August 2007
Volume 7, Issue 11
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Research Article  |   August 2007
The parallel between reverse-phi and motion aftereffects
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Journal of Vision August 2007, Vol.7, 8. doi:10.1167/7.11.8
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      Roger J. E. Bours, Marijn C. W. Kroes, Martin J. M. Lankheet; The parallel between reverse-phi and motion aftereffects. Journal of Vision 2007;7(11):8. doi: 10.1167/7.11.8.

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Abstract

Periodically flipping the contrast of a moving pattern causes a reversal of the perceived direction of motion. This direction reversal, known as reverse-phi motion, has been generally explained with the notion that flipping contrasts actually shifted the balance of motion energy toward the opposite direction. In this sense, the reversal is trivial because any suitable motion energy detector would be optimally excited in a direction opposite to that for regular motion. This notion, however, does not address the question how these two types of motion are initially detected. Here we show several perceptual phenomena indicating that low-level detection of the two types of motion is quite different. Reverse-phi motion percepts in many respects behave more like motion aftereffects than like regular motion. Motion adaptation causes reduced activity during a stationary test stimulus, which by means of directional opponency leads to motion perceived in the opposite direction. Our findings suggest that reverse-phi motion similarly reduces the activity of low-level motion detectors.

Introduction
Reverse-phi motion is the reversal of perceived direction when the contrast of a moving pattern is inverted during displacements (Anstis, 1970; Anstis & Mather, 1985; Anstis & Rogers, 1975). It is one of the most compelling motion phenomena, similar in strength to the well-known motion aftereffect. Unlike the common account for motion aftereffects, which result from reduced activity after prolonged motion adaptation, the explanation for reverse-phi motion has remained controversial. 
The classical account points out that contrast reversals shift the balance of Fourier energy toward the opposite direction, which any suitable motion detector (Adelson & Bergen, 1985; Krekelberg & Albright, 2005; van Santen & Sperling, 1985) would pick up. In this sense, the reversal is trivial and merely reflects stimulus properties rather than characteristics of mechanisms underlying motion detection. The notion that contrast reversals shift motion energy to the opposite direction, however, does not explain how and at what level the direction reversal originates. Here we investigate whether properties of reverse-phi percepts can provide insight into the way how low-level motion mechanisms are organized. 
In reverse-phi stimuli, motion information consists of correlations between contrast increments and decrements. Low-level contrast information is separated in two channels: ON-center cells in the retina and LGN signal positive contrasts and OFF-center cells signal negative contrasts. Mo and Koch (2003) studied models of low-level motion detectors and concluded that sensitivity for reverse-phi motion cannot be easily explained by the assumption of a strictly separate processing of signals from ON-center and OFF-center cells. Instead, they propose that information from ON-center and OFF-center cells gets combined at the first level of motion detection. In this paper, we address the question how correlations across different contrasts lead to perceptual direction reversals. 
Mo and Koch (2003) proposed a model in which interactions between ON and OFF cells generate excitatory signals for detectors tuned to the direction opposite to the displacement. Reverse-phi stimuli thus excite detectors tuned to the opposite direction of regular motion. Notice, however, that a similar result could also be obtained if reverse-phi motion does not excite detectors for the direction opposite to the displacement but instead inhibits detectors tuned to the “same” direction, that is, in the direction of displacement. Because motion is opponently organized, such response reductions become perceptually equivalent to response increments in the opposite direction. Under the assumption that reverse-phi results from combining information from ON and OFF cells, two different configurations are possible, as illustrated in Figure 1. The diagrams show how local ON and OFF cell signals are combined in generating directional selectivity. The circles with solid or dashed arrows represent directionally selective operators for the different combinations of local ON and OFF cell signals, which combine into a single directionally selective cell (for instance in V1). Directionality is determined by the type of operator (combination of either same cell type or of different cell types) and by the position of the delay (one side delayed or the opposite side). This initial stage of motion detection is then followed by an integration stage (not shown) which implements integration across space and directions and which also implements directional opponency. Figure 1B is functionally equivalent to the scheme proposed by Mo and Koch. In this case, a detector tuned to rightward motion would sum excitations from operators tuned to regular rightward motion and contrast reversed leftward motion. Similarly, rightward reversed contrast motion would excite an operator tuned to leftward motion. In this way, both regular and reverse-phi motion leads to excitations of low-level motion detectors. Figure 1A shows the alternative, in which contrast reversed motion in the same direction causes an inhibition. In this case, regular motion causes excitations and reverse-phi motion causes inhibitions of detectors tuned to the same direction. If this initial motion detection stage is followed by opponent directional interactions, it also explains direction reversals for reverse-phi motion. Please notice that Scheme A is also equivalent to first subtracting ON and OFF cell responses, and then performing a spatiotemporal correlation. As long as such combined signals are not translated into a rectifying spike train before correlation this would yield similar results. Both Schemes A and B utilize the full contrast signal, as suggested in motion energy models. They differ however in the order of the operations. In Scheme A, directions initially remain the same but the sign inverts; in Scheme B, the sign remains the same but directions reverse. 
Figure 1
 
