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Research Article  |   December 2009
Spatiotemporally coherent motion direction perception occurs even for spatiotemporal reversal of motion sequence
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Journal of Vision December 2009, Vol.9, 6. doi:10.1167/9.13.6
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      Souta Hidaka, Masayoshi Nagai, Jiro Gyoba; Spatiotemporally coherent motion direction perception occurs even for spatiotemporal reversal of motion sequence. Journal of Vision 2009;9(13):6. doi: 10.1167/9.13.6.

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

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Abstract

Thus far, it has been pointed out that motion representation is completed in motion trajectory, and that motion representation interferes with a single physical input at a specific time and space in the motion trajectory. However, it has not been fully investigated whether the internal motion representation could interact with multiple physical inputs across time and space in motion trajectory. Thus, the current research investigated whether spatiotemporally coherent motion perception could be established in a situation involving the spatiotemporal reversal of motion sequences. In a five-point motion display, we found that the motion direction perception of the last two stimuli containing the spatiotemporal reversal was consistent with three preceding stimuli. This failure to perceive motion direction reversal occurred when the shapes of motion trajectory (to upper or lower) were randomly changed. Moreover, we confirmed that one preceding stimulus (three-point motion) was sufficient to produce the failure to perceive motion direction reversal, and the effect of the prior stimuli saturated when the preceding sequence contained two or more stimuli. These findings suggest that the flexible internal motion representation mechanisms reorganize the spatiotemporal irregularities in motion trajectory and establish spatiotemporally coherent motion perceptions.

Introduction
The inputs from continuously moving objects often become discrete or incomplete images in our perceptual systems. For example, blinking or occlusion induces the discontinuity of retinal inputs. We can also perceive smooth motion from a cinematograph that comprises only 24 frames per second. However, we rarely are aware of such discontinuity, and the resulting motion perception is usually continuous. This fact indicates that the visual systems complete internal motion representation and establish continuous motion perception from discrete physical inputs. The typical example of this internal motion representation mechanism is the phenomenon known as apparent motion (Kolers, 1972; Wertheimer, 1912). When two or more stimuli that are spatially apart from each other are alternately turned on and off at an optimal interval, we can perceive motion between the stimuli that is indistinguishable from real motion (Korte, 1915). It has been pointed out that the internal motion representation is completed in between the locations of physically presented stimuli along the motion trajectory (Burr, 1979; Shepard & Zare, 1983). Yantis and Nakama (1998) showed that, in a bistable apparent motion display, letter discrimination performance was impaired when the letters were presented in the perceived motion trajectory. This motion masking effect indicated that internal motion representation could interfere with the physical inputs in the motion trajectory. Some neuroimaging studies also indicated the existence of an internal motion representation mechanism. It was revealed that both the primary visual cortex, including V1 (Muckli, Kohler, Kriegeskorte, & Singer, 2005), and the higher cortical area overlapping MT+ and LOC (Liu, Slotnick, & Yantis, 2004) are involved in the processing of the internal motion representation in apparent motion trajectory. Moreover, the existence of a feedback modulation from hMT+ to V1 (Sterzer, Hynes, & Rees, 2006; Wibral, Bledowski, Kohler, Singer, & Muckli, 2009) has been suggested. In line with the phenomenological finding (Korte, 1915), these findings indicated that apparently moving objects are internally represented as actual physical inputs in the motion trajectory where there are no physical inputs. 
Thus far, the existence of the internal motion representation is psychophysically confirmed by the interaction between the internal motion representation and a single physical input at a specific time and space in motion trajectory. The motion masking effect, namely the impaired letter discrimination performance in motion trajectory, was a typical example of this (Yantis & Nakama, 1998). Hogendoorn, Carlson, and Verstraten (2008) showed that the motion masking effect occurred in future positions along the motion trajectory when apparently moving objects moved with spatiotemporal coherence. In addition, the motion masking effect occurred along the updated motion trajectory when the motion direction was unpredictably reversed. These findings suggested that the spatiotemporal properties of the internal motion representation are determined to be consistent with the resulting motion perception established by the spatiotemporal properties (spatial positions, spatial distances, and temporal intervals) of inducers (see also Schwiedrzik, Alink, Kohler, Singer, & Muckli, 2007; Shioiri, Cavanagh, Miyamoto, & Yaguchi, 2000). Kanai, Sheth, and Shimojo (2007) also investigated the display in which gaps of motion sequence or changes of an object's features (contrast, shape, or color) occurred in motion trajectory with continuously moving objects. They showed that whereas the sensitivity to these transient changes is higher when the changes occurred soon after the motion onset (<200 ms), it became worse when the transient signal appeared later (>300 ms). These results suggested that internal motion representation was established with 300-ms history of continuous motion, making it difficult to detect changes that were inconsistent with the predicted motions (including spatiotemporal locus, objects' features like contrast, shape, color, etc.). These findings indicated that internal motion representation could establish coherent motion perception against irregularities along motion trajectory. 
Previous research has shown that internal motion representation is completed in motion trajectory and interferes with a single physical input at a spatiotemporal position along motion trajectory. The temporal resolution of the visual systems is limited, so that perceived moving objects may appear to be blurred images. Nevertheless, we perceive sharp images of moving objects. This indicated that motion perception is established from the integration or spatiotemporal summation of multiple visual inputs across time and space (Burr, 1980). Therefore, it was hypothesized that internal motion representation could establish a coherent motion perception not only against a single irregularity at a specific time and space in motion trajectory (suppression; Kanai et al., 2007), but also against the spatiotemporal irregularities between the inputs across time and space (spatiotemporal reorganization). The latter mechanism would benefit the visual systems because it could establish spatiotemporally coherent motion perception. However, this possibility has not been fully investigated so far. The current research investigated whether spatiotemporally coherent motion perception could be established in a situation involving the spatiotemporal reversal of motion sequences. Thus, we examined whether the observers could correctly report the motion direction of the last two stimuli whose spatiotemporal order was reversed relative to prior stimuli. The results of the experiments showed that the failure to perceive motion direction reversal occurred even when the observers engaged in a direction judgment task. 
Experiment 1
Experiment 1 investigated whether the observers could detect motion reversal in motion trajectory. We measured the direction of motion perceived from the last two points of a five-point motion display, in which the spatiotemporal order of the sequences was reversed or not relative to the previous ones. 
Methods
Participants
One author (S. H.) and five volunteers (graduate or undergraduate students in Tohoku University) participated in this experiment. All of them were experienced observers in psychophysics experiments, and five volunteers were naive to the purpose of this experiment. All had normal or corrected-to-normal vision. 
Apparatus
The stimuli were presented on a CRT display (Sony Trinitron GDM-FW900, 24 inch) with a resolution of 1280 × 960 pixels and a refresh rate of 75 Hz. An Apple Power Mac G4 and MATLAB (The Mathworks) with the Psychophysics Toolbox (Brainard, 1997; Pelli, 1997) were used to control the experiment. The participants set their heads on a chin rest and reported their response using the “1” (indicating leftward) or “3” (indicating rightward) key of a numeric keyboard. 
Stimuli
Figure 1a shows the schematic illustration of the display used in Experiment 1. It consisted of five rectangle stimuli (0.4 × 0.8 deg each) horizontally aligned with a gap of 0.4 deg on a black background (0 cd/m 2). The stimuli were presented sequentially. Both the durations and ISIs were 13.33 ms (30 deg/s). A fixation cross (0.2 × 0.2 deg) was presented 5 deg above the center of the third rectangle stimulus. The fixation cross was corresponded to the center of the display. The luminance of each rectangle stimulus and the fixation cross was 70.2 cd/m 2. Participants saw the stimuli binocularly, and observation distance was 114.6 cm. 
Figure 1
 
