Different parameters control motion perception above and below a critical density

Motion perception: behavior and neural substrate

Visual motion perception is vital for survival. Single-unit recordings in primate primary visual cortex (V1) have revealed the existence of specialized motion sensing neurons; perceptual effects such as the motion after-effect demonstrate their importance for motion perception. Human psychophysical data on motion detection can be explained by a computational model of cortical motion sensors. Both psychophysical and physiological data reveal at least two classes of motion sensor capable of sensing motion in luminance-defined and texture-defined patterns, respectively. Psychophysical experiments also reveal that motion can be seen independently of motion sensor output, based on attentive tracking of visual features. Sensor outputs are inherently ambiguous, due to the problem of univariance in neural responses. In order to compute stimulus direction and speed, the visual system must compare the responses of many different sensors sensitive to different directions and speeds. Physiological data show that this computation occurs in the visual middle temporal (MT) area. Recent psychophysical studies indicate that information about spatial form may also play a role in motion computations. Adaptation studies show that the human visual system is selectively sensitive to large-scale optic flow patterns, and physiological studies indicate that cells in the middle superior temporal (MST) area derive this sensitivity from the combined responses of many MT cells. Extraretinal signals used to control eye movements are an important source of signals to cancel out the retinal motion responses generated by eye movements, though visual information also plays a role. A number of issues remain to be resolved at all levels of the motion-processing hierarchy. WIREs Cogni Sci 2011 2 305-314 DOI: 10.1002/wcs.110 For further resources related to this article, please visit the WIREs website Additional Supporting Information may be found in http://www.lifesci.sussex.ac.uk/home/George_Mather/Motion/index.html.

Neuropsychological evidence for three distinct motion mechanisms

We describe psychophysical performance of two stroke patients with lesions in distinct cortical regions in the left hemisphere. Both patients were selectively impaired on direction discrimination in several local and global second-order but not first-order motion tasks. However, only patient FD was impaired on a specific bi-stable motion task where the direction of motion is biased by object similarity. We suggest that this bi-stable motion task may be mediated by a high-level attention or position based mechanism indicating a separate neurological substrate for a high-level attention or position-based mechanism. Therefore, these results provide evidence for the existence of at least three motion mechanisms in the human visual system: a low-level first- and second-order motion mechanism and a high-level attention or position-based mechanism.

A motion-energy model predicts the direction discrimination and MAE duration of two-stroke apparent motion at high and low retinal illuminance

Two-stroke apparent motion offers a challenge to current theoretical models of motion processing and is thus a useful tool for investigating motion sensor input. The stimulus involves repeated presentation of two pattern frames containing a spatial displacement, with a blank inter-stimulus interval (ISI) at one of the two-frame transitions. The resulting impression of continuous motion was measured here using both direction discrimination and motion after-effect duration in order to assess the extent to which data using the two measures can be explained by a computational model without reference to attentive tracking mechanisms. The motion-energy model was found to offer a very good account of the psychophysical data using similar parameters for both tasks. The experiment was run under both photopic and scotopic retinal illumination. Data revealed that the optimum ISI for perceiving two-stroke apparent motion shifts to longer ISIs under scotopic conditions, providing evidence for a biphasic impulse response at low luminance. Best-fitting model parameters indicate that motion sensors receive inputs from temporal filters whose central temporal frequency shifts from 2.5 to 3.0 Hz at high retinal illuminance to 1.0–1.5 Hz at low retinal illuminance.

Low- and high-level first-order random-dot kinematograms: evidence from fMRI

Maximum motion displacement (Dmax) represents the largest dot displacement in a random-dot kinematogram (RDK) at which direction of motion can be discriminated. Direction discrimination thresholds for maximum motion displacement (Dmax) are not fixed but are stimulus dependent. For first-order RDKs, Dmax is larger as dot size increases and/or dot density decreases. Dmax may be limited by the receptive field size of low-level motion detectors when the dots comprising the RDK are small and densely spaced. With RDKs of increased dot size/decreased dot density, however, Dmax exceeds the spatial limits of these detectors and is likely determined by high-level feature-matching mechanisms. Using functional MRI, we obtained greater activation in posterior occipital areas for low-level RDKs and greater activation in extra-striate occipital and parietal areas for high-level RDKs. This is the first reported neuroimaging evidence supporting proposed low-level and high-level models of motion processing for first-order random-dot stimuli.

