spans the range for best apparent motion, which as we show below occurred for jump rates close to 10/s, or just over 1 revolution/s. The local repetition rate in Hertz is the same as the revolution rate. 
During its circuit, the wedge appeared successively at the 4 possible major axis positions interleaved with 4 diagonal positions. The luminances of the 4 diagonal wedges were identical, and those of the 4 major axis wedges (the ones aligned vertically or horizontally with the center of rotation) were also identical in a trial. However, the luminances of the diagonal and major axis wedges were markedly different. A luminance of 36.6 cd/m2 was randomly assigned to either the major axis locations or the diagonal locations, and the other locations were presented at 7.3 cd/m2. These luminances were 0.5 times and 0.1 times the maximum luminance of the monitor (73.3 cd/m2), respectively. The stimulus chromaticity was equal energy white for the standard observer whose cone fundamentals are described in Stockman, MacLeod, and Johnson (1993) and based on Stiles and Burch 2-deg color matching functions (Stiles & Burch, 1955); the only exception was in Experiment 5, in which chromaticity of the stimulus was an experimental parameter. In our results, stimulus luminance is represented as Y, scaled so that Y = 1 represents the maximum available equal energy white luminance, Y = 0.5 for the bright wedge luminance, and Y = 0.1 for the dark wedge luminance. 
Preliminary experiment: Effect of motion velocity on single vs. multiple object perception
As noted, the impression of a single object in motion occurs only at intermediate rotation rates. In a preliminary experiment, we determined which motion velocity gave the strongest impression of a single object in motion, an impression we call “objectness” for brevity. 
The observer adjusted the inter-flash interval (the number of video frames) between wedge flashes during the stimulus presentation while fixating the fixation cross. Each observer made 16 settings of maximum objectness. In the results, the mean motion velocity corresponding to the strongest objectness impression across the successive views was 9.36 jumps/s, a value within the range of our 4 motion velocities. The impression of a single object was accompanied by an optimal or nearly optimal impression of apparent motion at this intermediate velocity. This is consistent with much previous research indicating that a moderate separation in time and space is important for large-scale apparent motion perception (e.g., Burt & Sperling, 1981; Gepshtein & Kubovy, 2007). We refer to the motion velocity corresponding to the strongest perception of a single object as the “optimal object-persistence velocity” (or OOPV for brevity). Since the main factor determining object persistence is not surface features but spatiotemporal configuration information (Kahneman et al., 1992; Mitroff & Alvarez, 2007), we can reasonably expect that the OOPV is almost invariant whether there is a luminance difference between wedges or not. 
Procedure
In the main experiment, the stimulus was automatically set in motion from the start of a trial and continued to move until the observer responded. There were two kinds of trials: light match trials and dark match trials. The diagonal wedges were lighter than the major axis wedges in a light match trial, and vice versa in a dark match trial. The observer adjusted the luminance of the central reference disk by moving a mouse cursor until its brightness matched that of the diagonal wedges. After the adjustment was finished, the observer pressed a mouse button and the trial was done. 
There were 20 trials for each combination of 2 kinds of matches and 4 motion velocities in a session, corresponding to 160 trials in total. Each observer conducted a session. 
Results and discussion
The mean matched luminance of the matching blob for each type of trial (light match and dark match) was calculated from the experimental results. Since we were mainly interested in the perceived brightness difference between the light wedges and dark wedges, we subtracted the mean matched log luminance for the dark match trials from that for the light match trials; the calculated results show the perceived brightness difference expressed in terms of the matching luminance Y
The results for four observers are shown by the four continuous lines, one line for each observer, in Figure 2. The horizontal axis shows the motion velocity expressed as flashes per second. The vertical axis shows the difference between the light and dark matched log10(Y) values; thus, the ordinate for a physical luminance match would be log10(0.5/0.1) or 0.7 (the horizontal bold line in Figure 2), with greater values indicating a contrast effect and lower ones indicating an assimilation or perceptual averaging of the light and dark values. The gray vertical bar represents the “optimal object-persistence velocity” (OOPV; see Preliminary experiment: Effect of motion velocity on single vs. multiple object perception section above) and its width spans the 95% confidence interval for the OOPV. We used a log scale of luminance because in the domain of the Weber–Fechner law, just noticeable differences in brightness correspond to approximately equal increments in log luminance rather than linear luminance. 
Figure 2
 
Results of Experiment 1. The solid lines are the results of the main experiment, and the dashed lines are the results of the complementary control experiment in which all the wedges flashed simultaneously. The difference between log luminance (log Y) matched to the light wedges and that to the dark wedges is shown on the ordinate axis. The error bar represents ±1 standard error of mean. The gray vertical bar represents the 95% confidence interval for the motion velocity where single object perception is strongest. The horizontal bold line represents the expected result if the observer matches the brightness based on physical luminances.
Figure 2
 