Schematic of stimuli and conditions in Experiment 1. (a) Display used in Experiment 1. The rectangles were presented sequentially in the experiment. The fixation cross was presented at the center of the display. (b) The gray lined arrow indicates the motion direction of the prior sequence, and the white filled arrow indicates the motion direction of the test sequence.
Figure 1
 
Schematic of stimuli and conditions in Experiment 1. (a) Display used in Experiment 1. The rectangles were presented sequentially in the experiment. The fixation cross was presented at the center of the display. (b) The gray lined arrow indicates the motion direction of the prior sequence, and the white filled arrow indicates the motion direction of the test sequence.
We manipulated the spatiotemporal order of the last two stimuli (the test sequence). The first three stimuli (the prior sequence) were sequentially presented from either left or right side of the display to the center of the display. In the continuous condition, the presentation order of the test sequence was consistent with the prior sequence (i.e., the test sequence moved outward). In contrast, the spatiotemporal orders of the test sequence were the reverse of the prior sequence in the reversal condition (i.e., the test sequence moved inward; Figure 1b). The motion direction of the prior sequence (leftward or rightward) was randomized and counterbalanced within each condition. In addition to the display with the prior sequence, we presented the display without the prior sequence wherein all of the stimulus parameters were identical, except that only the test sequence was presented. We assigned the outward/inward motion direction judgments concerning physical motion from the center of the display to the test sequences in the without prior sequence condition. 
Procedure
The experiment was conducted in a dark room. The motion sequences were presented followed by the presentation of the fixation cross for 1000 ms. The participants were asked to fixate their eyes on it. After the presentation of the motion sequence, we asked the participants to report the perceived motion direction of the test sequence (leftward or rightward) using corresponding buttons of the keyboard. The displays with the prior sequence and those without the prior sequence were separated into two blocks. The order of the blocks was counterbalanced among the participants. Each block consisted of 10 practice trials, followed by 40 trials consisting of test sequences (2; continuous/reversal or outward/inward) × locations of test sequence (2; left/right from the center of the display) × repetitions (10). 
Results and discussion
For each participant, we calculated the proportion correct for each condition in both the displays with and those without the prior sequences in which motion direction perception was consistent with the physical inputs. The averaged proportion correct across the observers is shown in Figure 2. We separately analyzed the data with and without the prior sequence conditions. A two-tailed paired t-test revealed that the proportion correct of the reversal condition was significantly lower than that of the continuous condition in the display with the prior sequence ( t(5) = 6.13, p < 0.005). In contrast, there was no significant difference between the outward and inward conditions in the display without the prior sequence ( t(5) = 0.66, p = 0.54). 
Figure 2
 