S-cone contributions to linear and non-linear motion processing

We investigated the characteristics of mechanisms mediating motion discrimination of S-cone isolating stimuli and found a double dissociation between the effects of luminance noise, which masks linear but not non-linear motion, and chromatic noise, which masks non-linear but not linear motion. We conclude that S-cones contribute to motion via two different pathways: a non-linear motion mechanism via a chromatic pathway and a linear motion mechanism via a luminance pathway. Additionally, motion discrimination and detection thresholds for drifting, S-cone isolating Gabors are unaffected by luminance noise, indicating that grating motion is mediated via chromatic mechanisms and based on higher-order motion processing.

Deficient maximum motion displacement in amblyopia

Direction discrimination thresholds for maximum motion displacement (Dmax) are not fixed, but are stimulus dependent. Dmax increases with reduced dot probability or increased dot size. We previously reported abnormal Dmax in the fellow eyes of amblyopic children for dense patterns of small dots. To determine how deficits of Dmax in amblyopic eyes compare to those in fellow eyes, thresholds were obtained in both eyes of 9 children with unilateral amblyopia and 9 control children. The expected increase in Dmax was observed for reduced dot probability and increased dot size conditions relative to baseline in both control and amblyopic groups. Both eyes of the amblyopic group demonstrated significant deficits. Our findings implicate abnormal binocular motion processing, which may involve both low-level and high-level motion mechanisms, in the neural deficit underlying amblyopia.

The perception of motion in chromatic stimuli

The issue of whether there is a motion mechanism sensitive to purely chromatic stimuli has been pertinent for the past 30 or more years. The aim of this review is to examine why such different conclusions have been drawn in the literature and to reach some reconciliation. The review critically examines the behavioral evidence and concludes that there is a purely chromatic motion mechanism but that it is limited to the fovea. Examination of motion performance for chromatic and luminance stimuli provides convincing evidence that there are at least two different mechanisms for the two kinds of stimuli. The authors further argue that the chromatic mechanism may be at a particular disadvantage when the integration of multiple local motion signals is required. Finally, the authors present a descriptive model that may go some way toward explaining the reasons for the differences in collected data outlined in this article.

The Ferrier Lecture 2004 what can transcranial magnetic stimulation tell us about how the brain works?

Transcranial magnetic stimulation (TMS) is a technique whereby parts of the cerebral cortex and underlying white matter can be excited by a brief electrical current induced by a similarly brief, rapidly fluctuating magnetic field which is itself produced by rapidly discharging a current through an insulated coil held against the scalp. When combined with magnetic resonance structural and functional images of the subject's brain, the stimulation can be directed at specific cortical areas. Over a period of only 15 years, TMS has revealed hitherto unsuspected aspects of brain function, such as the role of distant parts of the brain in recovery from stroke, and has helped to resolve several previously intractable disputes, such as the neuronal basis of conscious awareness. This article describes and discusses the origins and nature of TMS, its applications and limitations, and its especial usefulness in conjunction with other techniques of evaluating or imaging brain activity.

No effect of spatial phase randomisation on direction discrimination in dense random element patterns

Two computational strategies have been proposed for motion analysis in the human visual system. Energy-based schemes involve detection of spatiotemporal Fourier energy in the frequency components comprising a moving pattern. Edge-based schemes track shifts in the position of local edges in the pattern over time. This paper describes a stimulus manipulation, spatial phase randomisation, that acts as a diagnostic test for the involvement of energy-based processes, and describes the results of two experiments which apply the manipulation to random element patterns. Both experiments compared direction discrimination performance in patterns before and after the spatial phase of their components was randomised in the Fourier domain. For dense patterns, there was no effect of phase randomisation on the maximum displacement supporting reliable direction discrimination, indicating that energy-based responses were dominant. For sparse patterns, a significant effect of phase randomisation was obtained, indicating a greater role for edge-based responses.