Results of Experiment 1. The solid lines are the results of the main experiment, and the dashed lines are the results of the complementary control experiment in which all the wedges flashed simultaneously. The difference between log luminance (log Y) matched to the light wedges and that to the dark wedges is shown on the ordinate axis. The error bar represents ±1 standard error of mean. The gray vertical bar represents the 95% confidence interval for the motion velocity where single object perception is strongest. The horizontal bold line represents the expected result if the observer matches the brightness based on physical luminances.
At the fastest and slowest rotation rates, where there was no strong impression of progressive rotation, the ratio of luminances chosen for a match was close to the veridical value of 0.7. However, at a velocity of 6.25 jumps/s (0.80 log jumps/s), the velocity closest to the OOPV, brightness differences between the light and dark wedges were severely underestimated: the average difference in log matching luminance was 0.33, corresponding to a ratio of matching luminances of 2.1:1 instead of 5:1. This result may support the idea of a perceptual regression toward constant brightness in the moving object. 
These results remain equivocal in one respect. In our experiment, the local flash frequency was necessarily confounded with the motion velocity. The underestimation of luminance difference near the OOPV might be due to an influence of the local flash frequency. We ran a control experiment to check this point. The stimulus was identical to that in Experiment 1 except that all 8 wedges were flashed simultaneously, with the same local flash frequency as in Experiment 1. The results are shown by dashed lines in Figure 2. The brightness difference in the control experiment did not decrease at the intermediate frequency but instead decreased monotonically as the frequency increased. The difference between the results of Experiment 1 and the control experiments supports the interpretation that the luminance difference compression near the OOPV in Experiment 1 was due to the apparent motion seen at those velocities. 
In Figure 2, the matches made in synchronous presentation (dashed lines) at all but the highest repetition rates deviate from luminance matches in the way expected owing to simultaneous contrast, and as expected, this contrast effect is hardly apparent in the sequential presentation results for the lowest repetition rate (continuous curves, leftmost points). Assimilation or averaging of successive views is evident where the continuous lines fall below the heavy horizontal line in Figure 2; this occurs only at the repetition rate closest to the OOPV (and the net assimilation bias there, though substantial, is clear for only 3 of the 4 observers). At 25 jumps/s (1.4 log jumps/s), non-veridical matching in the contrast direction (a difference in log luminance exceeding 0.7) was marked in both the experimental (sequential) and control (synchronous) conditions. This is understandable since the sequential and synchronous presentations are both affected by simultaneous contrast when the presentation rate becomes sufficiently high. 
The luminance difference compression could not originate from integration by low-level neurons with small spatiotemporal receptive field such as V1 and V2 neurons (Gegenfurtner et al., 1996; Tamura et al., 1996), because the width between the wedges (1.7–3.5 deg) was large enough to eliminate almost all the effects of adjacent stimuli on neurons with the small receptive fields characteristic of V1 and V2 (Levitt, Kiper, & Movshon, 1994; Snodderly & Gur, 1995). As discussed below, this suggests that the luminance difference underestimation originates from a higher level mechanism that combines multiple targets into a single object with apparent motion; this process need not be necessarily based on voluntary attentional tracking, since it could equally be an automatic part of the operation of motion-sensing mechanisms. 
Experiment 2: Distinct differences; role of background
Experiment 1 revealed that suprathreshold brightness fluctuations were underestimated near the OOPV. We might, therefore, expect that the luminance difference necessary to perceive a distinct brightness difference would be larger near the OOPV. In Experiment 2, we measured the luminance difference necessary to clearly perceive a brightness difference at different motion velocities. 
Methods
The spatial configuration of the stimulus was identical to Experiment 1, except that it did not have the central matching blob but only the wedges and the fixation cross. The luminances of the 4 diagonal wedges were identical, and those of 4 major axis wedges were also identical in a trial as in Experiment 1. The luminance of the major axis wedges was 22.0 cd/m2, and the observer adjusted that of the diagonal wedges during a trial. Each wedge was presented for 10 ms at a time as in Experiment 1. We used 8 inter-flash intervals: 0, 10, 30, 70, 150, 310, 630, and 1270. These inter-flash intervals correspond to different motion velocities: 100, 50, 25, 12.5, 6.25, 3.13, 1.56, and 0.78 jumps/s, respectively. 
The stimulus automatically started and continued to move until the observer responded. The observer was required to fixate the fixation cross during a trial as in Experiment 1. Experiment 2 also had 2 kinds of trials: light trials alternated with dark trials. At the start of a trial, the luminances of the major axis and diagonal wedges were identical. The observer adjusted the luminance of diagonal wedges to the light direction in a light trial, or to the dark direction in a dark trial, by moving a mouse cursor until the brightnesses of diagonal and major axis wedges were perceived as “clearly different.” The intent was to define the upper limit of the range of uncertainty in discrimination, a higher criterion for discrimination than the threshold. The observer pressed a mouse button when satisfied with the adjustment. 
There were 20 trials for each combination of the 2 adjustment directions and the 8 moving velocities in a session. Each observer conducted a session. Two authors participated in Experiment 2 as observers. 
Results and discussion
The results of Experiment 2 are shown by the continuous curves in Figure 3a. The motion velocity is shown on the horizontal axis, and the adjusted luminance of the diagonal wedges (expressed as a fraction of the maximum luminance available) is shown on the vertical axis. The bold horizontal line represents the luminance of the major axis wedges. The plots in the upper half of the graph are the results of the light trials, and those in the lower half are the results of the dark trials. Each symbol corresponds to each observer's result. The vertical gray bar shows the confidence interval of the motion velocity corresponding to the strongest “objectness.” 
Figure 3
 
(a) Results of Experiment 2. The solid lines are the results of the main experiment, and dashed lines are the results of the complementary experiment in which all the wedges flashed simultaneously. The luminance (Y) value of the diagonal wedges that were just clearly lighter or darker than the major axis wedges is shown on the ordinate. The bold horizontal line represents the Y value of the major axis wedges. The error bar represents ±1 standard error of mean. (b) Results of the main experiment repeated with a white background instead of a dark background.
Figure 3
 
(a) Results of Experiment 2. The solid lines are the results of the main experiment, and dashed lines are the results of the complementary experiment in which all the wedges flashed simultaneously. The luminance (Y) value of the diagonal wedges that were just clearly lighter or darker than the major axis wedges is shown on the ordinate. The bold horizontal line represents the Y value of the major axis wedges. The error bar represents ±1 standard error of mean. (b) Results of the main experiment repeated with a white background instead of a dark background.
The continuous curves in the upper half plots tend to increase, and in the lower half plots to decrease, near the OOPV and, particularly, slightly below the OOPV. This result means that more luminance difference was needed for the observer to clearly perceive a brightness difference. As in Experiment 1, we conducted a control experiment in which all the wedges flashed simultaneously. The results are the dashed lines in Figure 3a. Here as in Experiment 1, the results of the control experiment do not suggest the reduced discrimination near the OOPV seen in the main results—only a slight monotonic trend in sensitivity (which is the same in sensitivity direction for the light and dark trials). Thus, the results of Experiment 2 and its control support those of Experiment 1 in suggesting that spatiotemporal integration process for apparent motion makes fluctuations less salient when they are associated with a single moving object. 
In the experiments described thus far, the wedges appeared in a dark surround. Presentation in a uniform and unvarying light surround creates a very different situation. The wedges have more of a real object quality instead of being perceived as self-luminous. Unlike the black background, the luminance of the white background can serve as an “anchor” for brightness perception (Gilchrist et al., 1999): that is, the observer can see a small brightness difference from the white background by adopting the background as a brightness reference, whereas the black background provides no such reference. 
In order to test whether the effects described are still observed when the stimulus appears against a light background, we repeated Experiment 2 with a white background of the maximum available luminance (73.3 cd/m2) instead of the dark background. Note that the background luminance itself corresponds to an ordinate of 1 in the figure. Thus, the wedges were always darker than the ground, the reference wedges being 30% of the background luminance. Despite the availability of a contrast cue, the results (Figure 3b) again show underestimation of luminance difference near the OOPV. Indeed, the darkened wedge views can be brought close to black without becoming obviously darker than the reference views. Rather similarly, for adjustments in the lightward direction, the match with the reference at the OOPV held until the lightened wedges became low in contrast relative to the surround. 
Experiment 3: Forced-choice discrimination and occlusion
Although Experiments 1 and 2 both indicated that apparent motion and object perception influenced perceived brightness, the judgments involved were not very well defined. For example, in Experiment 1, observers reported that it was difficult to extract an instantaneous brightness estimate from the moving wedges to match with the matching blob, especially at velocities near the OOPV. In Experiment 2, the judgment criterion of “clearly different” was not well defined or linked to objective performance measures, and this allowed the observer's unconstrained choice of a criterion to influence the measured “clearly brighter/darker” perceptual boundary in unknown ways across the experimental conditions of interest. Impressions of object persistence might strongly influence how things look and yet have no effect on reliability of detection. It is a plausible view that in the performance of well-defined detection tasks, vision efficiently exploits the information available in the afferent input, and that the noise that leads to incorrect decisions in difficult detection tasks arises at earlier stages of visual processing than the one at which a central impression of object persistence can begin to influence judgment. If so, the effects seen in our previous experiments with self-chosen criteria might be expected to disappear in an objective measurement of the reliability of detection. 
To address these issues, Experiment 3 measured the luminance difference threshold for brightness discrimination between major axis and diagonal wedges more formally with a two-alternative forced-choice (2AFC) task. 
In this experiment, we also investigated the influence of a visible occluder. In a multiple object-tracking task in which objects to be tracked temporarily disappeared during the tracking, performance was better when the objects disappeared and reappeared smoothly as if they went behind an occluder than when they disappeared and reappeared abruptly (Scholl & Pylyshyn, 1999; but see Horowetz, Birnkrant, Fencsik, Tran, & Wolfe, 2006). This suggests that the visual system can maintain some representation of putatively occluded objects as they move behind the occluder even although the object information is not represented in the retinal output. In addition, Yantis and Nakama (1998) demonstrated that the occluder could change perceptual motion from element motion to group motion in an apparent motion display as if the occluder were specifying the relationship between 1st and 2nd elements. These results suggest that occluders may be inputs to motion perception, and this suggests that apparent motion may be stronger when there are occluders than when there are none. For example, in Movie 1, you may see smoother motion in (a) than (b). Therefore, if a persisting object representation underlies our brightness difference compression, a visible occluder, interposed between the visible station points of the moving wedge, might strengthen the brightness difference compression by helping to sustain the object's perceptual representation. 
Methods
There were two conditions in Experiment 3: a basic condition and an occlusion condition. The spatial configuration of the stimulus for the basic condition in Experiment 3 was identical to that in Experiment 2 except that the center angle of the wedges was 20 deg instead of 28 deg. As before, each wedge was presented for 10 ms at a time, and the same 8 motion velocities as Experiment 2 were used. The luminances of the 4 diagonal wedges were identical, and those of the 4 major axis wedges were also identical in a stimulus interval. The luminance of the major axis wedges was 16.3 cd/m2, and that of the diagonal wedges was adaptively adjusted to estimate the threshold. 
For the occlusion condition, an occluder was added to the stimulus (Figure 4). The occluder consisted of an annulus with 8 sectored spokes that filled the spaces between the station points of the moving wedge. The radius of the inner circle was 4.9 deg. The center angle of each spoke was 25 deg, and the length of each spoke from the screen center was 13.7 deg. There was no spatial gap between the wedges and occluder spokes. The luminance of the occluder contour was 73.3 cd/m2, and that of the inner portion was 3.7 cd/m2. In the basic condition, the stimulus was essentially as in Experiment 2 with no occluder. As expected, all the observers reported that motion perception and the perception of the sequence as a single object at or near the OOPV were stronger in the occlusion condition than in the basic condition. 
Figure 4
 