The result of Experiment 1. The error bars denote the standard errors of the means ( N = 6).
Figure 2
 
The result of Experiment 1. The error bars denote the standard errors of the means ( N = 6).
The results showed that the observers failed to detect the motion reversal in the test sequence and perceived the continuous motion direction to be consistent with the prior sequence. This failure to perceive motion direction reversal indicates that spatiotemporally coherent motion perception occurs regardless of the reversal of motion sequences. Since the failure to perceive motion direction did not occur in the motion sequences without the prior sequence, the results could not be fully explained by the basic uncertainty of motion direction perception with the rapid presentation of the motion sequence (duration and ISI were 13.33 ms). 
Experiment 2
In Experiment 1, it was unclear whether the participants actually judge the motion direction between the fourth and fifth stimuli (test sequence) in the display with the prior sequence. One would assume that the judgments were made, for example, between the third (i.e., the last stimulus in the prior sequence) and fourth (i.e., the first stimulus in “time” in the test sequence) stimuli so that the reported motion direction was consistent with that of the prior sequence in the reversal conditions. In Experiment 2, the stimulus located in the fourth and fifth stimuli in “space” (the test sequence) in a five-point motion display was always filled with a different color from the other stimuli ( Figure 3a). This procedure enabled the participants to know where the test sequence was presented and to avoid misjudgment of motion direction between the third and fourth stimuli. If the result of Experiment 1 was replicated, we could exclude the above-mentioned possibility. 
Figure 3
 
Schematic of the stimuli and the result in Experiment 2. (a) Display used in Experiment 2. The stimuli were colored with red (R) or green (G). The colors of the stimulus located in the fourth and fifth spatial positions were always different from the others. (b) The result of Experiment 2. The error bars denote the standard errors of the means ( N = 7).
Figure 3
 
Schematic of the stimuli and the result in Experiment 2. (a) Display used in Experiment 2. The stimuli were colored with red (R) or green (G). The colors of the stimulus located in the fourth and fifth spatial positions were always different from the others. (b) The result of Experiment 2. The error bars denote the standard errors of the means ( N = 7).
Methods
Participants and apparatus
One author (S. H.) and five volunteers (graduate or undergraduate students in Tohoku University) participated in this experiment. All of them were experienced observers in psychophysics experiments. Five volunteers were naive to the purpose of this experiment. All had normal or corrected-to-normal vision. The apparatus were identical to those in the previous experiment. 
Stimuli and procedure
Stimuli and procedures were identical to those in Experiment 1 except that they were colored red (13.93 cd/m 2) or green (13.97 cd/m 2). The colors of the fourth and fifth stimuli in “space” (the test sequence) were different from those of the others (the prior sequence; Figure 3a). Participants were told that the test sequence was shown in a different color than the other stimuli. In each block, participants completed 40 trials consisting of test sequences (2; continuous/reversal or outward/inward) × locations of test sequence (2; left/right from the center of the display) × colors at the test sequence (2; red/green) × repetitions (5). The order of the blocks was counterbalanced across the participants. 
Results and discussion
The averaged proportion correct for each condition across the observers is shown in Figure 3b. A two-tailed paired t-test revealed that the proportion correct in the reversal condition was significantly lower than that of the continuous condition in the display with the prior sequence ( t(5) = 4.67, p < 0.01). In contrast, there was no significant difference of test sequence in the display without the prior sequence ( t(5) = −0.70, p = 0.52). 
In the current experiment, the participants correctly understood the location of the test sequence because the stimuli in the test sequence were always filled with a color that was different from those in the prior sequence. Since the results of Experiment 1 were replicated in the current experiment, we confirmed that the failure to detect motion direction reversal occurred in the test sequence containing the spatiotemporal reversal. 
Experiment 3
It has been noted that that spatial attention invokes motion perception (Hikosaka, Miyauchi, & Shimojo, 1993a). Hikosaka, Miyauchi, and Shimojo (1993b) presented a four-point motion sequence followed by a spatial cue at the last stimulus or no cue. Without the cue, motion was perceived in the direction from the first to the fourth inducing stimulus. With the cue, the attentional shift from the cue at the fourth to the first inducing stimulus occurred in the direction opposite to the actual motion direction. They showed that the resulting motion direction perception was consistent with attentional shift. This result indicated that a shift of spatial attention could overcome the motion perception consistent with the spatiotemporal physical inputs. In our previous experiments, the presentation from the first to fourth stimuli might induce the shift of spatial attention. Thus, it could be possible that this attentional shift was critical to the failure to perceive motion direction reversal in the reversal condition with the prior sequence. 
The current experiment investigated the effect of spatial attention on the failure to perceive motion direction reversal using the display in which the five-point motion sequence was presented above a two-point test sequence ( Figure 4a). Here, the observers were asked to judge the motion direction of the two-point sequence while the five-point motion sequence served to draw the observers' attention. If the shift of spatial attention is a critical factor, the failure to perceive motion direction reversal would occur in the two-point test sequence with the nearby five-point motion sequence. 
Figure 4
 
