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

The effect of eccentricity on the linear-radial speed bias: Testing the motion-in-depth model

Radial motion is perceived as faster than linear motion when local spatiotemporal properties are matched. This radial speed bias (RSB) is thought to occur because radial motion is partly interpreted as motion-in-depth. Geometry dictates that a fixed amount of radial expansion at increasing eccentricities is consistent with smaller motion in depth, so it is perhaps surprising that the impact of eccentricity on RSB has not been examined. With this issue in mind, across 3 experiments we investigated the RSB as a function of eccentricity. In a 2IFC task, participants judged which of a linear (test - variable speed) or radial (reference - 2 or 4°/s) stimulus appeared to move faster. Linear and radial stimuli comprised 4 Gabor patches arranged left, right, above and below fixation at varying eccentricities (3.5°-14°). For linear stimuli, Gabors all drifted left or right, whereas for radial stimuli Gabors drifted towards or away from the centre. The RSB (difference in perceived speeds between matched linear and radial stimuli) was recovered from fitted psychometric functions. Across all 3 experiments we found that the RSB decreased with eccentricity but this tendency was less marked beyond 7° - i.e. at odds with the geometry, the effect did not continue to decrease as a function of eccentricity. This was true irrespective of whether stimuli were fixed in size (Experiment 1) or varied in size to account for changes in spatial scale across the retina (Experiment 2). It was also true when we removed conflicting stereo cues via monocular viewing (Experiment 3). To further investigate our data, we extended a previous model of speed perception, which suggests perceived motion for such stimuli reflects a balance between two opposing perceptual interpretations, one for motion in depth and the other for object deformation. We propose, in the context of this model, that our data are consistent with placing greater weight on the motion in depth interpretation with increasing eccentricity and this is why the RSB does not continue to reduce in line with purely geometric constraints.

Low-level processing deficits underlying poor contrast sensitivity for moving plaids in anisometropic amblyopia

Many studies using random dot kinematograms have indicated a global motion processing deficit originated from extrastriate cortex, specifically middle temporal area (MT) and media superior temporal area (MST), in patients with amblyopia. However, the nature of this deficit remains unclear. To explore whether the ability of motion integration is impaired in amblyopia, contrast sensitivity for moving plaids and their corresponding component gratings were measured over a range of stimulus durations and spatial and temporal frequencies in 10 control subjects and 13 anisometropic amblyopes by using a motion direction discrimination task. The results indicated a significant loss of contrast sensitivity for moving plaids as well as for moving gratings at intermediate and high spatial frequencies in amblyopic eyes (AEs). Additionally, we found that the loss of contrast sensitivity for moving plaids was statistically equivalent to that for moving component gratings in AEs, that is, the former could be almost completely accounted for by the latter. These results suggest that the integration of motion information conveyed by component gratings of moving plaids may be intact in anisometropic amblyopia, and that the apparent deficits in contrast sensitivity for moving plaids in anisometropic amblyopia can be almost completely attributed to those for gratings, that is, low-level processing deficits.

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.

Ambiguity in the perception of moving stimuli is resolved in favour of the cardinal axes

The aim of this study was to determine whether there is a link between the statistical properties of natural scenes and our perception of moving surfaces. Accordingly, we devised an ambiguous moving stimulus that could be perceived as moving in one of three directions of motion. The stimulus was a circular patch containing three square-wave drifting gratings. One grating was always either horizontal or vertical; the other two had component directions of drift at 120 degrees to the first (and to each other), producing four possible stimulus geometries. These were presented in a pseudorandom sequence. In brief presentations, subjects always perceived two of the gratings to cohere and move as a pattern in one direction, and the third grating to move independently in the opposite direction (its component direction). Although there were three equally plausible axes (one cardinal and two oblique) along which the coherent and independent motions could occur, subjects routinely saw motion along one of the cardinal axes. Thus, the visual system preferentially combines the two oblique gratings to form a pattern that drifts in the opposite direction to the cardinal grating. It was only when the contrast of one of the oblique gratings was changed that an oblique axis of motion was perceived. This perceptual anisotropy can be related to naturally occurring bias in the visual environment, notably the predominance of horizontal and vertical contours in our visual world.