The detection of motion in chromatic stimuli: first-order and second-order spatial structure

This study provides evidence for the existence of a low-level chromatic motion mechanism and further elucidates the conditions under which its operation becomes measurable in an experimental stimulus. Observers discriminated the direction of motion of amplitude modulated (AM) gratings that were defined by luminance or chromatic variation and masked with spatiotemporally broadband luminance or chromatic noise. The size and retinal location of the stimuli were varied and the effects of broadband noise and grating masks were both compared with the cohort of stimuli. Some significant disparities in the published literature were well explained by the results. In conclusion, evidence for a chromatically sensitive motion mechanism that evades the, detrimental effects of a luminance mask was found only at the fovea and only when the stimulus was small and centrally placed.

First-order and second-order motion: neurological evidence for neuroanatomically distinct systems

An unresolved issue in visual motion perception is how distinct are the processes underlying 'first-order' and 'second-order' motion. The former is defined by spatio-temporal variations of luminance and the latter by spatio-temporal variations in other image attributes such as contrast or depth, for example. Using neuroimaging and psychophysics we present data from four neurological patients with unilateral and mostly cortical infarcts, which strongly suggest that first- and second-order motion have a different neural substrate. We found that from the early stages of processing, these two types of motions are mediated by two distinct pathways: first-order motion is carried out by mechanisms along the dorsal pathway in the occipital lobe, while the second-order motion by mechanisms mostly along the ventral pathway. The data reported here also suggest that different cortical regions may be in charge of processing direction-discrimination in second-order motion defined by different second-order attributes.

Motion detection and the coincidence of structure at high and low spatial frequencies

We used filtered random dot kinematograms and natural images to examine how motion detection depends the relative locations of structures defined at low and high spatial frequencies. The upper displacement limit of motion (D(max)), the lower displacement limit (D(min)) and motion coherence thresholds were unaffected by the degree of spatial coincidence between high and low spatial frequency structures i.e. whether they were consistent or inconsistent with a single feature. However motion detection was possible between band-pass filtered random dot patterns whose peak frequencies were separated by up to 4 octaves. The first result implicates spatial frequency selective motion detectors that operate independently. The second result implicates a motion system that can integrate the displacements of edges defined by widely separated spatial frequencies. Both are required to account for the two results, and they appear to operate under very similar conditions.

Failure of direction identification for briefly presented second-order motion stimuli: evidence for weak direction selectivity of the mechanisms encoding motion

We sought to investigate why the direction of second-order motion, unlike first-order motion, cannot be identified when the stimulus exposure duration is brief (<200 ms). In a series of experiments observers identified both the orientation (vertical or horizontal) and the direction (left, right, down or up) of a drifting sinusoidal modulation (0.93 c/ degrees ) in either the luminance (first order) or the contrast (second order) of a two-dimensional noise carrier. All motion stimuli were equated for visibility, and the duration was varied using the method of constant stimuli. Performance was measured for second-order motion over a range of drift temporal frequencies (0.63-5.04 Hz) and for first-order motion stimuli composed of two, opposite drifting modulations in luminance of unequal modulation depth. Orientation-identification performance was nearly 100% correct for both first-order and second-order motion stimuli, even at the briefest stimulus duration tested (26.49 ms). Direction identification for first-order motion was also typically good with brief presentations, but was poor for second-order motion when the exposure duration was < approximately 200 ms. Importantly increasing either the drift temporal frequency of second-order motion or the bidirectional nature of the first-order motion patterns produced comparable levels of performance for the two varieties of motion (i.e. the minimum duration required for reliable direction identification could be equated). As orientation-identification performance for the first-order and second-order motion stimuli was comparably good and minimally affected by duration, the marked differences on the direction-identification task must be specific to mechanisms that encode drift direction, rather than spatial structure. We propose that second-order motion detectors are much less selective for stimulus direction than first-order motion sensors, and thus are more susceptible to the deleterious effects of limiting stimulus duration (which introduces spurious motion in the opposite direction, particularly at low drift rates). Alternative explanations based on the delayed propagation of second-order motion signals or the temporal characteristics of the underlying motion mechanisms are not supported by our findings.