Stimulus used in the occlusion condition of Experiment 3. The stimulus for the basic condition was the same as this stimulus except that there was no occluder.
Figure 4
 
Stimulus used in the occlusion condition of Experiment 3. The stimulus for the basic condition was the same as this stimulus except that there was no occluder.
The stimuli were presented when the observer was ready and pressed a mouse button, and the observer was required to fixate the fixation cross during a trial as usual. In each two-alternative temporal forced-choice trial, there were two stimulus intervals separated by a 500-ms blank interval in which only the black background and the fixation cross were presented. The luminances of the major axis and diagonal wedges of the stimulus presented in one of the stimulus intervals were identical, while those in the other were different. After stimulus presentation, the observer indicated which of the two stimulus intervals contained the stimulus in which the diagonal and major axis wedges were of different luminance. 
The lengths of the stimulus intervals varied depending on the motion velocities. They were 1.3, 1.3, 1.3, 1.3, 2.6, 2.6, 5.1, and 10.2 s, corresponding to 16, 8, 4, 2, 2, 1, 1, and 1 cycles of circular motion, respectively, at motion velocities of 100, 50, 25, 12.5, 6.25, 3.13, 1.56, and 0.78 jumps/s. We varied the length of the stimulus intervals with the motion velocity in order to keep the stimulus interval short and equate the effect of the stimulus interval length on the task performance between the motion velocities as well as possible. In a preliminary experiment, we informally checked that longer stimulus intervals than those used here in the main experiment for each motion velocity had no strong influence on the results. 
The luminance of the diagonal wedges was adaptively adjusted using either QUEST (Watson & Pelli, 1983) or a 2-up 1-down staircase procedure; trials of these two types were randomly interleaved and were combined in the final data analysis in which psychometric functions were estimated using Psignifit (Wichmann & Hill, 2001). Trials were further randomly differentiated by whether the luminance deviation of the variable sectors from the fixed reference sectors was incremental or decremental, but here again, it was found acceptable to pool both types of trials for data analysis. The task in all cases was to identify the interval in which the sector luminance varied. 
We derived a psychometric function for percent correct vs. the log luminance difference between the diagonal and major axis wedges by summing the data of 2 kinds of staircase methods and 2 luminance directions for each motion velocity. A logistic function was fitted to the data with the maximum likelihood method, and the luminance difference corresponding to 75% correct was defined as a threshold. There was no substantial difference between the results for the 2 luminance directions when the results were separately analyzed. 
Two of the authors and a naive observer participated in Experiment 3
Results and discussion
The results for the basic conditions are shown in Figure 5a. The motion velocity is shown on the horizontal axis, and the threshold in log luminance between the diagonal and major axis wedges is shown on the vertical axis. The loss of differential sensitivity at near-OOPV velocities is still fully apparent in the forced-choice thresholds of Figure 5. In fact, the forced-choice log thresholds were approximately doubled. If, as we have assumed, the effect of remote spatiotemporal context depends upon high-level processing, we have here a case where high-level processing strongly influenced the forced-choice threshold. The effect of motion or object persistence on perceived brightness is here supported more strongly than in Experiment 2 because the judgment criterion in this experiment was clearer than in Experiment 2. It also becomes evident that the apparent motion can affect not only the suprathreshold appearance judgments of previous experiments but also small luminance differences at the threshold of forced-choice discrimination. 
Figure 5
 
Results of Experiment 3. (a) Results for 3 observers in the basic condition. (b) Results for the visible occluder condition. The confidence interval of the OOPV for each condition is the gray bar in each panel. The error bars are ±1 standard errors of thresholds, which were calculated from the inverse of the Fisher information matrix in the Psignifit results.
Figure 5
 
Results of Experiment 3. (a) Results for 3 observers in the basic condition. (b) Results for the visible occluder condition. The confidence interval of the OOPV for each condition is the gray bar in each panel. The error bars are ±1 standard errors of thresholds, which were calculated from the inverse of the Fisher information matrix in the Psignifit results.
The results of the occlusion conditions are shown in Figure 5b. Thresholds in the occlusion condition were slightly lower than in the basic condition. A possible explanation for this is that the occluder moved the space-average luminance a little closer to the reference wedge luminance: the log luminance discrimination threshold is generally lowest near the luminance to which the observer is adapted (Craik, 1938). However, we are more interested in the relation between the threshold near the OOPV and those at other velocities. To analyze this, the thresholds were normalized by the mean of the thresholds in each condition and observer. These normalized thresholds are shown in Figure 6. The continuous lines are the results for the basic condition, averaged over observers, and the dashed lines are for the occlusion condition. 
Figure 6
 
Thresholds of Experiment 3 normalized by the average threshold for each experimental condition and observer. The solid lines are the average results of 3 observers for the basic condition, and the dashed lines are the results for the occlusion condition. The dark gray bar is the confidence interval of the OOPV for the basic condition, and the light gray bar is that for the occlusion condition. The error bars are ±1 standard errors.
Figure 6
 