Combining signals from local, ON and OFF cells into motion detectors. A minimal requirement for motion sensitivity is the combination of two signals separated in space and time. In each of the two locations, we have an ON-center cell and an OFF-center cell. One can pair each local unit with a delay to one of the two units in the other pair. This provides two signals based on similar contrasts (indicated by the solid arrows) and two signals based on opposite contrasts (dashed arrows). The two configurations differ in the directionality and sign of the opposite contrast combinations. In panel A, that is, the scheme we propose, the four directions are the same, but the sign is inverted. The alternative (B) is to keep the sign positive but reverse directions for opposite contrast combinations. Squares represent a time delay. In Scheme A, reverse-phi motion leads to an inhibition of the low-level motion detector, which by means of opponency at a higher level (not shown) results in a direction reversal.
Figure 1
 
Combining signals from local, ON and OFF cells into motion detectors. A minimal requirement for motion sensitivity is the combination of two signals separated in space and time. In each of the two locations, we have an ON-center cell and an OFF-center cell. One can pair each local unit with a delay to one of the two units in the other pair. This provides two signals based on similar contrasts (indicated by the solid arrows) and two signals based on opposite contrasts (dashed arrows). The two configurations differ in the directionality and sign of the opposite contrast combinations. In panel A, that is, the scheme we propose, the four directions are the same, but the sign is inverted. The alternative (B) is to keep the sign positive but reverse directions for opposite contrast combinations. Squares represent a time delay. In Scheme A, reverse-phi motion leads to an inhibition of the low-level motion detector, which by means of opponency at a higher level (not shown) results in a direction reversal.
In combination with opponent directional interactions as found in area MT, both schemes result in reversals of perceived direction. The two types of responses are, however, not equivalent. In fact excitations and inhibitions at the lower detection level behave quite differently, especially under transparent motion conditions. This has been extensively documented for motion aftereffects. Aftereffects result from reduced activity after prolonged adaptation, which by means of disinhibition presumably induces perceived motion in the opposite direction (He, Cohen, & Hu, 1998; Krekelberg, Boynton, & van Wezel, 2006; Petersen, Baker, & Allman, 1985; Tootell et al., 1995; Taylor et al., 2000). 
Directional tuning for aftereffects, however, differs from that for direct motion vision. Two populations of dots moving in different directions are easily seen to move transparently, yet the aftereffect of two such components is mostly unidirectional, opposite to the vector sum of the components (Alais, Verstraten, & Burr, 2005; Mather, 1980; Verstraten, Fredericksen, & van de Grind, 1994). For example, adaptation to two motion vectors, one to the upper left and one to the upper right, causes a single aftereffect in the downward direction. The differences in directional tuning are easily explained if excitatory interactions are narrowly tuned, and inhibitory interactions more broadly tuned (Grunewald & Lankheet, 1996). Narrow tuning for excitations supports transparency for multiple, regular motion components. However, reduced activity in the adapted directions leads, through broad disinhibition, to a single, wide distribution during the aftereffect, which is perceived as a single, unified motion component. 
Here we ask the question whether reverse-phi motion behaves like motion aftereffects, or like real motion stimuli. To answer this question, we study directional interactions between two reverse-phi motion components shown transparently. If reverse-phi motion results from reduced activity we would expect it to behave like motion aftereffects. However, if it results from increased activity it should behave like direct motion percepts. 
In pilot experiments, we tested this prediction with random dot patterns containing two motion components, one moving to the upper left and one to the upper right. Without contrast reversals during displacements, the dots were perceived as two sheets moving transparently. The two motion components remained clearly segregated. However, when the contrast of each dot was inverted during displacements, the percept consisted of a single vector, in the downward direction. This suggests that reverse-phi motion, like motion aftereffects, is based on a reduction of activity in the same direction rather than an increase in the opposite direction. It suggests that the scheme as presented in Figure 1A is the most likely candidate for combining low-level contrast information. We further tested and corroborated this hypothesis in two quantitative psychophysical experiments. 
Methods
To specifically study directional interactions for either regular or reverse-phi stimuli, we developed a stimulus in which motion information was limited to either same-polarity correlations (regular motion) or to opposite polarity correlations (reverse-phi motion). To this end, we used a single-step dot lifetime stimulus similar to that used in a previous paper (Bours, Stuur, & Lankheet, 2007). Dot patterns were randomly refreshed after each displacement, thus removing a correlation bias over multiple time steps. 
All motion stimuli consisted of dynamic, sparse random dot patterns presented on a gray background of 50 cd/m 2. Half of the dots was brighter and half was darker than the mean background (contrast 96%). A single pattern consisted of 2,500 dots, displayed in an 8° × 8° window on a computer monitor (120 Hz frame rate). Stimuli consisted of two such patterns shown transparently. Dots (0.02° × 0.02°) were dynamically refreshed on every frame of the monitor but reappeared once again at a displaced location and after a specified interval. Refreshed dots and displaced dots were shown on every frame of the monitor. Thus, each frame statistically contained the same amount of coherent motion information, irrespective of step size or temporal interval. 
For regular motion, the contrast of a dot remained the same upon displacement; white remained white and black remained black. For reverse-phi motion, the contrasts were reversed; white became black and black became white. Stimuli therefore contained equal numbers of black and white dots on each frame of the monitor. Because both regular and reverse-phi stimuli consisted of equal numbers of bright and dark dots, random correlations were the same for both types of stimulus. The only difference is that regular motion stimuli contain a directional bias for same-polarity correlations and reverse-phi for opposite polarity correlations. 
Motion coherence levels were varied by varying the percentage of dots moving coherently. Incoherent dots were displaced to a new random position. At 100% coherence, all reincarnated dots, that is, half of all dots, were coherently displaced. 
Figure 2 shows space–time plots for both types of motion. The examples show a single pattern displaced rightward 3 pixels every three frames. Coherent motion corresponds to an oriented pattern in such space–time plots. Without a contrast reversal, one easily perceives the orientation in the space–time plot. The right-hand column in Figure 2 shows the same motion, combined with reversals of contrast on each displacement. The only consistent correlation is the correspondence between dots of opposite contrast polarity. Spatiotemporal correlations for dots of similar polarity are maximally randomized across directions. Contrast reversals in this stimulus completely abolish the overall orientation in the space–time plot (Burr & Ross, 2006). Yet, observers are very sensitive to this type of motion, which is perceived in the direction opposite to the displacements. Despite the clear differences in Fourier transforms as shown in Figure 2, observers are nearly equally sensitive to the two types of motion. 
Figure 2
 
