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.     

Exposure duration affects the perceived direction of cyclopean type II plaids

This study investigated the effect of exposure duration on the perceived direction of cyclopean Type I and Type II plaids moving in the X/Y plane. The cyclopean plaids were created from grating components defined by binocular disparity embedded in a dynamic random-dot stereogram. The results showed that the cyclopean Type I plaid appeared to move in the intersection-of-constraints (IOC) direction across the range of exposures tested. However, the cyclopean Type II plaids appeared to move in a direction different from the IOC with short exposures but near the IOC with long exposures. This perceived directional shift was also obtained with luminance-defined Type II plaids. A common pattern-motion mechanism that processes cyclopean and luminance motion signals appears responsible for the perceived directional shift of the Type II plaids.     

An explanation of why component contrast affects perceived pattern motion

Component contrast is an essential element in computing spatio-temporal motion energy, and has been shown to bias perceived motion (Thompson, 1982). More recently, Champion, Hammett, and Thompson (2007) concluded that two-dimensional features in the stimulus was the explanation for this motion bias. Here a method was used that eliminated two-dimensional features as the source of the bias. Bowns (1996) showed that Type II plaids shifted from the intersection of constraints direction (IOC) to the vector average direction (VA) as a function of the speed ratio of the components at short durations. It was therefore argued that if the speed of the components could be increased or decreased by varying the component contrast, then this should be reflected in the change from the IOC to the vector average. Perceived direction was markedly affected by contrast. Contrast can bias perceived motion even when two-dimensional features are controlled for, but the source of the bias is not from computing the IOC from motion energy, or by tracking two-dimensional features, but instead is predicted by the Component Level Feature Model developed to be predominantly invariant to contrast.     

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.     

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.     

An independent effect of spatial frequency on motion integration reveals orientation resolution

Problem

To investigate the independent role of spatial frequency on component motion integration.

Method

Two Type II plaids were presented at varying spatial frequencies. The velocity vectors of the underlying components were constructed so that predicted speed and direction from the components; the Intersection of Constraints; the vector average; and distortion products, remained constant for each of the two plaids across spatial frequency. Perceived direction was measured using a method of adjustment.

Results

Perceived direction changed as a function of spatial frequency, approaching the pattern direction only at spatial frequencies greater than 0.5 cpd.

Conclusions

Spatial frequency has an independent effect on the component integration stage that determines perceived pattern motion direction. The results appear to reflect the resolution of orientation for recombination of the components at low spatial frequencies. These results have implications for motion modelling and possible clinical applications.     

Perceived direction of moving two-dimensional patterns depends on duration, contrast and eccentricity.

Type II two-dimensional motion is produced by superimposing two one-dimensional drifting cosine gratings with velocity vectors lying on the same side of the intersection-of-constraints (IOC) resultant. When type II patterns were constructed with components having the same spatial frequency and contrast, perceived direction was found to be biased toward the vector sum direction at short durations and approached the direction predicted by IOC only after some time lag. This time lag was contrast dependent. At 5% contrast, the perceived direction after 1 sec of presentation remained biased by more than 20 degrees. Direction perception was also measured at 15 degrees eccentricity. At this eccentricity the perceived direction of type II patterns was grossly biased away from the IOC prediction in the direction of the component vectors by an average of 25 degrees.     

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.     

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.     

Analysis of the motion of 2-dimensional patterns: evidence for a second-order process.

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 studied the apparent direction of motion of plaids made by adding two components that had the same spatial frequency and contrast, and were symmetrically oriented about the vertical axis. The gratings moved in jumps, and we studied the effect of varying the size of the jump, the angle between the component gratings, and the temporal interval between the jumps, on the perceived direction of motion. When the size of the jumps was increased to 3/8 of their spatial period, the perceived direction of motion of the plaid pattern reversed, although if one component were presented alone, its direction of movement did not reverse. Reversed motion of this type was consistently obtained if the angle between the components was greater than about 140 degrees, if the interval between jumps was at least 25 msec, and if the spatial frequency of the component gratings was less than about 4 c/deg. When the angle between the components was smaller, or the time between jumps was greater, most observers saw normal motion in the direction predicted by the two-stage hypothesis. When the spatial frequency was raised, observers saw no consistent motion.(ABSTRACT TRUNCATED AT 250 WORDS)     

Large shifts in perceived motion direction reveal multiple global motion solutions

Moving objects are thought to be decomposed into one-dimensional motion components by early cortical visual processing. Two rules describing how these components might be re-combined to produce coherent object motion are the intersection of constraints and the vector average rules. Using stimuli for which these combination rules predict different directional solutions, we found that adapting one of the solutions through motion adaptation switched perceived direction to the other solution. The effects were symmetrical: shifts from IOC to VA, and from VA to IOC, were observed following adaptation. These large shifts indicate that multiple solutions to global motion processing coexist and compete to determine perceived motion direction.     

IOC, vector sum, and squaring: three different motion effects or one?

Bowns (Vision Research, 36(22) (1996), 3685) argued that there are distinct features in two-component moving patterns (plaids) that if tracked move in the same direction as (1) the intersection of constraints direction (IOC) Adelson and Movshon (Nature, 300 (1992), 523); and (2) the vector sum direction (VS) Yo and Wilson (Vision Research, 32(1) (1992), 135). The IOC and VS are hypotheses of how the motion of single components is combined to give pattern motion. This paper shows that there are also features that provide an explanation for a reversed motion described by Derrington, Badcock, and Holroyd (Vision Research, 32(4), (1992), 699), and investigates why reversals only occur under specific conditions. Section 3 replicates the original study by Derrington et al. (1992) and confirms that the reversals are limited to low temporal frequencies. Section 4 varies the spatial displacement of features that also predict reversals and shows that the temporal frequency at which reversals occur varies and is linearly dependent on the displacement of these specified features. Derrington et al. (1992) showed that reversals only occur when components have oblique angles, and suggested an explanation in terms of speed differences. Section 5 was not consistent with this hypothesis. An alternative explanation for why reversals only occur at oblique angles, and at low spatial frequencies is provided in terms of feature properties. Results supporting the IOC, vector sum, and squaring have previously been interpreted in terms of three disparate mechanisms. This may not be necessary.     