Thresholds of Experiment 3 normalized by the average threshold for each experimental condition and observer. The solid lines are the average results of 3 observers for the basic condition, and the dashed lines are the results for the occlusion condition. The dark gray bar is the confidence interval of the OOPV for the basic condition, and the light gray bar is that for the occlusion condition. The error bars are ±1 standard errors.
Although, in conformity with the previous work cited, the apparent motion perception (and perhaps single object perception also) was subjectively improved by adding an occluder to our stimulus, the elevation of the difference threshold near the OOPV was, if anything, smaller for the occlusion condition than for the basic condition (though the difference was not statistically significant by parametric bootstrap testing). This calls into question our working hypothesis that an object persistence or global apparent motion process is responsible for the luminance difference compression. We return to this issue below in the General discussion section. 
The other interesting fact in Figure 6 is that the velocity where the threshold was highest tended to be larger for the occlusion condition than for the basic condition. What caused this velocity-threshold function shift? One possibility is that the occluder changes the OOPV. On the hypothesis that spatiotemporal integration process for apparent motion was responsible for the loss of differential luminance sensitivity, the occluder might increase both the OOPV and the velocity-threshold function similarly. To investigate this, we measured the OOPV for the occlusion condition and the basic condition in the same fashion as in the preliminary experiment of Experiment 1. The gray bars in Figures 5a and 5b, and the dark and light gray bars in Figure 6, are the confidence intervals of the OOPV measured for the basic condition and occlusion conditions, respectively. The OOPV is indeed significantly higher for the occlusion condition (1.06 ± 0.01 log jumps/s) than for the basic condition as expected (0.93 ± 0.02 log jumps/s). Therefore, this velocity-threshold function shift does not refute the idea that spatiotemporal integration process for apparent motion mediates the luminance difference compression; rather, it could be viewed as additional support for it. 
Experiment 4: Binding
Observers in Experiment 1 found that the matching task was somewhat difficult because even when they could perceive a luminance difference, it was difficult for them to bind spatial position and perceived brightness: that is, they felt uncertain in which views of the object it appeared bright and in which views it appeared dim. We conducted Experiment 4 in an attempt to confirm this introspective impression. Here, we use the term “binding” to represent linking between spatial position and brightness, regarding spatial position as one of the object features. 
Methods
The spatial configuration of the stimulus was identical to that in Experiment 3. The luminances of the 4 diagonal wedges were identical, and those of the 4 major axis wedges were also identical in a stimulus interval. Either the diagonal or the major axis wedges were brighter than the other set; mean luminance was held constant at 16.3 cd/m2, and the luminance difference varied over trials. The same motion velocities as those in Experiment 3 were used. Both the basic conditions and the occlusion condition were tested. 
The stimulus interval for each motion velocity was twice as long as that in Experiment 3, but there was only one stimulus interval in a trial. The stimulus was initiated when the observer was ready and pressed a mouse button, and the observer fixated the fixation cross during the stimulus presentation. After the presentation, the observer stated whether the diagonal or major axis wedges were brighter. Although this task is similar to that of Experiment 3 in that the observer judged the brightness difference, there is an important difference: in this experiment, the observer had to judge not only the luminance difference but also the connection between spatial position and brightness. The Y value difference between the diagonal and major axis wedges was adjusted by the QUEST and the 1-down 2-up staircase method, both series of which were included in a session. There were 16 series in a session (2 staircase method and 8 motion velocities). Each series included 20 trials in a session, and each observer conducted 6 sessions. The threshold was estimated as the log Y difference corresponding to 75% correct after summing the data from the 2 kinds of staircase methods in each motion velocity as in Experiment 3
Two of the authors and one naive observer participated in Experiment 4
Results and discussion
The results for the basic condition are shown in Figure 7a, and those for the occlusion condition are shown in Figure 7b. The threshold of difference in log luminance between the diagonal and major axis wedges is shown on the vertical axis. The gray bars represent the confidence intervals of the OOPV measured in Experiment 3
Figure 7
 
(a) Results for the basic condition and (b) results for the occlusion condition of Experiment 4. The error bars are ±1 standard errors.
Figure 7
 
(a) Results for the basic condition and (b) results for the occlusion condition of Experiment 4. The error bars are ±1 standard errors.
The thresholds for both the conditions tend to increase near the OOPV. This is not surprising because the observer's judgment in this experiment should have been based on perceived brightness, and the prior experiments already showed that the perceived brightness difference between light and dark wedges is underestimated near the OOPV. 
To compare the thresholds for the basic and occlusion conditions, Figure 8 shows the thresholds for both conditions normalized by the threshold averaged in each condition and observer as in Experiment 3. The solid lines are the results for the basic condition, and the dashed lines are for the occlusion condition. The relationship was also similar to that in Experiment 3. The increase in threshold at the OOPV was larger for the basic condition than for the occlusion condition. Moreover, the velocity corresponding to the highest threshold was again larger for the occlusion condition than for the basic condition, and as in Experiment 3, this shift was accompanied by a corresponding shift in the OOPV in the occlusion condition, consistent with the idea that spatiotemporal integration process for a moving object was implicated in the brightness difference compression. 
Figure 8
 
Thresholds of Experiment 4 normalized by the average threshold for each experimental condition and observer. The dark gray bar is the confidence interval of the OOPV for the basic condition, and the light gray bar is that for the occlusion condition, which were the same as those in Experiment 3. The error bars are ±1 standard errors.
Figure 8
 
Thresholds of Experiment 4 normalized by the average threshold for each experimental condition and observer. The dark gray bar is the confidence interval of the OOPV for the basic condition, and the light gray bar is that for the occlusion condition, which were the same as those in Experiment 3. The error bars are ±1 standard errors.
Most critically, we compared the magnitude of threshold increase near the OOPV in Experiment 4 (where appropriate binding was required) to that in Experiment 3 (where appropriate binding was not required). The light gray continuous and dashed lines in Figure 8 show the thresholds obtained in Experiment 3, for comparison with the continuous lines from Experiment 4. It is clear that the threshold increase was larger in Experiment 4 than in Experiment 3 for both conditions. The sole difference between Experiments 3 and 4 was the requirement to correctly associate the greater luminance with the appropriate spatial position. Accordingly, this result implies that perception of a single object with apparent motion not only compresses the perceived brightness difference between successive views of an object but, even when the brightness difference is perceived, additionally obscures the relationship between spatial position (or temporal order) and perceived brightness. Here, consistent with the reports of the observers, the visual system appears to encounter a “binding problem” in linking different visual features (Treisman, 1996, 1998), in this case luminance and spatial location. 
Experiment 5: Color
The previous experiments show that differences in luminance are perceptually underestimated, and less detectable, when the successive stimuli are perceived as a moving single object. Here, we investigate whether there is a similar perceptual compression for color differences. 
Methods
The stimulus was the same as Experiments 3 and 4 except that the difference between the diagonal and major axis wedges was not in luminance but in chromaticity. The luminance of all wedges was 16.3 cd/m2. The chromaticities of the 4 diagonal wedges were identical, and those of 4 major axis wedges were also identical in any given trials, as were the luminances in Experiments 3 and 4. However, over the course of the trials, the chromaticities of the diagonal and major axis wedges varied along the r (or L–M) axis (MacLeod & Boynton, 1979). We utilized both the discrimination task of Experiment 3 and the binding task of Experiment 4. For the discrimination task, the chromaticity of the major axis wedges was the same as the equal energy white, and that of the diagonal wedges varied over trials. For the binding task, the chromaticities of the diagonal and major axis wedges varied over trials while the mean chromaticity was held constant at equal energy white. We used only the basic condition (not the occlusion condition). 
The procedures for the two tasks were identical to those for Experiments 3 and 4, respectively, though the judgments were based on color, not brightness; in the discrimination task, the observer judged which of the first and second rotating stimulus displays had the color alternation, and in the binding task, which of the diagonal or the major axis wedges was redder. One author and one naive observer participated. 
Results and discussion
The results are shown in Figure 9. The solid line and filled symbols show the results for the discrimination task; the dashed line and open symbols refer to the binding task. The threshold, normalized by the average threshold for each observer and experimental condition, is shown on the vertical axis. Each symbol represents the result for one observer, and the lines are the results averaged between observers. The results for the discrimination task are different from those for Experiment 3: the threshold did not increase near the OOPV but monotonically decreased with increasing motion velocity. Evidently, perceived color and luminance behaved differently here: color was not averaged between successive views even when the views were perceived as a moving single object. At least, the compression effect at the OOPV was considerably larger for brightness perception than for color perception. On the other hand, the results with the binding task were similar to those in Experiment 4; the threshold increased at the OOPV, suggesting that the observer could not determine which color was linked with which view of the moving object. 
Figure 9
 