Space–time plots, and corresponding Fourier transforms for a single component of regular and reverse-phi motion. Stimuli consisted of a set of dots dynamically refreshed on every frame of the monitor. Each dot re-appeared once again at a displaced location, and after a specified interval. The contrast between the first and second instance of a dot was either held constant (regular motion) or inverted (reverse-phi). To reduce the three-dimensional (XYT) stimulus space to two dimensions, we plotted a single row of (horizontal) pixels as a function of time (along the vertical axis). Spatial displacement was set to three pixels and temporal interval to three frames. Fourier transforms were averaged over 100 frames.
Figure 2
 
Space–time plots, and corresponding Fourier transforms for a single component of regular and reverse-phi motion. Stimuli consisted of a set of dots dynamically refreshed on every frame of the monitor. Each dot re-appeared once again at a displaced location, and after a specified interval. The contrast between the first and second instance of a dot was either held constant (regular motion) or inverted (reverse-phi). To reduce the three-dimensional (XYT) stimulus space to two dimensions, we plotted a single row of (horizontal) pixels as a function of time (along the vertical axis). Spatial displacement was set to three pixels and temporal interval to three frames. Fourier transforms were averaged over 100 frames.
The advantage of these stimuli is that they optimally isolate both types of motion information, and randomize unintended motion components. This is also true for two such patterns transparently combined because the patterns are uncorrelated and contain equal numbers of dark and bright dots (see Figure 3). 
Figure 3
 
Space–time plots of transparent motion stimuli and corresponding Fourier transforms. The left-hand side shows an example of transparent regular motion consisting of a leftward and rightward moving pattern. Space–time plots and Fourier plots are shown for the direction parallel to displacements, and orthogonal to displacements. The right-hand side shows the same analysis for two reverse-phi patterns moving in opposite directions. Combining two opponent motion stimuli clearly does not introduce motion energy orthogonal to the displacements. Fourier transforms were averaged over 100 frames.
Figure 3
 