Color and luminance in the perception of 1- and 2-dimensional motion

An isoluminant color grating usually appears to move more slowly than a luminance grating that has the same physical speed. Yet a grating defined by both color and luminance is seen as perceptually unified and moving at a single intermediate speed. In experiments measuring perceived speed and direction, it was found that color- and luminance-based motion signals are combined differently in the perception of 1-D motion than they are in the perception of 2-D motion. Adding color to a moving 1-D luminance pattern, a grating, slows its perceived speed. Adding color to a moving 2-D luminance pattern, a plaid made of orthogonal gratings, leaves its perceived speed unchanged. Analogous results occur for the perception of the direction of 2-D motion. The visual system appears to discount color when analyzing the motion of luminance-bearing 2-D patterns. This strategy has adaptive advantages, making the sensing of object motion more veridical without sacrificing the ability to see motion at isoluminance.

Visual discrimination of direction changes based upon two types of angular motion

We address the question of how the visual system analyses changes in direction. Using plaid stimuli, we define type O direction changes which entail a change in the orientations of the plaid components, and type V direction changes in which the orientations of the components remain constant, relative to the observer but their relative speeds change. Lower thresholds for discriminating type O and type V direction changes were compared. Type O thresholds for clockwise/anticlockwise direction change were very low (0.2-0.5 degree), were resistant to directional noise, and showed a low-pass relationship with drift velocity. Type V thresholds on the other hand were higher (1-5 degrees), and exhibited a bandpass relationship with drift velocity. Type O direction changes gave low thresholds at short inter-stimulus intervals (ISI) (< 160 ms) and higher thresholds (successive orientation discrimination) at long ISI (240 ms-12.8 s). Type V thresholds, on the other hand, exhibited no short-range process and performance at short ISI, was no better than for successive direction discrimination at long ISI. A two-stage rotary motion model is sufficient to explain the discrimination of type O direction changes and results rule out a model based on velocity discrimination. For type V direction changes, a two-stage mechanism is insufficient and results are consistent with a minimum of three computational stages.

Reference repulsion when judging the direction of visual motion

While humans are very reliable (i.e. give highly reproducible answers) when repeatedly judging the direction of a moving random-dot pattern (RDP) we find that their accuracy (i.e. the direction they so reliably report) shows systematic errors. To quantify these errors, we presented a complete set of closely spaced directions and mapped the directional misjudgments by asking subjects to compare the perceived direction of a moving RDP with the direction of a test line. The results show misjudgments of up to 9 degrees, which are best accounted for by a tendency of the subjects to overestimate the angle between the observed motion and an internal reference direction. A control experiment in which subjects had to judge the spatial distance between a point and a line demonstrates that these misjudgments are not confined to motion stimuli but rather seem to reflect a general tendency to overestimate the distance between a stimulus and a reference when they are close to each other.

Mechanisms specialized for the perception of image geometry

Angle discrimination thresholds were obtained for V-shaped targets with a base angle of 90 deg at four different pattern orientations (0, 45, 90 and 135 deg). A comparison of these thresholds with the orientation discrimination thresholds for the single lines from which the patterns had been constructed, revealed that angle acuity cannot be predicted from component acuity. Angle acuity is finer than the corresponding orientation acuity in all cases and does not exhibit the pronounced oblique effect that is found for orientation discrimination. Other experiments showed that acuity for pattern angle depends critically on base angle, with minima close to 0, 90 and 180 deg. The shape and amplitude of this function are independent of pattern orientation. It was found that the angle acuity was unaffected by excluding a large portion of the target in the region of the vertex, and that the pattern of dependence of acuity on angle changed radically when the target was reduced ultimately to three blobs that defined the cardinal points of the stimulus. The data suggest that when the target comprises line segments, angle discrimination is not limited by noise that arises at early levels of processing and that angle perception is mediated by mechanisms that are specialized for the perception of image geometry. An opponent process model, that is based on the combined outputs of just two types of filter, is proposed as the basis for the perception of image geometry. This type of system is appropriate for computing one of the differential invariants in an optic flow field.