Results of Experiment 5. The solid lines are the thresholds for the discrimination task, and the dashed lines are those for the binding task. The error bars are ±1 standard errors.
Figure 9
 
Results of Experiment 5. The solid lines are the thresholds for the discrimination task, and the dashed lines are those for the binding task. The error bars are ±1 standard errors.
General discussion
We conducted a series of experiments to investigate the effect of the inter-flash intervals (or apparent motion velocities) between wedge flashes. Our experiments reveal large effects of long-range apparent motion on perceived brightness. At or near the motion velocity in which perception of a moving single object was strongest (the OOPV), luminance differences between successive views were perceptually attenuated (Experiment 1), luminance differences necessary for the observer to clearly perceive the brightness difference were increased (Experiment 2), and the forced-choice luminance discrimination threshold was highest (Experiment 3). These results suggest that spatiotemporal integration process for apparent motion perception of an object affects perceived brightness. 
Shimozaki et al. (1999) showed similarly that the object perception affected the luminance difference judgment using the reviewing paradigm (Kahneman et al., 1992). In their results, the luminance difference judgment of two objects was influenced by luminances of previously viewed objects linked by apparent motion. They explained this phenomenon by invoking the object file concept. Our results could be explained by the same object file scheme; an object file was created at the first presentation of a wedge, and then the perceived brightness of the later wedges (interpreted as later views of the same moving object) were affected by the existing contents of the object file. The contents of the object file in our experiments, including values of object parameters such as brightness, could be cumulatively averaged over successive views so that the perceived brightness approaches the averaged brightness. 
If this object file idea is correct, the benefit of this strategy may arise from a purpose of a computational economy. Because an object's inherent properties rarely change while seeing it in the real world, it is no wonder that the visual system has an assumption that an object's internal properties do not vary. 
Color. Our phenomenon is at least superficially similar to the color mixture along a trajectory of a moving object (Nishida et al., 2007). Although their results did not conflict with the idea that a mechanism contributing to object or global apparent motion perception affects the apparent brightness or color, they did not clarify whether a global motion (or object) mechanism or a lower level mechanism with a small spatiotemporal window was responsible for the color mixture. However, since our stimulus has a larger spatial gap (1.7–3.5 deg) between wedges, our results suggest that the perceptual brightness difference compression is mediated by a mechanism with a larger receptive field than those of V1/V2 neurons (mean and SD of their size for V1 is about 0.5 deg at 2–7 deg of eccentricity and that for V2 is 1 deg with SD of 0.32 deg at 1–6 deg of eccentricity; Ito & Gilbert, 1999; Ito & Komatsu, 2004; Kapadia, Westheimer, & Gilbert, 2000). Many physiological and brain imaging studies have demonstrated that whereas MT/hMT activity (Goebel, Khorram-Sefat, Muckli, Hacker, & Singer, 1998; Mikami, Newsome, & Wurtz, 1986) or V1 activity that is fed back from hMT (Muckli, Kohler, Kriegeskorte, & Singer, 2005) processes long-range apparent motion, even lateral interactions between V1 neurons are too small to explain long-range apparent motion (Muckli et al., 2005). It should be noted that although the color mixture of Nishida et al. and our luminance compression look like similar phenomena, they have some different features. For example, the color mixture was much weakened when the bar was widened, while our brightness compression was observed using wedges that were much wider than their bars (4–12 min). The optimal inter-flash intervals were also different between the two phenomena (about 110 ms in our experiments, and 6.25–75 ms in Nishida et al.), though Nishida et al. showed that the optimal inter-flash interval varied with the bar width. Of course, the strengths of the two phenomena cannot be simply compared because the tasks and evaluation methods were different between the two studies. More experiments will be necessary to clarify the relationship between these two phenomena. 
Recently, visual phenomena where observers do not notice color modulations on moving stimuli composed of multiple elements have been reported (Shioiri, Ogawa, Matsubara, & Yaguchi, 2004; Suchow & Alvarez, 2010). These phenomena are similar to our brightness averaging in that brightness or color modulation on moving targets is less noticed. However, there is a large difference between the phenomena; their phenomena can be clearly seen only when there are many moving targets, while our phenomena can also be seen even for one easily tracked moving target. Therefore, we believe that visual mechanisms underlying their phenomena and our results are different. 
In Experiment 5, the perceived color, unlike brightness, was not averaged between wedges even when the wedges were perceived as a single moving object. This suggests that the averaging of color along an apparent motion trajectory is much weaker than that of brightness. However, the effect of local flashing rate on perceived color in the peripheral visual field, as with that on brightness that was investigated in the complementary experiment of Experiment 1, must be investigated to confirm this with certainty. This may not be interpreted simply with the object file idea, because both color and brightness reflect internal properties of an object. One possible explanation of the non-existence or weakness of the averaging effect of apparent motion on color perception is that the color may be averaged only in similar hues or in the same category. In Experiment 5, the colors to be compared might belong to different categories (gray vs. red or gray vs. green), while the wedges were always perceived as gray in other experiments. Although this explanation looks fragile because the color difference in our stimulus was small, some studies suggest that the color mechanisms for the L–M direction and −L + M directions are different (Sankeralli & Mullen, 2001). Thus, different color mechanisms may be involved in color perception for +r and −r directions against the reference achromatic color (background black) in spite of the small color difference in our experiment. For luminance modulation, however, because the background was black, both the dark and light wedges could be detected by the same “ON” mechanisms. Further experiments in which the reference color is not achromatic but more saturated will be necessary to substantiate this explanation. 
Occlusion. In Experiments 3 and 4, we added an occluder to the stimulus in the occlusion condition. When there was an occluder, motion perception and single object perception increased, but the amount of the brightness difference compression decreased. Although this raises a possibility that the motion or object mechanism do not play a role in the brightness compression, there were many factors that might affect our results for the occlusion condition. One of those is the noted effect of the occluder on adding edges with high luminance. However, in a control no-occluder condition where inner and outer annuli were added so as to add high luminance edges similarly to the occluder condition, the results were similar to those of the basic condition, suggesting that luminance is not the critical factor. 