Comparison of the spatial-frequency selectivity of local and global motion detectors

Convergent physiological and behavioral evidence indicates that the initial receptive fields responsible for motion detection are spatially localized. Consequently, the perception of global patterns of movement (such as expansion) requires that the output of these local mechanisms be integrated across visual space. We have differentiated local and global motion processes, with mixtures of coherent and incoherent moving patterns composed of bandpass filtered dots, and have measured their spatial-frequency selectivity. We report that local motion detectors show narrow-band spatial-frequency tuning (i.e., they respond only to a narrow range of spatial frequencies) but that global motion detectors show broadband spatial-frequency tuning (i.e., they integrate across a broad range of spatial frequencies), with a preference for low spatial frequencies.

Processing of second-order stimuli in the visual cortex

Naturally occurring visual stimuli are rich in examples of objects delineated from their backgrounds simply by differences in luminance, so-called first-order stimuli, as well as those defined by differences of contrast or texture, referred to as second-order stimuli. Here we provide a brief overview of visual cortical processing of second-order stimuli, as well as some comparative background on first-order processing, concentrating on single-unit neurophysiology, but also discussing relationships to human psychophysics and to neuroimaging. The selectivity of visual cortical neurons to orientation, spatial frequency, and direction of movement of first-order, luminance-defined stimuli is conventionally understood in terms of simple linear filter models, albeit with some minor nonlinearities such as thresholding and gain control. However, these kinds of models fail entirely to account for responses of neurons to second-order stimuli such as contrast envelopes, illusory contours, or texture borders. Second-order stimuli constructed from sinusoidal components have been used to analyze the neurophysiological mechanisms of such responses; these experiments demonstrate that the same neuron can exhibit three distinct kinds of tuning to spatial frequency, and also to orientation. These results can be understood in terms of a type of nonlinear 'filter-->rectify-->filter' model, which has been widely used in human psychophysics. Finally, several general issues will be discussed, including potential artifacts in experiments with second-order stimuli, and strategies for avoiding or controlling for them; caveats about definitions of first- vs. second-order mechanisms and stimuli; the concept of form-cue invariance; and the functional significance of second-order processing.

Motion detection in human vision: a unifying approach based on energy and features

Most studies of human motion perception have been based on the implicit assumption that the brain has only one motion-detection system, or at least that only one is operational in any given instance. We show, in the context of direction perception in spatially filtered two-frame random-dot kinematograms, that two quite different mechanisms operate simultaneously in the detection of such patterns. One mechanism causes reversal of the perceived direction (reversed-phi motion) when the image contrast is reversed between frames, and is highly dependent on the spatial-frequency content of the image. These characteristics are both signatures of detection based on motion energy. The other mechanism does not produce reversed-phi motion and is unaffected by spatial filtering. This appears to involve the tracking of unsigned complex spatial features. The perceived direction of a filtered dot pattern typically reflects a mixture of the two types of behaviour in any given instance. Although both types of mechanism have previously been invoked to explain the perception of motion of different types of image, the simultaneous involvement of two mechanisms in the detection of the same simple rigid motion of a pattern suggests that motion perception in general results from a combination of mechanisms working simultaneously on different principles in the same circumstances.

Centrifugal bias for second-order but not first-order motion

Limited-lifetime Gabor stimuli were used to assess both first- and second-order motion in peripheral vision. Both first- and second-order motion mechanisms were present at a 20-deg eccentricity. Second-order motion, unlike first-order, exhibits a bias for centrifugal motion, suggesting a role for the second-order mechanism in optic flow processing.