Schematic of the stimuli and the result in Experiment 3. (a) Display used in Experiment 3. Two-point test sequence was presented with or without nearby sequence. (b) The result of Experiment 3. The error bars denote the standard errors of the means (N = 5).
Figure 4
 
Schematic of the stimuli and the result in Experiment 3. (a) Display used in Experiment 3. Two-point test sequence was presented with or without nearby sequence. (b) The result of Experiment 3. The error bars denote the standard errors of the means (N = 5).
Methods
Participants and apparatus
One author (S. H.) and four volunteers (graduate or undergraduate students in Tohoku University) participated in this experiment. All of them were experienced observers in psychophysics experiments, and the four volunteers were naive to the purpose of this experiment. All had normal or corrected-to-normal vision. The apparatus were identical to those in the previous experiment. 
Stimuli and procedure
We presented a five-point motion sequence (the nearby sequence) that consisted of white squares (0.4 × 0.4 deg, 70.2 cd/m 2), which were the same as the squares used for motion stimuli in the two-point test sequence ( Figure 4a). Whereas the center of the stimuli in the nearby sequence was 4.2 deg below the fixation point, that in the test sequence was 5.0 deg below the center of the fixation point. The eccentricity of the test sequence was the same as that of the previous experiments. The horizontal positions of the test sequence were consistent with those of the last two stimuli in the nearby sequence. We always presented the continuous motion sequence as the nearby sequence, which draw the observers' attention to the fixed direction from the left to right side of the display, or vice versa. The onset of each stimulus in the test sequence was synchronized with that of the last two stimuli in the nearby sequence. The motion directions of the test sequences were either consistent (outward motion) or inconsistent (inward motion) with that of the nearby sequence. We asked the participants to judge the motion direction (leftward or rightward) of the test sequence. The motion direction of the test sequence was randomized and counterbalanced within each condition. In addition to the display with the nearby sequence, we also used a display without the nearby sequence. In this condition, all of the stimulus parameters were identical except that only the test sequence was presented. We assigned the outward/inward motion direction judgments concerning physical motion from the center of the display to the test sequences in the without nearby sequence condition. 
Trials with the nearby sequence and those without the nearby sequence were separated into two blocks. The order of the blocks was counterbalanced among the participants. In each block, participants completed 40 trials consisting of test sequences (2; consistent/inconsistent or outward/inward) × locations of test sequence (2; left/right from the center of the display) × repetitions (10). Except for the changes noted above, stimulus parameters and procedures were identical to those in Experiment 1
Results and discussion
The averaged proportion correct for each condition across the observers is shown in Figure 4b. A two-tailed paired t-test revealed no significant differences in both the display with the prior sequence ( t(4) = 0.59, p = 0.58) and that without the prior sequence ( t(4) = −0.95, p = 0.39). These results showed that the failure to perceive motion direction reversal in the test sequence did not occur when the test sequence was accompanied with a longer five-point (nearby) sequence to shift the observers' attention to the fixed direction. In other words, the observers' judgment of the motion direction of the test sequence was not affected by the direction of the attentional shift, and they correctly judged the motion direction of the test sequence. Therefore, it was suggested that the shift of spatial attention could not be critical to the failure to perceive motion direction reversal that we found in Experiments 1 and 2
Experiment 4
Experiments 1 and 2 showed that spatiotemporally coherent motion was perceived when the motion sequences contained a spatiotemporal irregularity along the motion trajectory. In Experiment 4, we investigated whether the spatiotemporally coherent motion could be perceived even when one stimulus diverted from a motion trajectory. Thus, we used the display where the shape of the motion trajectories (curved upper or lower) randomly diverted at the fourth stimulus in “space” in a five-point motion display ( Figure 5a). Note that the shape of the whole motion trajectory was undetermined until the presentation of the fifth stimulus in “time” (but the fourth in “space”) in the reversal condition with the prior sequence. In this situation, therefore, it should be more difficult to establish the spatiotemporally coherent motion perception compared with the simple direction reversal as tested in Experiments 1 and 2. If the failure to perceive motion direction reversal occurred even in this display, it would be additional, strong evidence that the spatiotemporally coherent motion perception could be flexibly established by the internal motion representation regardless of irregularity across space and time in motion trajectory. 
Figure 5
 
Schematic of the stimuli and the result in Experiment 4. (a) Display used in Experiment 4. The vertical positions of the stimulus located in fourth spatial position randomly diverted (±0.4 deg) in each trial. (b) The result of Experiment 4. The error bars denote the standard errors of the means ( N = 5).
Figure 5
 