Cortical magnification, scale invariance and visual ecology

The visual world of an organism can be idealized as a sphere. Locomotion towards the pole causes translation of retinal images that is proportional to the sine of eccentricity of each object. In order to estimate the human striate cortical magnification factor M, we assumed that the cortical translations, caused by retinal translations due to the locomotion, were independent of eccentricity. This estimate of M agrees with previous data on magnifications, visual thresholds and acuities across the visual field. It also results in scale invariance in which the resolution of objects anywhere in the visual field outside the fixated point is about the same for any viewing distance. Locomotion seems to be a possible determinant in the evolution of the visual system and the brain.

A biologically plausible model of early visual motion processing. II: psychophysical application

We test the model of early visual processing introduced in the companion paper by simulating a range of psychophysical phenomena. We present new data concerning our ability to discriminate the speed of drifting gratings when spatiotemporally apertured in a variety of ways. We shall investigate the role played by the aperture in modifying the grating's behaviour from its idealisation as a pure Fourier component and show that this is not negligible. Other phenomena which we simulate and explain relate to the way perceived velocity is influenced by contrast and spatial frequency. Many of our explanations are couched in terms of the relative number of cells occurring within each locale of the Fourier domain. This use of the cell density map is a unifying concept and avoids the necessity for a range of separate mechanisms. We argue that a neurophysiologically detailed model is necessary in order to explain psychophysical data (Weber fractions) which vary over less than an order of magnitude, and small deviations from veridical encoding of velocity.

A biologically plausible model of early visual motion processing. I: theory and implementation

A model of local image encoding is described which explicitly incorporates quantitative data about the number density, bandwidth and receptive field organisation of neurons involved in motion detection. The model solves the problem of extracting local velocity on the basis of inputs tuned to spatiotemporal frequency and sensitive to contrast. The spatiotemporally tuned, opponent motion filters are followed by a compressive non-linearity and comprise a first stage. The inter-stage signals are interpreted as those from single neurons and the second stage is modelled as a neural-network layer. The second stage uses semilinear units and models the effect of lateral, on-centre off-surround, intra-layer connections. Characterisation of the first stage leads to a clarification of the concept of the psychophysical 'channel' and its relation to physiological data. The quantitative parametrisation of the model allows the simulation of several psychophysical phenomena which are reported in a companion paper.

Rotation and radical motion thresholds support a two-stage model of differential-motion analysis

Lower motion thresholds for rotational and radial flow have been measured for stimuli consisting of four closely packed circular apertures, each containing patches of drifting grating or plaid. Detection and direction thresholds were measured for gratings and plaids as a function of the relative orientation of the pattern components. There was a similarity between both types of threshold, supporting the existence of specialised rotation and radial-flow detectors. Further, thresholds increased with the relative component orientation for both gratings and plaids. This suggests that component information from a first stage, tuned spatiotemporally and to orientation, is being used directly to compute the optic flow in a two-stage process. A model based on this architecture is described by means of simple template receptive-field arrays with separable temporal and spatial tuning at the first stage.

The discrimination of dynamic orientation changes in gratings

Thresholds were measured for discrimination of direction of a step angular rotation of gratings. The addition of simultaneous phase displacements (translation) had little effect on rotation thresholds for gratings over a considerable range; discrimination of rotation is unaffected by random directional translations an order of magnitude larger. Angular rotation discrimination thresholds increased with interstimulus interval (ISI). Thus discrimination is based at short ISIs (180 ms or less) on a percept of rotary motion, but at ISIs of several seconds by a spatial strategy (comparing static component orientations) relying on visual memory. Data points for the short-ISI region fell below the best-fitting straight line, and the slope of the short-ISI region of the curve was steeper than that of the long-ISI region. However, when either compound or simple gratings with uncorrelated spatial frequencies were used in the two stimulus frames, there was no evidence for a separate function at short ISIs. Orientation-change thresholds were measured for simple gratings as a function of contrast and spatial frequency. The contrast function showed saturation and the spatial frequency function was U-shaped. Rotation sensitivity for gratings is thus similar in its spatiotemporal properties to translation sensitivity. The findings support the proposal that rotation discrimination (at short ISIs) is achieved by a template mechanism combining signals from different directional detectors, rather than by congnitive comparison of the outputs of the directional mechanisms themselves.