Absence of a chromatic linear motion mechanism in human vision

We have investigated motion mechanisms in central and perifoveal vision using two-frame random Gabor kinematograms with isoluminant red-green or luminance stimuli. In keeping with previous results, we find that performance dominated by a linear motion mechanism is obtained using high densities of micropatterns and small temporal intervals between frames, while nonlinear performance is found with low densities and longer temporal intervals [Boulton, J. C., & Baker, C. L. (1994) Proceedings of SPIE, computational vision based on neurobiology, 2054, 124-133]. We compare direction discrimination and detection thresholds in the presence of variable luminance and chromatic noise. Our results show that the linear motion response obtained from chromatic stimuli is selectively masked by luminance noise; the effect is selective for motion since luminance noise masks direction discrimination thresholds but not stimulus detection. Furthermore, we find that chromatic noise has the reverse effect to luminance noise: detection thresholds for the linear chromatic stimulus are masked by chromatic noise but direction discrimination is relatively unaffected. We thus reveal a linear 'chromatic' mechanism that is susceptible to luminance noise but relatively unaffected by color noise. The nonlinear chromatic mechanism behaves differently since both detection and direction discrimination are unaffected by luminance noise but masked by chromatic noise. The double dissociation between the effects of chromatic and luminance noise on linear and nonlinear motion mechanisms is not based on stimulus speed or differences in the temporal presentations of the stimuli. We conclude that: (1) 'chromatic' linear motion is solely based on a luminance signal, probably arising from cone-based temporal phase shifts; (2) the nonlinear chromatic motion mechanism is purely chromatic; and (3) we find the same results for both perifoveal and foveal presentations.

Stereo correspondence in one-dimensional Gabor stimuli

Previous data [Prince, S.J.D., & Eagle, R.A., (1999). Size-disparity correlation in human binocular depth perception. Proceedings of the Royal Society of London B, 266, 1361-1365] have demonstrated that the upper disparity limit for stereopsis (DMax) is considerably smaller in filtered noise stereograms than in isolated Gabor patches of the same spatial frequency. This discrepancy is not currently understood. Here, the solution of the correspondence problem for bandpass stereograms was further examined. On each trial observers were presented with two one-dimensional Gabor stimuli containing disparities of equal magnitude but opposite sign. Subjects were required to indicate which interval contained the crossed disparity stimulus. It was found that matching behaviour changed as a function of Gabor envelope size. As a function of disparity magnitude, performance cycled between mostly correct and mostly incorrect at large envelope sizes but was always correct at small envelope sizes. At intermediate envelope sizes performance was cyclical at small disparities but always correct at large disparities. The critical envelope size at which performance changed from mostly correct to mostly incorrect at 270 degrees phase disparity was used as a measure of the matching performance as other parameters of the Gabor were varied. Both absolute and relative contrast were shown to influence the perceived sign of matches. Critical envelope size was also found to decrease as a function of spatial frequency, but more slowly than a phase-based limit would predict. These data cannot be predicted by current models of stereopsis, and can be used to constrain future models.

Two processes in stereoscopic apparent motion

This study investigated the human ability to discriminate the motion direction of sequentially presented depth patterns produced by random-dot stereograms. The stereoscopic (cyclopean) patterns used here consisted of 256 rectangle patches, each of which had an alternative depth position (near or far). Two successive frames of correlated depth patterns made impressions of lateral motion when the pattern position in the second frame shifted laterally. The density of the patches that were near was varied. The Dmax that was measured using the 2AFC method was short when the density was high. The effect of depth reversing in the second frame was also tested. Under low density conditions, the performance was still good against reversing 3-D polarity. However, when the density was high, with depth reversal, motion in the reversed direction was perceived. Reversed motion was observed more often when SOA was small and when the density of near patches was near 1/2. Two strategies seem to exist in stereoscopic motion detecting: a polarity-independent process which matches figures, ignoring their depth polarity, and a polarity-dependent process which operates locally, ignoring 2-D shapes. The latter suggests the existence of a passive process in stereoscopic motion.