Schematic of the stimuli and the result in Experiment 4. (a) Display used in Experiment 4. The vertical positions of the stimulus located in fourth spatial position randomly diverted (±0.4 deg) in each trial. (b) The result of Experiment 4. The error bars denote the standard errors of the means ( N = 5).
Methods
Participants and apparatus
One author (S. H.) and four volunteers (graduate or undergraduate students in Tohoku University) participated in this experiment. All of them were experienced observers in psychophysics experiments. The four volunteers were naive to the purpose of this experiment, although one of them had participated in Experiment 3. All had normal or corrected-to-normal vision. The apparatus were identical to those in the previous experiment. 
Stimuli and procedure
Stimuli were identical to those used in Experiment 1 (rectangles, 0.4 × 0.8 deg) except that the vertical position of the fourth stimulus in “space” in the continuous condition (the fourth in “time” as well) and that in the reversal condition (but the fifth in “time”) diverted as 0.4 deg upper or lower from the others ( Figure 5a). Thus, the participants perceived curved horizontal trajectories at the fourth stimulus in “space” in a five-point motion sequence. The direction of vertical offsets was randomized and counterbalanced among each condition. In each block with or without the prior sequence, the participants completed 40 trials consisting of test sequences (2; continuous/reversal or outward/inward) × locations of test sequence (2; left/right from the center of the display) × vertical offsets (2; upper/lower) × repetitions (5). Except for these, stimulus parameters and procedure were identical to those in Experiment 1
Results and discussion
The averaged proportion correct for each condition across the observers is shown in Figure 5b. A two-tailed paired t-test revealed that the proportion correct of the reversal condition was significantly lower than that of the continuous condition in the display with the prior sequence ( t(4) = 7.47, p < 0.005). In contrast, there was no significant difference of the test sequence in the display without the prior sequence ( t(4) = 1.58, p = 0.19). 
The failure to perceive motion direction reversal occurred even when the shape of the motion trajectories was uncertain until the presentation of the last stimulus. Thus, in addition to the results from Experiments 1 and 2, the present results also suggested that the flexible completion process of the internal motion representation could establish the spatiotemporally coherent motion perception regardless of the irregularity in motion trajectory. 
Because the amount of the vertical offsets was relatively small (±0.4 deg) the participants should not have perceived the vertical offsets or the changes of the motion trajectories. However, this was not the case. As a follow-up experiment, we asked the participants to report the direction of vertical offset (upper or lower) in the motion sequences with a prior sequence. The results showed that performance was almost perfect in both the continuous (95%) and the reversal (98%) conditions. There was no significant difference between the conditions ( t(4) = −1.50, p = 0.20). This confirmed that the failure to perceive motion direction reversal occurs when the participants are aware of vertical offsets or changes of motion trajectories. 
Experiment 5
Kanai et al. (2007) showed that 300-ms history of the prior inputs in continuous motion sequences was needed to induce failure in detecting single transient changes in motion trajectory. In Experiments 1, 2, and 4, the prior sequence was always comprised of three stimuli. This indicated that the failure to perceive motion direction reversal in motion trajectory could occur with only 79.98-ms history of the prior inputs in motion sequences. In Experiment 5, we further investigated how many prior inputs were needed to induce the failure to perceive motion direction reversal. Thus, the current experiment manipulated the number of the stimuli contained in the prior sequence (Figure 6a) from zero (two-point motion) to four (six-point motion). 
Figure 6
 
Schematic of the stimuli and the result in Experiment 5. (a) Display used in Experiment 5. The number of the prior stimuli was manipulated from zero (two-point motion) to four (six-point motion). (b) The result of Experiment 5. The error bars denote the standard errors of the means (N = 5).
Figure 6
 