A second possible influence is the tunnel effect (Burke, 1952; Michotte, Thinès, & Crabbé, 1964/1991). In a recent study of the tunnel effect (Flombaum & Scholl, 2006), the change of color or shape of an object before and after it passed behind an occluder could be more easily detected when the spatiotemporal relationship between pre- and post-occlusion views was appropriate. This suggests that the single object perception improves change detection (they called this phenomenon “same-object advantage” in change detection) even when the object goes behind an occluder. Moreover, the response time to judge whether the target changed during the target disappearance was shorter when there was a visible occluder than when there was no occluder (Kawachi & Gyoba, 2006), suggesting that object continuity might be stronger with a visible occluder than with an invisible occluder. Accordingly, the same-object advantage might weaken the brightness difference compression when there was a visible occluder in our experiments to ease change detection. Since these two object-based effects—averaging of entries in an object file and the same-object advantage in change detection—are opposite in their effects in our experiments, further work would be needed to assess their independent contributions. 
A third complication is introduced by the difference in OOPV between the basic and occlusion conditions. In the synchronously flashed control conditions, discrimination thresholds decreased with increasing repetition rate (Figures 2 and 3). Thus, since the OOPV for the occlusion condition is faster than that for the basic condition, an increased brightness averaging in the occlusion condition could be obscured by this velocity effect on thresholds. 
Binding. In Experiment 4, the threshold increase at the OOPV compared to the other velocities was much larger than in Experiment 3. This result suggests that the observer had difficulties in binding the perceived brightness and the spatial position even if she or he could perceive the luminance modulation, consistent with the observer's impression in Experiment 1. This phenomenon could be relevant to the so-called binding problem (Treisman, 1996, 1998). As is well known, there are a variety of experimental results supporting the theory that the visual system independently processes the different features such as motion, spatial position, shape, and color (Felleman & Van Essen, 1991; Livingstone & Hubel, 1987; Mishkin, Ungerleider, & Macko, 1983). If so, the visual system must integrate the different visual features of visual objects at some stage of visual information processing after initial feature processing sites to achieve veridical visual perception of them. In our stimulus, the selective binding of spatiotemporal positions to brightnesses was most unreliable at the motion velocity corresponding to the strongest single object perception. This phenomenon may have a common origin with the brightness difference compression: if the visual system can assume that internal features of an object are invariant, it will be unnecessary and inefficient to evaluate brightness at each spatiotemporal position independently. In the extreme case, a single cumulative average could suffice. However, since binding is at least partially successful, it appears that some history is represented, even if the history is fragmentary and only unreliably maintained and accessed. 
Differences between the time required to calculate brightness and spatial position might contribute to the binding problem. If there is a lag in processing brightness compared to both the inter-flash interval and the processing of spatial position, the visual system might incorrectly decide to which of the two wedges the calculated brightness should be assigned when trying to bind brightness and position. It is relevant that the processing times for the positions for moving objects and still objects are different (a traditional explanation of the flash-lag effect; Jancke, Erlhagen, Schoner, & Dinse, 2004; Whitney & Murakami, 1998), that processing times for color and motion are different (Moutoussis & Zeki, 1997), and that the color of moving stimuli is perceptually shifted in the direction of motion (e.g., Cai illusion; Cai & Schlag, 2001). Our data provide little basis for evaluating the role of such systematic asynchrony, but the observation that binding was always more successful than chance, and that errors in binding were most apparent at relatively slow velocities, discourage the “systematic mismatch” interpretation. 
Attentional tracking. Visual attention may be necessary for binding of features such as color and motion. For example, in Cavanagh, Holcombe, and Chou's (2008) investigation of attentional tracking, the stimulus was similar in some respects to ours: it could be perceived as a retinotopically moving target with alternation of motion and color between successive views. In this situation, attentional tracking dramatically enhanced identification of which color was associated with which motion, as if object features like color and motion that appear in a moving attentional window can be integrated into a single moving object. Because attention could track the motion in our stimuli, attention might have influenced our results. Feature integration by attention could contribute to brightness averaging by integrating the different colors and luminances successively presented, or it might diminish brightness averaging if attention helps bind color and spatial position and, therefore, segregate two colors. We cannot dissociate these alternatives. We did not investigate the effect of attention by manipulating it independently of the stimulus, and Cavanagh et al. did not investigate the case in which a single attention window captures different states of a feature (e.g., red and green, in color, similarly to our stimuli) in series, similarly to our display. Further experiments will be required to clarify these attention effects, but we note that a role for integration across successive attentional windows is compatible with the lack of an occluder effect in Experiment 3. It might also support the perceptual averaging observed in Experiments 3 to 5 at stimulus velocities somewhat lower than the OOPV—a situation that is still presumably favorable for attentional tracking. 
In conclusion, our results show that the perceived magnitude and detectability of differences in perceived brightness of moving wedges were reduced when the motion velocity yielded a strong percept of a moving object. This suggests that a mechanism involved in spatiotemporal integration for apparent motion perception affects perceived brightness. The visual system may save computational and storage resources by favoring a presumption that object properties such as brightness are relatively invariant over successive views. 
Supplementary Materials
Supplementary Movie - Supplementary Movie 
movie1(a) 
Supplementary Movie - Supplementary Movie 
movie1(b) 
Acknowledgments
This research was supported by National Institutes of Health Grant EY01711. 
Commercial relationships: none. 
Corresponding author: Takehiro Nagai. 
Email: nagai@tut.jp. 
Address: 1-1 Hibarigaoka, Tenpaku, Toyohashi, Aichi 441-8580, Japan. 
References
Blaser E. Pylyshyn Z. W. Holcombe A. O. (2000). Tracking an object through feature space. Nature, 408, 196–199. [CrossRef] [PubMed]
Braddick O. (1974). A short-range process in apparent motion. Vision Research, 14, 519–527. [CrossRef] [PubMed]
Burke L. (1952). On the tunnel effect. Quarterly Journal of Experimental Psychology, 4, 121–138. [CrossRef]
Burt P. Sperling G. (1981). Time, distance, and feature trade-offs in visual apparent motion. Psychological review, 88, 171–195. [CrossRef] [PubMed]
Cai R. H. Schlag J. (2001). Asynchronous feature binding and the flash-lag illusion. Investigative Ophthalmology & Visual Science, 42,
Cavanagh P. Holcombe A. O. Chou W. (2008). Mobile computation: Spatiotemporal integration of the properties of objects in motion. Journal of Vision, 8, (12):1, 1–23, http://www.journalofvision.org/content/8/12/1, doi:10.1167/8.12.1. [PubMed] [Article] [CrossRef]
Craik K. J. W. (1938). The effect of adaptation on differential brightness discrimination. The Journal of Physiology, 92, 406–421. [CrossRef] [PubMed]