Motion perception over long interstimulus intervals

Recent studies using moving arrays of textured micropatterns have suggested that motion perception can be supported by two mechanisms, one quasilinear and sensitive to the motion of luminance-defined local texture, the other nonlinear and coding motion of contrast-defined envelopes of texture (Baker & Hess, 1998; Boulton & Baker, 1993b). Here we used similar patterns to study motion perception under conditions previously shown to isolate the nonlinear mechanism (low micropattern densities and positive interstimulus intervals [ISIs]. We measured direction discrimination for two-flash apparent motion over a much larger range of ISIs, and susceptibility to masking by incoherently moving "distractor" micropatterns. The results suggest that two nonlinear mechanisms can support motion perception under these conditions. One operates only for relatively short ISIs (less than c. 100 msec), is sensitive to small spatial displacements, and is relatively insensitive to distractor masking. The other operates over much longer ISIs, is insensitive to small spatial displacements, and is highly disrupted by distractor masking. These results are in line with previous studies suggesting that three mechanisms support motion perception.

Comparison of motion and stereopsis: linear and nonlinear performance

To address the issue of whether the luminance-dependent (linear) and contrast-dependent (nonlinear) processes in stereo and motion have a common computational basis, we compare both carrier-dependent and envelope-dependent performance for these two modalities by using the same stimulus and task: two-flash apparent motion/depth for a wide range of displacements. We do this for different densities, bandwidths, contrasts, spatial frequencies, and exposure durations. The results suggest that there is concordance not only between the luminance-dependent (linear) processes of motion and stereo but also between the envelope-dependent (nonlinear) processes of both modalities. Only one exception was found, but we show this to be amenable to an explanation based on a different contrast dependence for the nonlinear mechanisms of stereo and motion. This suggests that the computational basis of linear and nonlinear processes may be similar for stereopsis and motion.

Measurement of the texture-coherence limit for bandpass arrays

Casual observation suggests that when the elements of a visual array are packed at a sufficiently high density they cohere to generate the percept of a texture. This 'texture-coherence limit' has been quantified by using arrays composed of Gabor functions, sixth Gaussian derivatives, or differences of Gaussians. In all cases the texture-coherence limit was a power-law function of the size of the elements as quantified by their space constants with an exponent averaging 0.7. Furthermore, the texture-coherence limit was independent of both element spatial frequency and contrast over a considerable range. A quantitative fit to the data is provided by a model in which the texture-coherence limit is determined by activation of complex cells, which pool a spatial range of subunit inputs, throughout the stimulus region. Possible extensions to two dimensions are considered.

A computational model of selective deficits in first and second-order motion processing

Recent neurological studies of selective impairments in first and second-order motion processing are of considerable relevance in elucidating the mechanisms of motion perception in normal human observers. We examine the stimuli which have been used to assess first and second-order motion processing capabilities in clinical subjects, and discuss the nature of the computations necessary to extract their motion. We find that a simple computational model of first and second-order motion processing is able to account for the data. The model consists of a first-order channel computing motion at coarse and fine scales, and a coarse scale second-order channel. The second-order channel is sensitive to motion information defined by variations in luminance, contrast, spatial frequency and flicker. When elements of the model are disabled, its performance on either first or second-order motion can be selectively impaired in line with the neurological data.

Detection of chromatic and luminance contrast modulation by the visual system

The data presented in this paper examine the ability of observers to detect a modulation in the contrast of chromatic and luminance gratings as a function of the carrier contrast, duration, and spatial frequency. The nature of the signal underlying this ability is investigated by examining both the paradigm used to make the measurement and the effect of grating masks on performance in the tasks. The results show that observers' ability to discriminate amplitude modulation from an unmodulated carrier is dependent on carrier contrast but only up to approximately 5-8 times carrier-detection threshold. Discrimination is, however, independent of spatial frequency [10-1 cycles per degree (cpd) component-frequency range], carrier color, and, most surprisingly, stimulus duration (1000-30 ms). This set of experiments compliments data from previous papers and assimilates many of the conclusions drawn from this previous data. There is absolutely no evidence for the existence of a distortion product mediating performance under any of the current conditions, and the data seriously question whether the visual system might use such a signal even if it does exist under more extreme conditions than those used here. The evidence suggests that the visual system detects variations in both chromatic and luminance contrast by means of a mechanism operating locally upon the spatial structure of the carrier.