Schematic of the stimuli and the result in Experiment 5. (a) Display used in Experiment 5. The number of the prior stimuli was manipulated from zero (two-point motion) to four (six-point motion). (b) The result of Experiment 5. The error bars denote the standard errors of the means (N = 5).
Methods
Participants and apparatus
One author (S. H.) and four volunteers (graduate or undergraduate students in Tohoku University) participated in this experiment. All of them were experienced observers in psychophysics experiments. Four volunteers were naive to the purpose of this experiment, although two of them had participated in Experiment 1. All had normal or corrected-to-normal vision. The apparatus were identical to those in the previous experiment. 
Stimuli and procedure
Stimuli were identical to those used in Experiment 1, except that the number of stimuli contained in the prior sequence changed from zero to four ( Figure 6a). The spatial position of the test sequence was fixed. The number of prior stimuli was randomized and counterbalanced within each condition. Thus, the participants perceived from two- to six-point motion. The display with zero prior stimulus was introduced as a control condition as well as the without prior sequence condition of the other experiments. The sequence moving outward was consistent with the test sequence in the continuous trials, and the sequence moving inward was consistent with the test sequence in the reversal trials. We also assigned the test sequences in the zero prior stimulus condition to continuous/reversal. 
The participants completed 200 trials consisting of prior stimuli (5) × test sequences (2; continuous/reversal) × locations of test sequence (2; left/right from the center of the display) × repetitions (10). The procedure was also identical to that in Experiment 1
Results and discussion
The averaged proportion correct for each condition across the observers is shown in Figure 6b. We conducted a two-way repeated measures ANOVA with prior stimulus (5; zero to four) × test sequence (2; continuous/reversal). This revealed the significant main effects of prior stimulus ( F(4,16) = 7.25, p < 0.005), test sequence ( F(1,4) = 313.36, p < 0.001), and a significant interaction between these factors ( F(4,16) = 24.46, p < 0.001). The simple main effect of test sequence showed that the proportion correct of the reversal condition was significantly lower than that of the continuous condition when the number of the prior stimuli ranged from one to four ( p < 0.001). With regard to the simple main effect of prior stimulus ( p < 0.001) in the reversal condition, Ryan's (1960) post hoc comparison revealed that the proportion correct in the one prior stimulus condition was significantly lower than that of the zero prior stimulus condition. Moreover, the proportion corrects from the two to four prior stimuli conditions were significantly lower than those of the zero and one prior stimulus conditions (p < 0.05). 
The results of Experiment 5 showed that a prior sequence containing only one stimulus could induce the failure to perceive motion direction reversal. This result indicated that 26.66-ms history (13.33 ms × 2 frames) of the prior motion inputs was enough to induce the failure to perceive motion direction reversal. Moreover, the effect of the prior sequence saturated when the prior sequence contained two or more stimuli. Thus, the failure to perceive motion direction reversal occurred with 53.32-ms history (13.33 ms × 4 frames) of the prior motion inputs. These histories of motion sequences were shorter than that (300 ms) shown in Kanai et al. (2007). This discrepancy might arise from differences in the effectiveness of internal motion representation between discrete motion sequence used in the current experiment and continuous motion sequences used in Kanai et al. (see the General discussion section for a detailed discussion of this possibility). 
General discussion
Previous studies have demonstrated that internal motion representation completed along motion trajectory interfered with a single physical input (Yantis & Nakama, 1998) and induced failure in detecting an irregularity at a specific time and space in motion trajectory (Kanai et al., 2007). However, it had not been fully investigated whether internal motion representation could interfere with spatiotemporal irregularities between multiple inputs across time and space. The present study showed evidence that internal motion representation induced the failure to perceive spatiotemporal irregularities (motion direction reversal) along motion trajectory, and coherent motion perception was established by the spatiotemporal reorganization of multiple visual inputs across time and space. 
In a five-point motion display, the motion direction perception of the last two sequences was consistent with three preceding stimuli even when the spatiotemporal orders of the last two sequences were reversed ( Experiments 1 and 2). The failure to perceive motion direction reversal occurred when the shape of the motion trajectory randomly changed ( Experiment 4). Moreover, we confirmed that one preceding stimulus (three-point motion) was sufficient to produce the failure to perceive motion direction reversal, and this effect saturated when the preceding sequence contained two or more stimuli ( Experiment 5). Note that the phenomenon reported here was strong, as evidenced by the fact that the observers failed to detect motion direction change even when they engaged in a direction judgment task. 
One might assume that attentional mechanisms were involved in our findings because the shift of spatial attention could induce motion direction perception inconsistent with the physical inputs (Hikosaka et al., 1993b). However, we confirmed that attentional shift itself did not induce the failure to perceive motion direction reversal. The failure to perceive motion direction reversal did not occur in two-point motion sequences when paired with a nearby five-point motion sequence, which drew the observers' attention to the fixed direction (Experiment 3). In addition, a reliable amount of the failure to perceive motion direction reversal was obtained in Experiment 4 in which the vertical positions of the fourth stimuli in “space” randomly changed; however, the changes might have attracted spatial attention to that location (Yantis & Jonides, 1984). These results suggested that attentional mechanisms are not critical to the failure to perceive motion direction reversal. 
The involvement of eye movement should also be considered. In addition to the fact that we presented a fixation point on the display in all the experiments, we found that the failure to perceive motion direction reversal occurred in three-point motion sequences ( Experiment 5). In that situation, the motion sequence was presented within 70 ms (13.33 ms × 5 frames), which was shorter than the minimum latency of saccadic eye movements (Fischer & Ramsperger, 1984; Fischer & Weber, 1993). Thus, it was suggested that eye movement was not the key factor for the failure to perceive motion direction reversal. 
The current findings suggested that the flexible completion process of motion representation could induce failure in detecting irregularity across time and space along motion trajectory and established spatiotemporally coherent motion perception. This would be reasonable, because the visual systems seem to be guided more by general, long-enduring physical principles than by specific laws (Shepard, 1984, 1994). Similarly, it was suggested that the multiple motion inputs should be integrated so as to establish perceived homogeneity in motion perception, based on the fact that the uniform motion velocity perception occurs against physical velocity changes (Schmerler, 1976). We could consider that the internal motion representation mechanisms could reorganize the physical inputs in order to induce spatiotemporally coherent motion perception based on the spatiotemporal integration of the multiple inputs across time and space (Burr, 1980). 