Space–time plots of transparent motion stimuli and corresponding Fourier transforms. The left-hand side shows an example of transparent regular motion consisting of a leftward and rightward moving pattern. Space–time plots and Fourier plots are shown for the direction parallel to displacements, and orthogonal to displacements. The right-hand side shows the same analysis for two reverse-phi patterns moving in opposite directions. Combining two opponent motion stimuli clearly does not introduce motion energy orthogonal to the displacements. Fourier transforms were averaged over 100 frames.
One might argue that the reverse-phi type of motion could be detected as an imbalance for same-contrast correlations because spatiotemporal correlation for opposite polarities automatically removes same-polarity correlations at the same space–time offset. The quantitative similarity in sensitivity for both types of motion, as shown for example in Experiment 2, strongly argues against a significant contribution from this effect. We will return to this issue in the discussion. 
Results
Experiment 1: Orthogonal reverse-phi motion
The experiment is based on the orthogonal motion aftereffect illusion. This illusion is perceived after adaptation to two patterns moving in opposite directions. In this case, the directional interactions as previously described cancel the imbalance along the axis of stimulation yet induce perceived motion in the orthogonal directions (Grunewald & Lankheet, 1996). If reverse-phi percepts similarly result from response reductions, then observers should also perceive two oppositely directed reverse-phi components to move along an orthogonal orientation. For example, transparent reverse-phi motion to the left and to the right should be seen to move upward and downward. Motion detectors in both stimulus directions now become inhibited, and orthogonal directions would be disinhibited. These two peaks in opposite directions, orthogonal to the displacements should then segregate like two regular, opponent motion components. 
We showed observers transparent motion consisting of two opposite motion vectors, which were either two regular motion components, or two reverse-phi components. The two components could be oriented along the rightward or leftward oblique. Figure 3 shows space–time plots and corresponding Fourier transforms of the two types of transparent motion. Combining two patterns moving in opposite direction has no effect on motion energy in the orthogonal directions. 
The task for the observer was to indicate the orientation along which motion was perceived. The experiment was constructed to minimize any perceptual difference between regular and reverse-phi motion. The only difference was the contrast reversal between the first and the second occurrence of a dot for reverse-phi stimuli, whereas for regular motion the contrast polarity for each dot remained the same. All other stimulus parameters were identical for regular and reverse-phi motion. The step size was 5 pixels (0.1°) and the temporal interval was three frames (25 ms). Both parameters were in the optimal range as determined in separate experiments. Psychometric curves were measured using a method of constant stimuli. In a single experiment, we randomly interleaved regular motion and reverse-phi motion, at different strengths of the motion signal, that is, different coherence values. Each stimulus was repeated 10 times in a single experiment, and experiments were repeated three times. Trials lasted 1 s, after which observers indicated the orientation along which they perceived motion (left or right oblique). For both regular motion and reverse-phi, “correct” performance corresponded to the axis along which dots were displaced. Psychometric curves and 95% confidence intervals were obtained by maximum likelihood fits of cumulative Gaussians and bootstrapping methods (Wichmann & Hill, 2001a, 2001b). 
Data for five subjects are shown in Figure 4. Transparent motion of two regular components (diamonds in Figure 4) was readily seen along the correct orientation. Performance was at chance level for low signal strengths and increased to nearly 100% correct performance for the highest signal strengths. The combination of two similar, transparent reverse-phi components (squares in Figure 4) gave a reversed result. In this case, observers consistently saw the motion along an orientation orthogonal to the displacements. They judged the orientation as if it were two real motion vectors orthogonal to the actual displacements. Naive observers generally reported afterward that they were unable to distinguish trials with regular motion from trials with reverse-phi motion. 
Figure 4
 
Two opponent reverse-phi motion components are perceived along an orientation orthogonal to their displacement. Two regular (diamonds) or two reverse-phi motion components (squares) were shown transparently along the left or right oblique directions. Observers indicated the orientation of perceived motion, as a function of motion coherence. Negative coherence values corresponded to the upper left oblique and positive values to the upper right oblique. We used a two-alternative forced-choice paradigm with a 1-s trial duration. All stimuli were interleaved in a single experiment and were repeated at least 30 times. Results shown are for a step size of 0.1° and a temporal interval of 25 ms. The contrast between the first and second instance of a dot was either held constant (regular motion) or reversed (reverse-phi). The two lower panels show data for individual, naive observers. The top panel shows results pooled for five subjects, including two authors.
Figure 4
 
