Moving two-dimensional patterns can capture the perceived directions of lower or higher spatial frequency gratings.

Coherent plaid motion is produced by superimposing two one-dimensional gratings of the same spatial frequency moving +/- 60 degrees from the intersection-of-constraints (IOC) resultant direction. These moving plaids were found to change the perceived direction of a third one-dimensional grating, either 6-fold lower or higher in spatial frequency, from traveling in one of the plaid's component direction to the IOC resultant direction. We describe this phenomenon as coherence capture. Coherence capture was found to be effective between plaids with 0.5, 1.0, and 1.5 c/deg components and gratings of 3.0, 6.0 and 9.0 c/deg respectively. It was also found to be effective between plaids with 3.0 c/deg components and gratings of 0.5 c/deg. However, coherence capture between higher spatial frequency plaids and lower spatial frequency gratings became less effective when the component spatial frequencies of the plaid increased.     

The role of color in the motion system.

We have examined the ability of observers to determine the direction of movement of a variety of colored plaid patterns. When the two plaid components are of unequal spatial frequency or of unequal luminance or chromatic contrast, observers judge the direction of movement incorrectly. These errors are correlated with a misjudgement of the speeds of the two components. Our results provide support for an initial decomposition into oriented components followed by a subsequent component-to-pattern recombination of moving equiluminant and colored plaids. At equal multiples of threshold contrast a moving luminance grating is about 8 times more powerful than a moving equiluminant grating in determining the apparent direction of motion of a plaid. When both are present, luminance and color do not interact linearly. Color and motion must be processed in parallel in at least partially separate pathways.     

Coherent motion perception fails at low contrast

If the Fourier components of a moving plaid have similar temporal frequency, spatial frequency and contrast, coherent motion is perceived according to subjective judgements. We have devised a more objective method of determining the conditions required for coherent motion. Moving plaid stimuli were created with one stationary component. Plaids with a stationary component always have a single perceived direction of motion, which is determined by the presence or absence of coherent motion. In a temporal two-interval forced-choice paradigm we used a direction discrimination task to investigate the effect of varying the temporal and spatial characteristics of the Fourier components and pattern contrast on the probability of coherent motion perception. Agreement across observers regarding the conditions required for coherent motion was excellent using this more objective method. We find that patterns do not produce coherent motion when presented at contrast threshold, irrespective of how similar the Fourier components are. We also confirm that when the temporal frequency, spatial frequency and contrast of the gratings are sufficiently similar, observers report the direction of motion indicating coherent motion.     

Motion-detection thresholds for first- and second-order gratings and plaids

The two-stage decomposition-recombination model of 2D motion perception has been criticised on the basis that the direction of plaid stimuli can be accurately discriminated at speeds so low that the direction of their Fourier components is not discriminable. The nature of this gap in performance between gratings and plaids was investigated across a range of spatial frequencies and durations for first- and second-order stimuli. Motion-detection thresholds were obtained using a 2AFC, constant stimuli procedure and it was found that although thresholds for detection of plaid motion were often lower than those for gratings, the gap in performance between first-order plaids and gratings was unreliable, varying in magnitude and occasionally direction with the spatial frequency of the stimulus, presentation duration and observer. Curiously, an analogous gap found between purely second-order gratings and second-order plaids was more reliable and stable. It has been suggested that the gap is the result of 'local motion detectors' or broadly tuned V1 cells. The data presented here suggest that second-order mechanisms are responsible for the gap and that first-order information may even disrupt it.     

Second-order motion discrimination by feature-tracking.

When a plaid pattern (the sum of two high spatial frequency gratings oriented +/- 84 degrees from vertical) jumps horizontally by 3/8 of its spatial period its contrast envelope, a second-order pattern, moves in the opposite direction to its luminance waveform. Observers report that the pattern moves in the direction of the contrast envelope when the jumps are repeated at intervals of more than 125 ms and in the direction of the luminance profile when they are repeated at longer intervals. When a pedestal [Lu, Z.-L. & Sperling, G. (1995). Vision Research, 35, 2697-2722] is added to the moving plaid a higher contrast is required to see motion of the contrast envelope but not to see the motion of the luminance profile, suggesting that the motion of the contrast envelope is sensed by a mechanism that tracks features. Static plaids with different spatial parameters from the moving pattern are less effective at raising the contrast required to see the motion of the contrast envelope and simple gratings of low or high spatial frequency are almost completely ineffective, suggesting that the feature-tracking mechanism is selective for the type of pattern being tracked and rejects distortion products and zero-crossings.     