De Bruyn and Orban (1988) showed that motion direction reversal was easy to detect in real motion displays when the target velocity was 30 deg/s, which is similar to our stimuli. However, this is not the case in our experiments, possibly because we used a discrete motion display (cf. apparent motion display). Kanai et al. (2007) explained the suppressive effect of motion representation on a single irregularity at a spatiotemporal position from the viewpoint of the tuning of the spatiotemporal filter. In their model, the more the inputs of prior stimuli are presented, the better the tuning of the spatiotemporal filter for motion perception is. They noted that failure in detecting transient changes in motion trajectory occurred with 300-ms history of the prior stimuli. In contrast, the results of Experiment 5 indicated that 26.66-ms history (one prior stimulus) was enough to induce the failure to perceive motion direction reversal. Moreover, the effect of the prior sequence saturated when the prior sequence contained two or more stimuli with 53.32 ms of history. This discrepancy might be based on differences in the effectiveness of internal motion representation. Whereas Kanai et al. used a continuous motion display in which the stimuli were spatiotemporally adjacent to each other, we used a discrete motion display that consisted of spatiotemporally discrete physical inputs with 0.4 deg of gaps and 13.33 ms of ISIs. The visual systems complete internal motion representation in motion trajectory where there are no physical inputs in order to establish continuous motion perception from discrete physical inputs (Burr, 1979; Shepard & Zare, 1983). Since the current research used a discrete motion display, the completion process of the internal motion representation might work more effectively relative to the continuous motion display, and a short previous history was enough to produce coherent motion perception. 
There are two mechanisms involved in the establishment of the internal motion representation: predictive extrapolation and postdictive interpolation mechanisms. With regard to predictive extrapolation, Kanai et al. (2007) demonstrated that sensitivity to an irregularity (gaps, contrast, shape, or color) in motion trajectory became worse with 300-ms history of motion sequences. They also illustrated that, different from precedent motion sequences, motion sequences presented after the transient changes were ineffective. These finding suggested that the predictive extrapolation mechanisms of internal motion representation made it difficult to detect changes that were inconsistent with predicted motions. Schwiedrzik et al. (2007) presented a target in motion trajectory using various timing and positions in repeated cycles of two-point apparent motion sequences. They found that target detection performance became better when the timing and the position of the target presentation were consistent with the estimated spatiotemporal positions of the internal motion representation. They suggested that the predictively extrapolated internal motion representation enhanced detection of the physical inputs in motion trajectory. 
The fact that we can perceive motion between stimuli that are spatiotemporally apart (cf. apparent motion) indicates that motion perception and its motion representation cannot be established until the subsequent stimulus is presented. Regarding this postdictive aspect of motion perception, Beck, Elsner, and Silverstein (1977) illustrated that the optimal spatiotemporal relationship between inducers (Korte's third law) was supported when the position of the second stimulus was uncertain in a two-point apparent motion display. This finding suggests that “only after” the next stimulus appeared, the visual systems interpolated the internal motion representation in the past position of motion trajectory based on the spatiotemporal characteristics (interval and distance) between the previous and subsequent inducers. Hogendoorn et al. (2008) also reported that the motion masking effect occurred in the future positions along the motion trajectory when apparently moving objects moved with spatiotemporal coherence. In addition, the motion masking effect also occurred along the updated motion trajectory when the motion direction was unpredictably reversed. In sum, these previous findings indicated that both the predictive and postdictive mechanisms are involved in the completion of the internal motion representation in motion trajectory. 
In line with the previous finding (Hogendoorn et al., 2008), the current research suggests that both predictive extrapolation and postdictive interpolation mechanisms of motion representation contribute to the spatiotemporal consistency of motion perception. In Experiment 5, the failure to perceive motion direction reversal occurred more frequently when multiple numbers of the stimuli were presented in the prior sequence. This indicated the involvement of predictive extrapolation mechanisms on failures to detect spatiotemporal irregularities in motion trajectory (Kanai et al., 2007; Schwiedrzik et al., 2007; Shioiri et al., 2000). In addition, the present data showed that one prior stimulus was sufficient to induce the failure to perceive motion direction reversal. In this situation, the history of motion sequences was absent, so the predictive extrapolation mechanism would not work (Kanai et al., 2007). Moreover, in Experiment 4, we also found that the failure to perceive motion direction reversal occurred even when the shape of the motion trajectories was uncertain until the presentation of the last stimulus. These findings suggested that the postdictive interpolation mechanism could also contribute to the establishment of spatiotemporally coherent motion perception (Beck et al., 1977; Hogendoorn et al., 2008). 
We assume that the visual systems effectively utilize both of these mechanisms, based on the processing stage of motion perception (Eagleman, 2008). The postdictive mechanisms might be dominant in situations having a relatively shorter history of motion sequences, where the internal motion representation is being established in response to incoming physical inputs. In contrast, the predictive mechanisms would be effective in cases in which a longer history of sequences is available to establish stable internal motion representation. In addition to the inducement of failure in detecting spatiotemporal irregularities by predictive motion representation (Kanai et al., 2007), postdictive motion representation might reorganize irregular physical inputs to the spatiotemporally coherent motion perception by integrating the inputs across time and space. In our daily life, blinking or occluders sometimes produce a lack of visual inputs of moving objects. Moreover, in some cases, we cannot follow a moving object with high temporal resolution. In such situations, the visual systems would require both of the internal motion representation mechanisms in order to establish spatiotemporal consistency of motion perception. 
In conclusion, failures to detect irregularity across time and space in motion trajectory occurred in a situation involving the spatiotemporal reversal of motion sequences. The flexible internal motion representation mechanisms reorganize the spatiotemporal irregularity of motion inputs into spatiotemporally coherent motion perception, and thereby establish constancy of our dynamic environment. 
Acknowledgments
We thank Takahiro Kawabe for his helpful comments and suggestions. We are also grateful to Pawan Sinha and two anonymous reviewers for their insightful comments and suggestions for early versions of the manuscript. This research was supported by Grant-in-Aid for JSPS Fellows (No. 19004400) to S.H., Grant-in-Aid for Young Scientists (B; Nos. 21730607 and 18730480) and Grant-in-Aid for Scientific Research on Innovative Areas (No. 21119527) from MEXT to M.N., and Grant-in-Aid for Scientific Research (B) from JPSP (No. 18330151) and Grant-in-Aid for Specially Promoted Research from MEXT (No. 19001004) to J.G. 
Commercial relationships: none. 
Corresponding author: Souta Hidaka. 
Email: hidaka@sal.tohoku.ac.jp. 
Address: Department of Psychology, Graduate School of Arts and Letters, Tohoku University, 27-1, Kawauchi, Aoba-ku, Sendai, Miyagi 980-8576, Japan. 
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Figure 1
 