Felleman D. J. Van Essen D. C. (1991). Distributed hierarchical processing in the primate cerebral cortex. Cerebral Cortex, 1, 1–47. [CrossRef] [PubMed]
Flombaum J. I. Scholl B. J. (2006). A temporal same-object advantage in the tunnel effect: Facilitated change detection for persisting objects. Journal of Experimental Psychology: Human Perception and Performance, 32, 840–853. [CrossRef] [PubMed]
Gegenfurtner K. R. Kiper D. C. Fenstemaker S. B. (1996). Processing of color, form, and motion in macaque area V2. Visual Neuroscience, 13, 161–172. [CrossRef] [PubMed]
Gepshtein S. Kubovy M. (2007). The lawful perception of apparent motion. Journal of Vision, 7, (8):9, 1–15, http://www.journalofvision.org/content/7/8/9, doi:10.1167/7.8.9. [PubMed] [Article] [CrossRef] [PubMed]
Gilchrist A. Kossyfidis C. Bonato F. Agostini T. Cataliotti J. Li X. J. et al. (1999). An anchoring theory of lightness perception. Psychological Review, 106, 795–834. [CrossRef] [PubMed]
Goebel R. Khorram-Sefat D. Muckli L. Hacker H. Singer W. (1998). The constructive nature of vision: Direct evidence from functional magnetic resonance imaging studies of apparent motion and motion imagery. European Journal of Neuroscience, 10, 1563–1573. [CrossRef] [PubMed]
Gordon R. D. Irwin D. E. (2000). The role of physical and conceptual properties in preserving object continuity. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26, 136–150. [CrossRef] [PubMed]
Horowetz T. S. Birnkrant R. S. Fencsik D. E. Tran L. Wolfe J. M. (2006). How do we track invisible objects? Psychonomic Bulletin & Review, 13, 516–523. [CrossRef] [PubMed]
Ito M. Gilbert C. D. (1999). Attention modulates contextual influences in the primary visual cortex of alert monkeys. Neuron, 22, 593–604. [CrossRef] [PubMed]
Ito M. Komatsu H. (2004). Representation of angles embedded within contour stimuli in area V2 of macaque monkeys. Journal of Neuroscience, 24, 3313–3324. [CrossRef] [PubMed]
Jancke D. Erlhagen W. Schoner G. Dinse H. R. (2004). Shorter latencies for motion trajectories than for flashes in population responses of cat primary visual cortex. The Journal of Physiology, 556, 971–982. [CrossRef] [PubMed]
Kahneman D. Treisman A. (1984). Changing views of attention and automaticity. In Parasuraman R. Davies D. R. (Eds.), Varieties of attention (pp. 29–61). New York: Academic Press.
Kahneman D. Treisman A. Gibbs B. J. (1992). The reviewing of object files: Object-specific integration of information. Cognitive Psychology, 24, 175–219. [CrossRef] [PubMed]
Kapadia M. K. Westheimer G. Gilbert C. D. (2000). Spatial distribution of contextual interactions in primary visual cortex and in visual perception. Journal of Neurophysiology, 84, 2048–2062. [PubMed]
Kawachi Y. Gyoba J. (2006). A new response-time measure of object persistence in the tunnel effect. Acta Psychologica, 123, 73–90. [CrossRef] [PubMed]
Levitt J. B. Kiper D. C. Movshon J. A. (1994). Receptive fields and functional architecture of macaque V2. Journal of Neurophysiology, 71, 2517–2542. [PubMed]
Livingstone M. S. Hubel D. H. (1987). Segregation of form, color, movement and depth: Anatomy, physiology, and perception. Science, 240, 740–749. [CrossRef]
Macleod D. I. A. Boynton R. M. (1979). Chromaticity diagram showing cone excitation by stimuli of equal luminance. Journal of the Optical Society of America, 69, 1183–1186. [CrossRef] [PubMed]
Michotte A. Thinès G. Crabbé G. (1964/1991). Les compléments amodaux des structures perceptives. In Thins G. Costall A. Butterworth G. (Eds.), Michotte's experimental phenomenology of perception (pp. 140–167). Hillsdale, NJ: Erlbaum.
Mikami A. Newsome W. T. Wurtz R. H. (1986). Motion selectivity in macaque visual cortex: II. Spatiotemporal range of directional interactions in MT and V1. Journal of Neurophysiology, 55, 1328–1339. [PubMed]
Mishkin M. Ungerleider L. G. Macko K. A. (1983). Object vision and spatial vision: Two cortical pathways. Trends in Neurosciences, 6, 414–417. [CrossRef]
Mitchell J. F. Stoner G. R. Reynolds J. H. (2004). Object-based attention determines dominance in binocular rivalry. Nature, 429, 410–413. [CrossRef] [PubMed]
Mitroff S. R. Alvarez G. A. (2007). Space and time, not surface features, guide object persistence. Psychonomic Bulletin & Review, 14, 1199–1204. [CrossRef] [PubMed]
Moutoussis K. Zeki S. (1997). A direct demonstration of perceptual asynchrony in vision. Proceedings of the Royal Society of London B: Biological Sciences, 264, 393–399. [CrossRef]
Muckli L. Kohler A. Kriegeskorte N. Singer W. (2005). Primary visual cortex activity along the apparent-motion trace reflects illusory perception. PLoS Biology, 3, 1501–1510. [CrossRef]
Nishida S. Watanabe J. Kuriki I. Tokimoto T. (2007). Human visual system integrates color signals along a motion trajectory. Current Biology, 17, 366–372. [CrossRef] [PubMed]
Sankeralli M. J. Mullen K. T. (2001). Bipolar or rectified chromatic detection mechanisms? Visual Neuroscience, 18, 127–135. [CrossRef] [PubMed]
Schoenfeld M. A. Tempelmann C. Martinez A. Hopf J. M. Sattler C. Heinze H. J. et al. (2003). Dynamics of feature binding during object selective attention. Proceedings of the National Academy of Sciences, 100, 11806–11811. [CrossRef]
Scholl B. J. Pylyshyn Z. W. (1999). Tracking multiple items through occlusion: Clues to visual objecthood. Cognitive Psychology, 38, 259–290. [CrossRef] [PubMed]
Shimozaki S. S. Eckstein M. Thomas J. P. (1999). The maintenance of apparent luminance of an object. Journal of Experimental Psychology, 25, 1433–1453. [PubMed]
Shioiri S. Ogawa M. Matsubara K. Yaguchi H. (2004). Effect of attention at high temporal frequencies [Abstract]. Journal of Vision, 4, (8):501, 501a, http://www.journalofvision.org/content/4/8/501, doi:10.1167/4.8.501. [CrossRef]
Snodderly D. M. Gur M. (1995). Organization of striate cortex of alert, trained monkeys (Macaca fascicularis): Ongoing activity, stimulus selectivity, and widths of receptive field activating regions. Journal of Neurophysiology, 74, 2100–2125. [PubMed]
Stiles W. S. Burch J. M. (1955). Interim report to the Commission Internationale de l'Eclairage Zurich, 1955, on the National Physical Laboratory's investigation of colour matching (1955) with an appendix by W. S. Stiles & J. M. Burch. Optica Acta, 2, 168–181. [CrossRef]
Stockman A. Macleod D. I. A. Johnson N. E. (1993). Spectral sensitivities of the human cones. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 10, 2491–2521. [CrossRef] [PubMed]
Suchow J. Alvarez G. (2010). Silent updating: Cross-dimensional change suppression [Abstract]. Journal of Vision, 10, (7):299, 299a, http://www.journalofvision.org/content/10/7/299, doi:10.1167/10.7.299. [CrossRef]
Tamura H. Sato H. Katsuyama N. Hata Y. Tsumoto T. (1996). Less segregated processing of visual information in V2 than in V1 of the monkey visual cortex. European Journal of Neuroscience, 8, 300–309. [CrossRef] [PubMed]
Treisman A. (1996). The binding problem. Current Opinion in Neurobiology, 6, 171–178. [CrossRef] [PubMed]
Treisman A. (1998). Feature binding, attention and object perception. Philosophical Transactions of the Royal Society B: Biological Sciences, 353, 1295–1306. [CrossRef]
Watanabe J. Nishida S. (2007). Veridical perception of moving colors by trajectory integration of input signals. Journal of Vision, 7, (11):3, 1–16, http://www.journalofvision.org/content/7/11/3, doi:10.1167/7.11.3. [PubMed] [Article] [CrossRef] [PubMed]
Watson A. B. Pelli D. G. (1983). QUEST: A Bayesian adaptive psychometric method. Perception & Psychophysics, 33, 113–120. [CrossRef] [PubMed]
Whitney D. Murakami I. (1998). Latency difference, not spatial extrapolation. Nature Neuroscience, 1, 656–657. [CrossRef] [PubMed]
Wichmann F. A. Hill N. J. (2001). The psychometric function: I. Fitting, sampling, and goodness of fit. Perception & Psychophysics, 63, 1293–1313. [CrossRef] [PubMed]
Wolfe J. M. Bennett S. C. (1997). Preattentive object files: Shapeless bundles of basic features. Vision Research, 37, 25–43. [CrossRef] [PubMed]
Yantis S. Nakama T. (1998). Visual interactions in the path of apparent motion. Nature Neuroscience, 6, 508–512. [CrossRef]
Figure 1
 