Evidence for a Feature Tracking Explanation of Why Type II Plaids Move in the Vector Sum Direction at Short Durations

When two moving sinusoidal gratings, with similar spatial frequency, contrast, phase, but different orientation are combined to form a plaid, their perceived direction of motion has been predicted by the intersection of constraints rule (IOC) (Adelson & Movshon, Nature, 300, 523–525, 1982). However, at short durations (60 msec) the direction of perceived motion has been predicted by the vector sum direction for “Type II” plaids (Yo & Wilson, Vision Research, 32, 1, 1992). Type II plaids are the set of plaids where the components are both located on one side of the resultant computed using the IOC rule. Yo and Wilson suggest that the vector sum direction is observed for Type II plaids at short durations because non-Fourier information is not available and direction is computed from Fourier information only. The first experiment in this study replicates the original Yo and Wilson result using similar stimuli but a simpler task; perceived direction was measured using a direction discrimination task instead of the method of adjustment used by Yo and Wilson. The second experiment provides evidence against generalizing the result to all Type II plaids. A systematic set of type II plaids that varied only in terms of the orientation of the second component provided an ideal set because their predicted motion direction followed very different patterns when predicted by the IOC and vector sum computations. The results obtained were predicted more accurately by the IOC than the vector sum. Experiment 3 provides further evidence that movement in the vector sum direction is not a general property of type II plaids. A small change to the velocity of one of the components of a plaid previously perceived in the vector sum direction had the effect of shifting the perceived motion in the IOC direction, despite increasing the difference between the IOC and VS predictions. This result is not consistent with Yo and Wilson's hypothesis that Type II plaids move in the vector sum direction because of a temporal delay between Fourier and non-Fourier information. Computational analysis of the stimuli used in both the current and original experiments revealed a possible explanation of the results in terms of a contribution from local feature tracking rather than a vector sum operation. Copyright © 1996 Elsevier Science Ltd.     

Two-stage analysis of the motion of 2-dimensional patterns, what is the first stage?

The sum of two differently orientated moving sinusoidal gratings of similar spatial frequency, contrast, and velocity appears as a single coherent "plaid" pattern. The visual system is thought to analyse the motion of plaids in two stages, first analysing the motion of the (1-D) components, and then calculating a speed and direction which is consistent with those 1-D motions. We find that the direction of motion of a plaid (components 1.6 c/deg orientated +60 degrees and -60 degrees) can be discriminated at velocities so low that the direction of motion of its components is not discriminable. This finding is not consistent with the "two-stage" hypothesis in the form that it is usually expressed. We suggest that mechanisms sensitive to the motion of local elements in the pattern, such as edges, could also contribute to the first stage of the analysis of plaid motion.     

Motion Coherence Across Different Chromatic Axes

It has been reported that equiluminant plaid patterns constructed from component gratings modulated along different axes of a cardinal colour space fail to create a coherent impression of two-dimensional motion Krauskopf and Farell (1990). Nature, 348, 328–331. In this paper we assess whether this lack of interaction between cardinal axes is a general finding or is instead dependent upon specific stimulus parameters. Type I and Type II plaids were made from sinusoidal components (1 cpd) each modulated along axes in a cardinal colour space and presented at equivalent perceived contrasts. The spatial angular difference between the two components was varied from 5 to 90 deg whilst keeping the Intersection of Constraints (I.O.C.) solution of the pattern constant. Observers were required to indicate the perceived direction of motion of the pattern in a single interval direction-identification task. We find that: (i) When plaids were made from components modulated along the same cardinal axis, coherent “pattern” motion was perceived at all angular differences. As the angular difference between the components decreased in a Type II plaid, the perceived direction of motion moved closer to the I.O.C. solution and away from that predicted by the vector sum. (ii) A plaid made from components modulated along red-green and blue-yellow cardinal axes (cross-cardinal axis) did not cohere at high angular differences (>30 deg) but had a perceived direction of the fastest moving component. At lower angular differences, however, pattern motion was detected and approached the I.O.C. solution in much the same way as a same-cardinal axis Type II plaid. (iii) A plaid made from a luminance grating and a cardinal chromatic grating (red-green or blue-yellow) failed to cohere under all conditions, demonstrating that there is no interaction between luminance and chromatic cardinal axes. These results indicate that there are conditions under which red-green and blue-yellow cardinal components interact for the purposes of motion detection. Copyright © 1996 Elsevier Science Ltd.     