Second-order motion shifts perceived position

Many studies have documented that first-order motion influences perceived position. Here, we show that second-order (contrast defined) motion influences the perceived positions of stationary objects as well. We used a Gabor pattern as our second-order stimulus, which consisted of a drifting sinusoidal contrast modulation of a dynamic random-dot background; this second-order carrier was enveloped by a static Gaussian contrast modulation. Two vertically aligned Gabors had carrier motion in opposite directions. Subjects judged the relative positions of the Gabors' static envelopes. The positions of the Gabors appeared shifted in the direction of the carrier motion, but the effect was narrowly tuned to low temporal frequencies across all tested spatial frequencies. In contrast, first-order (luminance defined) motion shifted perceived positions across a wide range of temporal frequencies, and this differential tuning could not be explained by differences in the visibility of the patterns. The results show that second-order motion detection mechanisms contribute to perceived position. Further, the differential spatial and temporal tuning of the illusion supports the idea that there are distinct position assignment mechanisms for first and second-order motion.     

Cross-domain adaptation reveals that a common mechanism computes stereoscopic (cyclopean) and luminance plaid motion

Across three experiments, this study investigated the visual processing of moving stereoscopic plaid patterns (plaids created with cyclopean components defined by moving binocular disparity embedded in a dynamic random-dot stereogram). Results showed that adaptation to a moving stereoscopic plaid or its components affected the perceived coherence of a luminance test plaid, and vice versa. Cross-domain adaptation suggests that stereoscopic and luminance motion signals feed into a common pattern-motion mechanism, consistent with the idea that stereoscopic motion signals are computed early in the motion processing stream.     

Two-dimensional optokinetic nystagmus induced by moving plaids and texture boundaries. Evidence for multiple visual pathways.

Horizontal and vertical components of optokinetic nystagmus (OKN) were measured using the magnetic search coil technique in normal human adults during presentation of simple and complex moving patterns. Simple patterns were gratings moving horizontally and obliquely. Complex moving patterns consisted of plaids formed by superimposed oblique motion of two sets of gratings or of illusory contours formed by offset discontinuities in gratings. Slow-phase OKN gains (eye velocity divided by stimulus velocity) induced by high-contrast type I and type II plaids were comparable with those generated by one-dimensional moving gratings. The axis of OKN for high-contrast plaids was along the resultant direction determined by the intersection-of-constraints rule and not along any component. With low-contrast presentations, OKN induced by type I patterns remained in the resultant direction, but the OKN direction induced by type II patterns was biased toward the components' directions. The OKN generated by texture boundaries embedded in real pattern motion was measured for motion of illusory contours having systematically varying directions. The gain of OKN induced by real motion was independent of the direction of illusory contour motion, but the gain to illusory contour motion decreased with increasing contour angles. All these results suggest that input signals for driving the optokinetic system come from visual areas extracting higher order two-dimensional motion information.     

Taking the energy out of spatio-temporal energy models of human motion processing: the Component Level Feature Model

Standard biologically inspired spatio-temporal energy models of how humans perceive moving two-dimensional patterns often have two critical stages. In the first stage, suitable filters are convolved with the pattern over time to extract information at the "component" level. Motion energy is then computed for each component. The second stage typically computes pattern velocity using the intersection of constraints rule (IOC). This paper describes a new implementation of the Component Level Feature Model (Bowns, 2002) that computes motion direction that is similar to these two stages except that it does not compute motion energy. Here the model computes direction for 200 randomly generated plaids. The output linearly matched that predicted by the IOC. The model was also able to predict the perceived direction even when it deviated from the IOC due to the following variables - speed ratio (Bowns, 1996); duration (Yo & Wilson, 1992); adaptation (Bowns & Alais, 2006). The model provides a novel explanation for each of the above and for why multiple directions can be represented for the same stimuli (Bowns & Alais, 2006); and why some second-order information attributed to non-linearities (Derrington, Badcock, & Holroyd, 1992) reverses perceived motion direction. Finally, CLFM is invariant to contrast and phase.     

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.     

Taking the energy out of spatio-temporal energy models of human motion processing: The Component Level Feature Model

Standard biologically inspired spatio-temporal energy models of how humans perceive moving two-dimensional patterns often have two critical stages. In the first stage, suitable filters are convolved with the pattern over time to extract information at the “component” level. Motion energy is then computed for each component. The second stage typically computes pattern velocity using the intersection of constraints rule (IOC). This paper describes a new implementation of the Component Level Feature Model (Bowns, 2002) that computes motion direction that is similar to these two stages except that it does not compute motion energy. Here the model computes direction for 200 randomly generated plaids. The output linearly matched that predicted by the IOC. The model was also able to predict the perceived direction even when it deviated from the IOC due to the following variables – speed ratio (Bowns, 1996); duration (Yo & Wilson, 1992); adaptation (Bowns & Alais, 2006). The model provides a novel explanation for each of the above and for why multiple directions can be represented for the same stimuli (Bowns & Alais, 2006); and why some second-order information attributed to non-linearities (Derrington, Badcock, & Holroyd, 1992) reverses perceived motion direction. Finally, CLFM is invariant to contrast and phase.     

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.     

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.