Stimulus used in our experiments. The 8 wedges were not presented simultaneously in the main experiments but were presented in rotation with a range of inter-flash intervals.
Figure 1
 
Stimulus used in our experiments. The 8 wedges were not presented simultaneously in the main experiments but were presented in rotation with a range of inter-flash intervals.
Figure 2
 
Results of Experiment 1. The solid lines are the results of the main experiment, and the dashed lines are the results of the complementary control experiment in which all the wedges flashed simultaneously. The difference between log luminance (log Y) matched to the light wedges and that to the dark wedges is shown on the ordinate axis. The error bar represents ±1 standard error of mean. The gray vertical bar represents the 95% confidence interval for the motion velocity where single object perception is strongest. The horizontal bold line represents the expected result if the observer matches the brightness based on physical luminances.
Figure 2
 
Results of Experiment 1. The solid lines are the results of the main experiment, and the dashed lines are the results of the complementary control experiment in which all the wedges flashed simultaneously. The difference between log luminance (log Y) matched to the light wedges and that to the dark wedges is shown on the ordinate axis. The error bar represents ±1 standard error of mean. The gray vertical bar represents the 95% confidence interval for the motion velocity where single object perception is strongest. The horizontal bold line represents the expected result if the observer matches the brightness based on physical luminances.
Figure 3
 
(a) Results of Experiment 2. The solid lines are the results of the main experiment, and dashed lines are the results of the complementary experiment in which all the wedges flashed simultaneously. The luminance (Y) value of the diagonal wedges that were just clearly lighter or darker than the major axis wedges is shown on the ordinate. The bold horizontal line represents the Y value of the major axis wedges. The error bar represents ±1 standard error of mean. (b) Results of the main experiment repeated with a white background instead of a dark background.
Figure 3
 
(a) Results of Experiment 2. The solid lines are the results of the main experiment, and dashed lines are the results of the complementary experiment in which all the wedges flashed simultaneously. The luminance (Y) value of the diagonal wedges that were just clearly lighter or darker than the major axis wedges is shown on the ordinate. The bold horizontal line represents the Y value of the major axis wedges. The error bar represents ±1 standard error of mean. (b) Results of the main experiment repeated with a white background instead of a dark background.
Figure 4
 
Stimulus used in the occlusion condition of Experiment 3. The stimulus for the basic condition was the same as this stimulus except that there was no occluder.
Figure 4
 
Stimulus used in the occlusion condition of Experiment 3. The stimulus for the basic condition was the same as this stimulus except that there was no occluder.
Figure 5
 
Results of Experiment 3. (a) Results for 3 observers in the basic condition. (b) Results for the visible occluder condition. The confidence interval of the OOPV for each condition is the gray bar in each panel. The error bars are ±1 standard errors of thresholds, which were calculated from the inverse of the Fisher information matrix in the Psignifit results.
Figure 5
 
Results of Experiment 3. (a) Results for 3 observers in the basic condition. (b) Results for the visible occluder condition. The confidence interval of the OOPV for each condition is the gray bar in each panel. The error bars are ±1 standard errors of thresholds, which were calculated from the inverse of the Fisher information matrix in the Psignifit results.
Figure 6
 
Thresholds of Experiment 3 normalized by the average threshold for each experimental condition and observer. The solid lines are the average results of 3 observers for the basic condition, and the dashed lines are the results for the occlusion condition. The dark gray bar is the confidence interval of the OOPV for the basic condition, and the light gray bar is that for the occlusion condition. The error bars are ±1 standard errors.
Figure 6
 
Thresholds of Experiment 3 normalized by the average threshold for each experimental condition and observer. The solid lines are the average results of 3 observers for the basic condition, and the dashed lines are the results for the occlusion condition. The dark gray bar is the confidence interval of the OOPV for the basic condition, and the light gray bar is that for the occlusion condition. The error bars are ±1 standard errors.
Figure 7
 
(a) Results for the basic condition and (b) results for the occlusion condition of Experiment 4. The error bars are ±1 standard errors.
Figure 7
 
(a) Results for the basic condition and (b) results for the occlusion condition of Experiment 4. The error bars are ±1 standard errors.
Figure 8
 
Thresholds of Experiment 4 normalized by the average threshold for each experimental condition and observer. The dark gray bar is the confidence interval of the OOPV for the basic condition, and the light gray bar is that for the occlusion condition, which were the same as those in Experiment 3. The error bars are ±1 standard errors.
Figure 8
 
Thresholds of Experiment 4 normalized by the average threshold for each experimental condition and observer. The dark gray bar is the confidence interval of the OOPV for the basic condition, and the light gray bar is that for the occlusion condition, which were the same as those in Experiment 3. The error bars are ±1 standard errors.
Figure 9
 
Results of Experiment 5. The solid lines are the thresholds for the discrimination task, and the dashed lines are those for the binding task. The error bars are ±1 standard errors.
Figure 9
 
Results of Experiment 5. The solid lines are the thresholds for the discrimination task, and the dashed lines are those for the binding task. The error bars are ±1 standard errors.
Supplementary Movie
Supplementary Movie
×
×

This PDF is available to Subscribers Only

Sign in or purchase a subscription to access this content. ×

You must be signed into an individual account to use this feature.

×