Bivectorial transparent stimuli simultaneously adapt mechanisms at different levels of the motion pathway

The motion aftereffect (MAE) to drifting bivectorial stimuli, such as plaids, is usually univectorial and in a direction opposite to the pattern direction of the plaid. This is true for plaids that are perceived as coherent, but also for other plaids which are seen as transparent for most or all of the adaptation period. The underlying mechanisms of this MAE are still not well understood. In order to assess these mechanisms further, we measured static and dynamic MAEs and their interocular transfer (IOT). Adaptation stimuli were plaids with small (coherent) and large (transparent) angles between the directions of the component gratings and a horizontal grating, which were adjusted in spatial frequency and drift velocity so that the pattern speed and vertical periodicity remained constant. Test stimuli were horizontal static or counterphasing gratings with the same periodicity as the adaptation stimuli. MAE duration was measured for monocular, binocular and IOT conditions. All static MAEs were smallest for the transparent plaid and largest for the grating, while all dynamic MAEs were constant across adaptation stimuli. IOT was twice as big for dynamic MAEs as for static MAEs, and did not vary with the adaptation stimuli. Other adaptation stimuli were plaids that differed in intersection luminance, contrast or spatial frequency, resulting in different amounts of perceived coherence. MAEs and IOT did not vary with perceived coherence. The results suggest that the MAE for bivectorial stimuli consists of low-level adaptation (dependent on local component properties, small IOT), as well as high-level adaptation (dependent on global integrated pattern properties, large IOT), which can be measured independently with static and dynamic test stimuli.     

Direction specific masking and the analysis of motion in two dimensions

We measured the effects of moving two-component cosine grating masks on the detectability of a moving spatially localized test pattern with a 1.0 octave spatial frequency bandwidth. Masking was used to distinguish between two-component patterns with fluid motion (blobs) and those with rigid motion (plaids). The two gratings which made up the two-dimensional masking patterns were always of the same spatial frequency and contrast, but moved in different directions. We find that plaid masks consistently produced threshold elevations that are 2.0-4.0 times greater than are produced by a single component mask at twice the contrast. Furthermore, this effect is nearly independent of the angle between the two mask components. For fluid motion, however, masking is determined by the mask component whose direction of motion is closest to that of the test. The results obtained with moving two-dimensional patterns demonstrate that, for blobs, the motion of the pattern as a whole has no effect on the degree of masking, whereas, for plaids, the signals arising from the two components interact in a nonlinear manner, thus producing a substantial enhancement of masking, which is clearly related to the coherent motion of the entire pattern. These data shed light on the properties of higher order motion units (possibly in MT cortex) that respond to the direction of two-dimensional pattern motion, suggesting that they combine, in a nonlinear manner, the outputs of units which respond independently to the direction of each mask component.     

Perception of direction of motion reflects the early integration of first and second-order stimulus spatial properties

Second-order Type I and Type II plaids were constructed by combining two orientation-filtered random-dot gratings. Each component consisted of a dynamic filtered random-dot field, the contrast of which was modulated by a drifting sinusoidal grating. Orienting the two components suitably and interleaving at 120 Hz allowed us to produce a two-dimensional plaid pattern made from one-dimensional second-order components. The perceived direction of motion of both Type I and Type II plaids was measured as a function of the orientation content of the carrier, the contrast, and the duration of the stimulus. Type I plaids had a perceived direction close to the intersection of constraints/vector sum solution (which coincide for Type I patterns) for all conditions when the motion was visible. Type II plaids had a perceived direction that moved away from the vector sum and toward the intersection of constraints solution as the orientation bandwidth of the carrier increased. The data explain discrepancies in previous work using comparable stimuli and are consistent with recent evidence that the previously considered parallel pathways of form and motion have a strong influence upon one another from early stages of cortical visual processing.     

The Barberplaid Illusion: Plaid Motion is Biased by Elongated Apertures

The perceived direction of motion of plaids windowed by elongated spatial Gaussians is biased toward the window's long axis. The bias increases as the relative angle between the plaid motion and the long axis of the window increases, peaks at a relative angle of ≈45 deg, and then decreases. The bias increases as the window is made narrower (at fixed height) and decreases as the component spatial frequency increases (at fixed aperture size). We examine several models of human motion processing (cross-correlation, motion-energy, intersection-of-constraints, and vector-sum), and show that none of these standard models can predict our data. We conclude that spatial integration of motion signals plays a crucial role in plaid motion perception and that current models must be explicitly expanded to include such spatial interactions. Published by Elsevier Science Ltd.     