Two opponent reverse-phi motion components are perceived along an orientation orthogonal to their displacement. Two regular (diamonds) or two reverse-phi motion components (squares) were shown transparently along the left or right oblique directions. Observers indicated the orientation of perceived motion, as a function of motion coherence. Negative coherence values corresponded to the upper left oblique and positive values to the upper right oblique. We used a two-alternative forced-choice paradigm with a 1-s trial duration. All stimuli were interleaved in a single experiment and were repeated at least 30 times. Results shown are for a step size of 0.1° and a temporal interval of 25 ms. The contrast between the first and second instance of a dot was either held constant (regular motion) or reversed (reverse-phi). The two lower panels show data for individual, naive observers. The top panel shows results pooled for five subjects, including two authors.
Observes were only slightly less consistent in their answers for the reverse-phi condition. Absolute slopes of the psychometric curves were only a factor of 2.1 smaller. At maximum signal strengths, observers scored on average 93% correct for regular motion and 74% incorrect for reverse-phi motion. The orthogonal effect is much stronger than observed for motion aftereffects (Grunewald & Lankheet, 1996). This probably results from the fact that for reverse-phi the percept is directly stimulus driven, whereas for aftereffects it starts fading immediately after adaptation. 
Experiment 2: Motion nulling
The orthogonal percept for transparent reverse-phi motion, as shown in the previous experiment, reveal that reverse-phi percepts behave like motion aftereffects rather then like regular motion percepts. It suggests that reverse-phi similarly causes inhibitions at the front-end level of motion detection. Directional interactions and disinhibition supposedly transform inhibitions into relative excitations that correspond to the motion percept. In a second experiment, we constructed a more direct test to study the sign of the low-level response. It is based on the finding that motion aftereffects can be nulled with real, regular motion (Blake & Hiris, 1993; Lankheet & Verstraten, 1995). Adding real motion to a test stimulus opposite to a perceived aftereffect does not result in transparent motion but cancels the motion percept altogether. The reason is that the aftereffect results from a response reduction. Adding real motion simply restores the reduced activity levels to their unadapted state, canceling the directional imbalance. Nulling thus implies cancellation of positive and negative responses (van de Grind, Lankheet, & Tao, 2003). If reverse-phi percepts also arise from inhibitions, we would predict similar nulling. If on the other hand reverse-phi results from excitations in the opposite direction, the two presumed excitations should induce a transparent motion percept. 
Stimuli consisted of one regularly moving pattern and a second, reverse-phi pattern. In a single experiment, the direction and coherence level (signal strength) for the contrast reversed pattern were held constant. Negative coherence values corresponded to (perceived) leftward motion, positive to rightward motion. The coherence level of the regularly moving pattern was varied in a method of constant stimuli. The spatial displacement for both patterns was 5 pixels (0.1°) and the temporal interval was three frames (25 ms). Trials lasted 1 s and each stimulus was repeated at least 30 times. In a two-alternative forced-choice experiment, observers indicated the direction of motion that could either be to the left or to the right. Psychometric curves and 95% confidence intervals were obtained by maximum likelihood fits of cumulative Gaussians and bootstrapping methods (Wichmann & Hill, 2001a, 2001b). 
Observers reported that they did not perceive the two patterns moving transparently but instead saw a single direction of motion. This was qualitatively different from combining two regular motion components, which always resulted in two components perceived to move transparently. Quantitative results are shown in Figure 5. Figure 5A shows full psychometric curves measured for a single combination of step size and temporal interval. The two panels on the left show data for individual observers. The right-hand panel shows results pooled for seven observers (two authors, five naive). Adding reverse-phi motion simply shifted the psychometric curve leftward or rightward. Slopes for different amounts of added reversed-contrast motion were not significantly different. In other words, the presence of the reversed-contrast motion component caused a large bias, without affecting direction discriminability. This is clearly different from detecting regular motion in the presence of another regular motion component, which only has a minor effect (Edwards & Nishida, 1999; Lindsey & Todd, 1998; Verstraten, Fredericksen, van Wezel, Boulton, & van de Grind, 1996). The coherence level for the reverse-phi stimulus required to fully cancel the regular motion component was only slightly lower than the coherence level of regular motion. A reverse-phi component of 50% was, on average, nulled with a regular component of 45%, and at 100% it was on average 87%. 
Figure 5
 
Nulling reverse-phi motion with regular motion. Stimuli consisted of one regularly moving pattern and a second, contrast reversed pattern. In a single experiment, the coherence level (signal strength) for the contrast reversed pattern was held constant, as indicated in the figure. Negative coherence values corresponded to (perceived) leftward motion, positive to rightward motion. The coherence level of the regularly moving pattern was variable. In a two-alternative forced-choice experiment, observers indicated the direction of motion that could either be to the left or to the right. Panel A shows examples of psychometric curves, and their 95% confidence intervals, measured with a step size of 5 pixels (0.1°) and temporal interval of three frames (25 ms). The two panels on the left show data for individual observers. The right-hand panel shows results pooled for seven observers (two authors, five naive). Panel B shows shifts of the psychometric curves for different combinations of step size and temporal interval, averaged for five observers (two authors, three naive). Error bars represent the standard error of the mean across five observers.
Figure 5
 