Effect of contrast and adaptation on the perception of the direction and speed of drifting gratings

Three experiments were conducted to analyse the effect of contrast and adaptation state on the ability of human observers to discriminate the motion of drifting gratings. In the first experiment, subjects judged the direction of briefly presented gratings, which slowly drifted leftward or rightward. The test gratings were enveloped in space by a raised cosine function and in time by a Gaussian. The centre of the spatial envelope was either 2 deg left or right of the fixation point. An adaptive staircase procedure was used to find the velocities, at which the observer judged the motion direction in 75% of the presentations as leftwards or rightwards, respectively. In the second experiment, subjects judged the relative speed of two simultaneously presented gratings. Stimulus contrast was varied in both experiments from 0.01 to 0.32. Discrimination threshold vs contrast functions were measured before and after adaptation to a high-contrast (0.4) grating drifting at rates between 2 and 32 Hz. In a third experiment, subjects matched, before and after adaptation, the relative speed of a test stimulus, which had a constant contrast (0.04 or 0.08) and a variable speed, to that of a reference stimulus having a variable contrast but a constant speed. The results indicate that, before adaptation, direction and speed discrimination thresholds are independent of test contrast, except when test contrast approaches the detection threshold level. Adaptation to a drifting grating increases the lower threshold of motion (LTM) and the speed discrimination threshold (delta V/V) for low test contrasts. In addition, the point of subjective stationarity (PSS) shifts towards the adapted direction and this shift is more pronounced for low test contrasts. The perceived speed of a drifting grating increases with increasing contrast level. Adaptation to a drifting grating shifts the perceived speed vs log contrast function downwards and to the right (toward higher contrast levels) and this shift is greatest for adaptation frequencies between 8 and 16 Hz. We further explored the effects of adaptation contrast (0.04, 0.4 and 0.9) and adaptation drift direction (iso- or contra-directional) on the perceived speed versus contrast function. The effect of adaptation is greatest for iso-directional drift and increases with increasing adaptation contrast. The results are discussed in terms of a contrast gain control model of adaptation.

Changes in the perceived direction of drifting plaids, induced by asymmetrical changes in the spatio-temporal structure of the underlying components

When a plaid pattern with symmetrical velocity components (Type I) is changed to a plaid pattern with asymmetrical velocity components (Type IA), the overall direction of drift appears to undergo a rotation without any other change to the spatial parameters of the components. This change in the perceived drift direction can be induced by altering either the temporal frequency of the components or by altering their spatial frequency. In separate experiments, we have estimated the magnitude of the temporal and spatial frequency thresholds that are necessary to create a liminal change in direction of this type. The results from both temporal and spatial frequency experiments are closely similar. We find that liminal rotations can be induced by changes in the spatio-temporal structure of the sine-wave grating components that are undetectable when these components are presented in isolation. Further, we find that the "velocity threshold for direction" is not a constant factor, but critically depends on the relative orientation of the two elements that form the plaid. Forced-choice experiments were also conducted to estimate the extent of the apparent rotation of the plaid pattern for differing levels of asymmetry in the spatial frequency and temporal frequency of the components. The magnitude of the pattern rotation is predicted by a model of motion direction that encodes the successive displacements of the intersections of the gratings. Finally, we demonstrate that the velocity thresholds for perceived rotation exhibit a meridional anisotropy that depends on the direction of drift of the overall pattern and not on the orientation of the components.(ABSTRACT TRUNCATED AT 250 WORDS)

The analysis of motion of two-dimensional patterns: do Fourier components provide the first stage?