A model of plaid motion perception based on recursive Bayesian integration of the 1-D and 2-D motions of plaid features

We describe a theoretical and computational model of the perception of plaid pattern motion which fully accounts for the majority of cases in which misperception of the direction of motion of Type II plaids has been observed [Yo, C., & Wilson, H. (1992). Perceived direction of moving two-dimensional patterns depends on duration, contrast, and eccentricity. Vision Research 32, 135-147]. The model consists of two stages: in the first stage local motion detectors signal both the one-dimensional (1-D) and two-dimensional (2-D) motion of the high luminance features (blobs) in the plaid pattern; in the second stage these local motion signals are combined using a recursive Bayesian least squares estimation process. We demonstrate both theoretically and using simulations of the computational model that the estimated direction of the plaid motion for Type II plaids is initially dominated by the 1-D motion of the longer edges of the elongated blobs, which is in a direction close to the vector sum direction of the component gratings. The recursive estimation process which combines the local motion signals in the second stage of the model results in a dynamic shift in the estimated plaid direction towards the direction of the 2-D motion of the blobs, which corresponds to the veridical plaid direction.     

The oblique plaid effect

Plaids are ambiguous stimuli that can be perceived either as a coherent pattern moving rigidly or as two gratings sliding over each other. Here we report a new factor that affects the relative strength of coherency versus transparency: the global direction of motion of the plaid. Plaids moving in oblique directions are perceived as sliding more frequently than plaids moving in cardinal directions. We term this the oblique plaid effect. There is also a difference between the two cardinal directions: for most observers, plaids moving in horizontal directions cohere more than plaids moving in vertical directions. Two measures were used to quantify the relative strength of coherency vs. transparency: C/[C+T] and RTtransp. Those measures were derived from dynamics data obtained in long-duration trials (>1 min) where observers continually indicated their percept. The perception of plaids is bi-stable: over time it alternates between coherency and transparency, and the dynamics data reveal the relative strength of the two interpretations [Vision Research 43 (2003) 531]. C/[C+T] is the relative cumulative time spent perceiving coherency; RTtransp is the time between stimulus onset and the first report of transparency. The dynamics-based measures quantify the relative strength of coherency over a wider range of parameters than brief-presentation 2AFC methods, and exposed an oblique plaid effect in the entire range tested. There was no interaction between the effect of the global direction of motion and the effect of gratings' orientations. Thus, the oblique plaid effect is due to anisotropies inherent to motion mechanisms, not a bi-product of orientation anisotropies. The strong effect of a plaid's global direction on its tendency to cohere imposes new and important constraints on models of motion integration and transparency. Models that rely solely on relative differences in directions and/or orientations in the stimulus cannot predict our results. Instead, models should take into account anisotropies in the neuronal populations that represent the coherent percept (integrated motion) and those that represent the transparent percept (segmented motion). Furthermore, the oblique plaid effect could be used to test whether neuronal populations supposed to be involved in plaid perception display tuning biases in favor of cardinal directions.     

Effect of contrast on the perceived direction of a moving plaid

We performed a series of experiments examining the effect of contrast on the perception of moving plaids. This was done to test the hypothesis put forth by Adelson and Movshon (1982) that the human visual system determines the direction of a moving plaid in a two-staged process: decomposition into component motion followed by application of the intersection of constraints rule. Although there is recent evidence that the first tenet of their hypothesis is correct, i.e. that plaid motion is initially decomposed into the motion of the individual grating components (Movshon, Adelson, Gizzi & Newsome, 1986; Welch, 1989), the nature of the second-stage combination rule has not as yet been established. We found that when the gratings within the plaid are of different contrast, the perceived direction is not predicted by the intersection of constraints rule. There is a strong (up to 20 deg) bias in the direction of the higher-contrast grating. A revised model, which incorporates a contrast-dependent weighting of perceived grating speed as observed for 1-D patterns (Thompson, 1982), can quantitatively predict most of our results. We discuss our results in the context of various models of human visual motion processing and of physiological responses of neurons in the primate visual system.     

Visual motion of missing-fundamental patterns: motion energy versus feature correspondence

Missing-fundamental gratings, generated by subtracting the fundamental Fourier components from square-wave gratings, appear to move backward when presented in quarter-cycle jumps, even though their edges and features all move forward. We used variants of these stimuli to test current models of motion perception. We found that missing-fundamental plaids, constructed from orthogonal missing-fundamental gratings, also appear to move backward. Forward motion was restored to missing-fundamental gratings and plaids by adding back small fractions of the original fundamental. In-phase and antiphase addition of the fundamental had similar effects on the perceived motion, despite having markedly different effects on the features, appearances and zero-crossings of the stimuli. The critical amplitude of fundamental needed to restore forward motion to plaids was the same as that needed to restore forward motion to their isolated component gratings, indicating that the plaids' emergent features, such as edge intersections and 'blobs', made little or no contribution to the perceived direction of motion in these stimuli. In two derivative experiments, missing-fundamental chromatic gratings and plaids, at approximate isoluminance, and missing-fundamental luminance barberpoles, also generated backward perceived motions, and these were also reversed by in-phase or antiphase addition of small amounts of fundamental.     