Nulling reverse-phi motion with regular motion. Stimuli consisted of one regularly moving pattern and a second, contrast reversed pattern. In a single experiment, the coherence level (signal strength) for the contrast reversed pattern was held constant, as indicated in the figure. Negative coherence values corresponded to (perceived) leftward motion, positive to rightward motion. The coherence level of the regularly moving pattern was variable. In a two-alternative forced-choice experiment, observers indicated the direction of motion that could either be to the left or to the right. Panel A shows examples of psychometric curves, and their 95% confidence intervals, measured with a step size of 5 pixels (0.1°) and temporal interval of three frames (25 ms). The two panels on the left show data for individual observers. The right-hand panel shows results pooled for seven observers (two authors, five naive). Panel B shows shifts of the psychometric curves for different combinations of step size and temporal interval, averaged for five observers (two authors, three naive). Error bars represent the standard error of the mean across five observers.
Figure 5B shows that nearly identical results were obtained for other combinations of step size and temporal interval. Data for different observers were highly consistent. 
Discussion
Explanations for reverse-phi motion so far were based on excitation of motion detectors tuned to the direction opposite to the displacement. Clearly, at a high level of analysis, this must be the case. It has been shown that the level of activity in monkey area MT (middle temporal), an area dedicated to motion analysis, corresponds to the monkeys motion percept (Britten, Shadlen, Newsome, & Movshon, 1993; Newsome, Britten, & Movshon, 1989; Newsome, Britten, Salzman, & Movshon, 1990; Shadlen, Britten, Newsome, & Movshon, 1996). Microstimulation in MT may bias the monkey's perceptual choice depending on the tuning properties of stimulated neurons (Salzman, Murasugi, Britten, & Newsome, 1992). Krekelberg and Albright (2005) have shown that MT activity for reverse-phi stimuli also corresponds to the monkey's percept. At the level of MT reverse-phi causes activation of cells tuned to the direction opposite to the displacement. 
These findings, however, do not reveal how the two types of motion are initially detected. The initial stage of motion detection in primates is located in primary visual cortex (V1), where simple and complex cells derive directional selectivity from nondirectionally sensitive geniculate cells. Contrast information in the retina and LGN is divided across two different channels: ON cells most effectively signal positive contrasts, whereas OFF cells signal negative contrasts. High sensitivity for reverse-phi stimuli suggests that low-level motion detectors specifically combine information from ON and OFF cells (Mo & Koch, 2003). These authors proposed a model in which such opposite contrast correlations excite detectors tuned to the direction opposite to the displacement (Figure 1B). However, here we show evidence that the alternative, as shown in Figure 1A, is more plausible. Motion signals based on correlations between ON and OFF channels probably cause inhibition of motion detectors tuned to the direction of displacement. 
The critical observation to support this conclusion is the similarity between motion aftereffects and reverse-phi motion. Directional interactions differ between direct motion percepts and motion aftereffects due to differences in directional tuning width for excitations and inhibitions. Low-level excitations remain narrowly tuned and as a result multiple components remain segregated. Response reductions after adaptation, however, induce the opposite percept through disinhibition (van de Grind et al., 2003, van de Grind, van der Smagt, & Verstraten, 2004). If inhibitions are more broadly tuned, this leads to broad directional tuning for aftereffects (Grunewald & Lankheet, 1996). It explains the orthogonal motion aftereffect and the fact that adaptation to multiple motion components mostly results in a single, unified motion aftereffect. We propose that the same interactions may be responsible for the behavior of reverse-phi percepts. This would imply that reverse-phi, like motion adaptation, causes a response reduction at the detection level, which through disinhibition transforms into a motion percept in the opposite direction. 
The proposal is further supported by results for the nulling experiment. Whereas two regular motion patterns are readily seen to move in opposite directions, one regular and one reverse-phi component always canceled each other. This shows that reverse-phi is fundamentally different from regular motion in the opposite direction. The behavior is similar to that observed for motion aftereffects, but the effect is much stronger. Motion aftereffects can also be nulled with real motion but the motion strength required is much lower (Blake & Hiris, 1993; Lankheet & Verstraten, 1995; van de Grind et al., 2003). The fact that nearly equal motion strengths were required to cancel the percept shows that cancellation was not due to a relatively small sensitivity for reverse-phi motion. In fact, in pilot experiments, we found observers to be equally sensitive to the two types of motion. Motion coherence thresholds measured for the same motion settings as in the nulling experiments did not differ significantly between regular and reverse-phi motion. 
Similarity of motion strengths required for nulling and quantitative similarity of motion sensitivity for regular and reverse-phi motion also rule out that the lack of same-contrast correlations in the reverse-phi stimulus can account for the present findings. If the main effect of reversing the contrast would be removing same-contrast correlations at the specific spatiotemporal offset, we should expect large differences in sensitivity. In this case, regular motion would result in a large bias in one specific direction whereas reverse-phi would correspond to incoherent noise in all directions, except one. Among other things, such a broad distribution of directions would largely cancel because most components would be balanced by their opponent counterpart. Equal sensitivity for regular and for reverse-phi motion thus strongly suggests that opposite polarity correlations are actually used for motion detection. 
The most likely explanation for the nulling results is that regular and reverse-phi motion cause excitations and inhibitions of similar strength, which are added at the very first level of motion detection. 
Clearly, this proposal does not deny the observation that the difference between regular motion and reverse-phi motion is embedded in the stimulus. Nor does it deny that ideal, linear processing of Fourier components could predict the reversal (Adelson & Bergen, 1985; Edwards & Nishida, 2004; Krekelberg & Albright, 2005). It rather addresses the level at which the reversal takes place. Our experiments show that we can differentiate between different schemes (Figure 1) of combining positive and negative contrast signals. We propose that, at low levels of motion detection (V1), contrast reversals reverse the sign of the response, not the direction. At the next level of global direction integration (area MT) this then gives rise to a direction reversal. 
Once we realize that contrast reversals may lead to perceived direction reversals through inhibitions rather than excitations, we may also appreciate the reason for this specific sensitivity. Combining opposite contrasts with a negative sign makes optimal use of all available information. If spatiotemporal correlations between pairs of ON cells or pairs of OFF cells signal coherent motion from one receptive field to the other, then correlations between ON and OFF cells signal the absence of coherent motion. Thus, correlations between equal contrast polarities provide positive evidence whereas correlations between opposite polarities provide negative evidence for the same motion. Weighing positive and negative evidence for the same motion at the first detection stage efficiently improves signal-to-noise ratios. 
It is interesting to notice that the space–time representation of our motion stimuli, as presented in Figure 2, is similar to Glass patterns that have been used to study orientation sensitivity. Results for orientation detection are, however, less consistent, and aftereffects and contrast reversals may yield different results. Burr and Ross (2006) showed that contrast reversals for Glass patterns can counteract the effect of equal-polarity correlations but do not result in orientation percepts. This would suggest inhibition without opponency. However, Clifford and Weston (2005) used a nulling procedure for adaptation to Glass patterns similar to the procedure we used for motion. They found clear orthogonal aftereffects, indicating opponency between orthogonal orientations. Dakin (1997) also reported induction of orthogonal percepts from contrast reversed Glass patterns. These different findings show an essential difference between orientation analysis and motion analysis. For orientation detection, aftereffects and reversed contrast stimuli may yield different results. For motion, however, aftereffects and reverse-phi percepts behave in similar ways. 
Our hypothesis is in line with neurophysiological results in the primate and feline visual system. Directional selectivity, the corner stone of motion sensitivity, arises in primary visual cortex, especially in complex cells. This is also the level were information from ON and OFF pathways merges (Schiller, 1992; Schiller, Sandell, & Maunsell, 1986). V1 complex cells in both cat (Emerson, Bergen, & Adelson, 1992) and macaque (Livingstone & Conway, 2003) respond with relative inhibitions to reversed contrast correlations. At this level, there is relatively little opponency (Snowden, Treue, Erickson, & Andersen, 1991). At the level of area MT, however, negative modulations have been transformed into positive modulations, and perceived motion corresponds to excitations (Krekelberg & Albright, 2005). Thus, it seems likely that directional interactions translating inhibitions to excitations (Grunewald & Lankheet, 1996) are effectuated in the projection of V1 to MT. 
Acknowledgments
We thank Wim van de Grind, Bert van den Berg, and Richard van Wezel for critical comments on the manuscript. This research was supported by the Helmholtz Institute, Utrecht University and by the Innovational Research Incentives Scheme (VIDI) of he Netherlands Organization for Scientific Research (NWO). 
Commercial relationships: none. 
Corresponding author: Martin J. M. Lankheet. 
Email: m.j.m.lankheet@uu.nl. 
Address: Padualaan 8, 3584 CH Utrecht, The Netherlands. 
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Figure 1
 