Human observers were required to report the direction of motion of simple two-dimensional (2-D) "plaid" patterns made by adding together two sinusoidal gratings of identical contrast (0.5 or 1.5 log units above threshold), spatial frequency (1 or 5 c/deg) and orthogonal orientations (horizontal and vertical, or +/- 45 deg). The patterns were made to move either by moving both gratings at the same speed (pattern motion) or by moving one component with the other stationary (component motion). In one task (direction discrimination) the observer knew the axis of motion, and was required to discriminate the direction of motion along that axis in a temporal two-alternative forced-choice paradigm; in the other task (direction identification) the observer did not know the axis of motion and was required to identify the direction of motion and the axis of motion. In both tasks the discrimination of pattern motion was consistently better than the discrimination of component motion, contrary to the predictions of the "two-stage" model of motion analysis, in which it is assumed that the motion of a 2-D pattern is calculated from the 1-D motions of its Fourier components. The variation in direction discrimination of pattern motion with speed did not have the form predicted under the assumption that the direction of motion of the pattern could be discriminated using the motion of either of its two component gratings. Finally, an elaborated version of the Adelson and Movshon [(1982) Nature, 300, 523-525] two-stage model, in which noise affects the two stages fails to predict the performance in identifying the pattern motion of the plaid pattern, except for 1 c/deg low contrast plaids. These results suggest that when 2-D patterns contain moderately high contrasts or high spatial frequencies observers may use other attributes, instead of, or in addition to Fourier components, to analyse their 2-D motion.

Motion capture changes to induced motion at higher luminance contrasts, smaller eccentricities, and larger inducer sizes

In the stimulus configuration for "motion capture" phenomenon, we varied luminance contrast of the center disk (target), eccentricity and stimulus size. The subjects had to judge the direction of perceived target motion. We found that motion capture changed to induced motion (the direction of illusory motion was reversed) at smaller eccentricities and larger stimulus sizes. At intermediate eccentricities, motion capture changed to induced motion with increasing luminance contrast of the target. By using magnitude estimation, we also found that even a luminance-defined target was captured ("homochromatic motion capture") and that a moving target was captured by a stationary inducer ("position capture"). Both motion and position capture effects were commonly observed at lower luminance contrasts of the target, larger eccentricities and smaller sizes. From these results, we propose a model of center-surround antagonistic motion contrast detectors in motion processing.

Determinants of two-dimensional motion aftereffects induced by simultaneously- and alternately-presented plaid components

Wenderoth, Bray and Johnstone [(1988) Perception, 17, 81-91] measured motion aftereffects induced on stationary vertical sine-wave gratings by horizontally drifting two-dimensional patterns (plaids). The adapting plaid component gratings were simultaneously or alternately presented and were oriented left and right of vertical by 15, 45 or 75 degrees. It was found that aftereffects decreased linearly in the alternating conditions as the plaid component orientations changed but this was not the case in the simultaneous adaptation conditions, a finding taken to be consistent with the hypothesis that one-dimensional aftereffects have a low level site (possibly V1) whereas two-dimensional effects have a higher level site (possibly MT). In three experiments, we have examined in more detail the determinants of aftereffects induced by simultaneous and alternating plaid components. The data suggest that the mechanisms involved are more complex than those put forward by Wenderoth et al. and that plaid perception utilizes both higher and lower level processes which can be referred to, respectively, as an intersection of constraints algorithm and a moving "blob" detector.

Dependence of stereomotion on the orientation of spatial-frequency components

It is known that sensitivity to stereoscopic motion in depth is not based upon the fine analysis of static disparities but instead is based on the binocular combination of motion-sensitive mechanisms. We show in this paper that an 'aperture problem' arises for the analysis of motion in depth, just as it does for monocular motion sensitivity. We extend Adelson and Movshon's solution to the aperture problem by intersection of perpendicular constraints to the three-dimensional case, and show that it predicts velocity matches for oblique gratings moving in depth, for orientations close to vertical. We show that binocular plaids give rise to motion in depth when the component orientations match in each eye, and the monocular motions are horizontal. The match velocities are consistent with intersection of perpendicular constraints. In three dimensions intersection of perpendicular constraints may be necessary, but is not a sufficient condition for the perception of coherent stereoscopic motion in depth.