Lower threshold of motion for one and two dimensional patterns in central and peripheral vision.

Lower motion thresholds for discriminating opposing motion directions were compared for one dimensional (grating) and two dimensional (plaid) stimuli in central and peripheral vision. The results were consistent with a two-stage model of motion sensitivity in which threshold-limiting noise occurs at both stages, and the speed as well as the direction of the resultant motion is determined by intersection-of-constraints (IOC) from the component motions. The results do not support a purely geometric interpretation of the IOC model, in which thresholds for plaid stimuli are related to thresholds of component gratings by a geometric factor. Neither do the data favour explanations in which local luminance features (i.e. blobs) are detected and their velocity determined. Monte-Carlo simulations of the two-stage process predict thresholds across variations in component direction, contrast, and visual field eccentricity. Lower motion thresholds for gratings and plaids both follow a saturating function of contrast; the fit between grating and plaid data is improved when the plaid contrast is expressed in terms of the contrast of its components. Although less contrast saturation was found in the periphery, in relative terms, plaid and grating motion thresholds were similar in central and peripheral vision, implying cortical magnifications are similar for mechanisms which process grating and plaid motion.     

Plaid perception is only subtly impaired in strabismic amblyopia

Amblyopes exhibit a global motion anomaly that implicates processing beyond the local motion analysis of V1 possibly involving areas MT and MST in the extra-striate cortex. Here, we sought to further investigate this deficit by measuring the perception of moving plaid stimuli by amblyopic observers, since there is good physiological evidence that the motion of such stimuli is determined by processes beyond V1. The conditions under which the two moving components constituting the plaids were seen to cohere or move transparently over one another were investigated by manipulating their relative spatial frequencies. Percepts were measured using both short presentation durations, where both the percept and the direction of motion were reported, and long presentation durations where the bi-stability of the stimulus was directly measured. In addition, we measured the ability of amblyopic eyes to perceive globally coherent motion in a multiple aperture stimulus. We found a small increased tendency for both amblyopic and fellow-fixing eyes to perceive short duration plaid stimuli as coherent relative to control eyes, but no difference for long duration plaids. In addition, amblyopic eyes saw less coherence in multiple aperture stimuli than fellow-fixing eyes but were not reliably different from control eyes. We therefore conclude that the neural mechanisms underlying plaid perception are only subtly abnormal in amblyopia.     

Perceived direction of plaid motion is not predicted by component speeds

It has been shown that the perceived direction of a plaid with components of unequal contrast is biased towards the direction of the higher-contrast component [Stone, L. S., Watson, A. B., & Mulligan, J. B. (1990). Effect of contrast on the perceived direction of a moving plaid. Vision Research 30, 1049-1067]. It was proposed that this effect is due to the influence of contrast on the perceived speed of the plaid components. This led to the conclusion that perceived plaid direction is computed by the intersection of constraints (IOC) of the perceived speed of the components rather than their physical speeds. We tested this proposal at a wider range of component speeds (2-16deg/s) than used previously, across which the effect of contrast on perceived speed is seen to reverse. We find that across this range, perceived plaid direction cannot be predicted either by a model which takes the IOC of physical or perceived component speed. Our results are consistent with an explanation of 2D motion perception proposed by [Bowns, L. (1996). Evidence for a feature tracking explanation of why Type II plaids move in the vector sum direction at short durations. Vision Research, 36, 3685-3694.] in which the motion of the zero-crossing edges of the features in the stimulus contribute to the perceived direction of motion.     

Apparent speed of type I symmetrical plaids

The apparent speed of plaids made up of two gratings having the same spatial frequency and the same speed was evaluated (symmetrical type 1). The plaids were moving vertically as defined by the intersection-of-constraints (IOC) rule with a mean duration of 300 msec. The comparison-stimulus was a horizontal line moving vertically. The main goal of the study was to test the effect of the spatial frequency of the Distortion Product (DP). Here the DP velocity is identical to the IOC velocity. The main effect is that reducing the DP spatial frequency from 4 to 1 c/deg decreases apparent speed. A smaller effect is due to the speed of the components: when this speed becomes relatively smaller than the IOC speed, apparent speed of the plaid decreases. Finally, the DP temporal frequency seems to determine the upper limit (about 16 Hz) beyond which the plaid appears as a non-rigid moving and flickering pattern.