Combining signals from local, ON and OFF cells into motion detectors. A minimal requirement for motion sensitivity is the combination of two signals separated in space and time. In each of the two locations, we have an ON-center cell and an OFF-center cell. One can pair each local unit with a delay to one of the two units in the other pair. This provides two signals based on similar contrasts (indicated by the solid arrows) and two signals based on opposite contrasts (dashed arrows). The two configurations differ in the directionality and sign of the opposite contrast combinations. In panel A, that is, the scheme we propose, the four directions are the same, but the sign is inverted. The alternative (B) is to keep the sign positive but reverse directions for opposite contrast combinations. Squares represent a time delay. In Scheme A, reverse-phi motion leads to an inhibition of the low-level motion detector, which by means of opponency at a higher level (not shown) results in a direction reversal.
Figure 1
 
Combining signals from local, ON and OFF cells into motion detectors. A minimal requirement for motion sensitivity is the combination of two signals separated in space and time. In each of the two locations, we have an ON-center cell and an OFF-center cell. One can pair each local unit with a delay to one of the two units in the other pair. This provides two signals based on similar contrasts (indicated by the solid arrows) and two signals based on opposite contrasts (dashed arrows). The two configurations differ in the directionality and sign of the opposite contrast combinations. In panel A, that is, the scheme we propose, the four directions are the same, but the sign is inverted. The alternative (B) is to keep the sign positive but reverse directions for opposite contrast combinations. Squares represent a time delay. In Scheme A, reverse-phi motion leads to an inhibition of the low-level motion detector, which by means of opponency at a higher level (not shown) results in a direction reversal.
Figure 2
 
Space–time plots, and corresponding Fourier transforms for a single component of regular and reverse-phi motion. Stimuli consisted of a set of dots dynamically refreshed on every frame of the monitor. Each dot re-appeared once again at a displaced location, and after a specified interval. The contrast between the first and second instance of a dot was either held constant (regular motion) or inverted (reverse-phi). To reduce the three-dimensional (XYT) stimulus space to two dimensions, we plotted a single row of (horizontal) pixels as a function of time (along the vertical axis). Spatial displacement was set to three pixels and temporal interval to three frames. Fourier transforms were averaged over 100 frames.
Figure 2
 