Schematic of stimuli and conditions in Experiment 1. (a) Display used in Experiment 1. The rectangles were presented sequentially in the experiment. The fixation cross was presented at the center of the display. (b) The gray lined arrow indicates the motion direction of the prior sequence, and the white filled arrow indicates the motion direction of the test sequence.
Figure 1
 
Schematic of stimuli and conditions in Experiment 1. (a) Display used in Experiment 1. The rectangles were presented sequentially in the experiment. The fixation cross was presented at the center of the display. (b) The gray lined arrow indicates the motion direction of the prior sequence, and the white filled arrow indicates the motion direction of the test sequence.
Figure 2
 
The result of Experiment 1. The error bars denote the standard errors of the means ( N = 6).
Figure 2
 
The result of Experiment 1. The error bars denote the standard errors of the means ( N = 6).
Figure 3
 
Schematic of the stimuli and the result in Experiment 2. (a) Display used in Experiment 2. The stimuli were colored with red (R) or green (G). The colors of the stimulus located in the fourth and fifth spatial positions were always different from the others. (b) The result of Experiment 2. The error bars denote the standard errors of the means ( N = 7).
Figure 3
 
Schematic of the stimuli and the result in Experiment 2. (a) Display used in Experiment 2. The stimuli were colored with red (R) or green (G). The colors of the stimulus located in the fourth and fifth spatial positions were always different from the others. (b) The result of Experiment 2. The error bars denote the standard errors of the means ( N = 7).
Figure 4
 
Schematic of the stimuli and the result in Experiment 3. (a) Display used in Experiment 3. Two-point test sequence was presented with or without nearby sequence. (b) The result of Experiment 3. The error bars denote the standard errors of the means (N = 5).
Figure 4
 
Schematic of the stimuli and the result in Experiment 3. (a) Display used in Experiment 3. Two-point test sequence was presented with or without nearby sequence. (b) The result of Experiment 3. The error bars denote the standard errors of the means (N = 5).
Figure 5
 
Schematic of the stimuli and the result in Experiment 4. (a) Display used in Experiment 4. The vertical positions of the stimulus located in fourth spatial position randomly diverted (±0.4 deg) in each trial. (b) The result of Experiment 4. The error bars denote the standard errors of the means ( N = 5).
Figure 5
 
Schematic of the stimuli and the result in Experiment 4. (a) Display used in Experiment 4. The vertical positions of the stimulus located in fourth spatial position randomly diverted (±0.4 deg) in each trial. (b) The result of Experiment 4. The error bars denote the standard errors of the means ( N = 5).
Figure 6
 
Schematic of the stimuli and the result in Experiment 5. (a) Display used in Experiment 5. The number of the prior stimuli was manipulated from zero (two-point motion) to four (six-point motion). (b) The result of Experiment 5. The error bars denote the standard errors of the means (N = 5).
Figure 6
 
Schematic of the stimuli and the result in Experiment 5. (a) Display used in Experiment 5. The number of the prior stimuli was manipulated from zero (two-point motion) to four (six-point motion). (b) The result of Experiment 5. The error bars denote the standard errors of the means (N = 5).
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