Space–time plots, and corresponding Fourier transforms for a single component of regular and reverse-phi motion. Stimuli consisted of a set of dots dynamically refreshed on every frame of the monitor. Each dot re-appeared once again at a displaced location, and after a specified interval. The contrast between the first and second instance of a dot was either held constant (regular motion) or inverted (reverse-phi). To reduce the three-dimensional (XYT) stimulus space to two dimensions, we plotted a single row of (horizontal) pixels as a function of time (along the vertical axis). Spatial displacement was set to three pixels and temporal interval to three frames. Fourier transforms were averaged over 100 frames.
Figure 3
 
Space–time plots of transparent motion stimuli and corresponding Fourier transforms. The left-hand side shows an example of transparent regular motion consisting of a leftward and rightward moving pattern. Space–time plots and Fourier plots are shown for the direction parallel to displacements, and orthogonal to displacements. The right-hand side shows the same analysis for two reverse-phi patterns moving in opposite directions. Combining two opponent motion stimuli clearly does not introduce motion energy orthogonal to the displacements. Fourier transforms were averaged over 100 frames.
Figure 3
 
Space–time plots of transparent motion stimuli and corresponding Fourier transforms. The left-hand side shows an example of transparent regular motion consisting of a leftward and rightward moving pattern. Space–time plots and Fourier plots are shown for the direction parallel to displacements, and orthogonal to displacements. The right-hand side shows the same analysis for two reverse-phi patterns moving in opposite directions. Combining two opponent motion stimuli clearly does not introduce motion energy orthogonal to the displacements. Fourier transforms were averaged over 100 frames.
Figure 4
 
Two opponent reverse-phi motion components are perceived along an orientation orthogonal to their displacement. Two regular (diamonds) or two reverse-phi motion components (squares) were shown transparently along the left or right oblique directions. Observers indicated the orientation of perceived motion, as a function of motion coherence. Negative coherence values corresponded to the upper left oblique and positive values to the upper right oblique. We used a two-alternative forced-choice paradigm with a 1-s trial duration. All stimuli were interleaved in a single experiment and were repeated at least 30 times. Results shown are for a step size of 0.1° and a temporal interval of 25 ms. The contrast between the first and second instance of a dot was either held constant (regular motion) or reversed (reverse-phi). The two lower panels show data for individual, naive observers. The top panel shows results pooled for five subjects, including two authors.
Figure 4
 
Two opponent reverse-phi motion components are perceived along an orientation orthogonal to their displacement. Two regular (diamonds) or two reverse-phi motion components (squares) were shown transparently along the left or right oblique directions. Observers indicated the orientation of perceived motion, as a function of motion coherence. Negative coherence values corresponded to the upper left oblique and positive values to the upper right oblique. We used a two-alternative forced-choice paradigm with a 1-s trial duration. All stimuli were interleaved in a single experiment and were repeated at least 30 times. Results shown are for a step size of 0.1° and a temporal interval of 25 ms. The contrast between the first and second instance of a dot was either held constant (regular motion) or reversed (reverse-phi). The two lower panels show data for individual, naive observers. The top panel shows results pooled for five subjects, including two authors.
Figure 5
 
Nulling reverse-phi motion with regular motion. Stimuli consisted of one regularly moving pattern and a second, contrast reversed pattern. In a single experiment, the coherence level (signal strength) for the contrast reversed pattern was held constant, as indicated in the figure. Negative coherence values corresponded to (perceived) leftward motion, positive to rightward motion. The coherence level of the regularly moving pattern was variable. In a two-alternative forced-choice experiment, observers indicated the direction of motion that could either be to the left or to the right. Panel A shows examples of psychometric curves, and their 95% confidence intervals, measured with a step size of 5 pixels (0.1°) and temporal interval of three frames (25 ms). The two panels on the left show data for individual observers. The right-hand panel shows results pooled for seven observers (two authors, five naive). Panel B shows shifts of the psychometric curves for different combinations of step size and temporal interval, averaged for five observers (two authors, three naive). Error bars represent the standard error of the mean across five observers.
Figure 5
 
Nulling reverse-phi motion with regular motion. Stimuli consisted of one regularly moving pattern and a second, contrast reversed pattern. In a single experiment, the coherence level (signal strength) for the contrast reversed pattern was held constant, as indicated in the figure. Negative coherence values corresponded to (perceived) leftward motion, positive to rightward motion. The coherence level of the regularly moving pattern was variable. In a two-alternative forced-choice experiment, observers indicated the direction of motion that could either be to the left or to the right. Panel A shows examples of psychometric curves, and their 95% confidence intervals, measured with a step size of 5 pixels (0.1°) and temporal interval of three frames (25 ms). The two panels on the left show data for individual observers. The right-hand panel shows results pooled for seven observers (two authors, five naive). Panel B shows shifts of the psychometric curves for different combinations of step size and temporal interval, averaged for five observers (two authors, three naive). Error bars represent the standard error of the mean across five observers.
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