First- and second-order motion perception in Gabor micropattern stimuli: psychophysics and computational modelling

This paper examines the perception of first- and second-order motion in human vision. In an extension of previous work by Boulton and Baker [J.B. Boulton, C.L. Baker, Motion detection is dependent on spatial frequency not size, Vision Res., 31 (1991) 77-87; J.B. Boulton, C.L. Baker, Different parameters control motion perception above and below a critical density, Vision Res., 33 (1993) 1803-1811], the direction of two-frame apparent motion is measured for stimuli composed of Gabor or Gaussian micropatterns. Three conditions are investigated. Condition 1 is that used by Boulton and Baker, in which motion is defined by the displacement of Gabor micropatterns. In condition 2, motion is defined by the displacement of Gaussian micropatterns. In condition 3, the envelopes of Gabor micropatterns are displaced while their carriers remain static. Using sparsely distributed micropatterns, direction judgements in all three conditions are determined by the spacing of the micropatterns. With a dense stimulus, direction judgements vary as a function of displacement in qualitatively different ways for the three conditions. The psychophysical results are predicted by a two-channel computational model. In one channel, motion is calculated directly from stimulus luminance, while in the other it is preceded by a texture-grabbing operation. The relative activities of the two channels dictates which governs direction judgements for any given stimulus.

A nonlinear chromatic motion mechanism

Previous research has demonstrated two categorically distinct mechanisms mediating apparent motion of kinematograms composed of eccentricity-confined, randomly placed Gabor micropatterns: a quasi-linear mechanism operating for high micropattern densities and short time separations, and a nonlinear mechanism operating at low micropattern densities or longer time separations. Here we compare the performance of these two mechanisms using color (isoluminant) and luminance-defined stimuli. When these stimuli are defined only by their color contrast, the response of the quasi-linear mechanism is severely impaired, while the nonlinear mechanism remains fully operative. This result further strengthens the dichotomy between the two kinds of motion perception, and suggests that when color vision supports motion perception it does so primarily, or perhaps entirely, via a nonlinear mechanism.

Spatial summation in simple (Fourier) and complex (non-Fourier) texture channels

Complex (non-Fourier, second-order) channels have been proposed to explain aspects of texture-based region segregation and related perceptual tasks. Complex channels contain two stages of linear filtering with an intermediate pointwise nonlinearity. The intermediate nonlinearity is crucial. Without it, a complex channel is equivalent to a single linear filter (a simple channel). Here we asked whether the intermediate nonlinearity is piecewise-linear (an ordinary rectifier), or compressive, or expansive. We measured the perceptual segregation between element-arrangement textures where the contrast and area of the individual elements were systematically varied. For solid-square elements, the tradeoff between contrast and area was approximately linear, consistent with simple linear channels. For Gabor-patch elements, however, the tradeoff was highly nonlinear, consistent with complex channels in which the intermediate nonlinearity is expansive (with an exponent somewhat higher than 2). Also, substantial individual differences in certain details were explainable by differential intrusion from "off-frequency" complex channels. Lastly, the results reported here (in conjunction with those of other studies) suggest that the strongly compressive intensive nonlinearity previously known to act in texture segregation cannot be attributed to a compressive nonlinearity acting locally and relatively early (before the spatial-frequency and orientation-selective channels) but could result from inhibition among the channels (as in a normalization network).

The effects of distractor elements on direction discrimination in random Gabor kinematograms

For both Fourier and non-Fourier moving patterns, models have been proposed which detect motion based on either the net orientation of energy in the stimulus (after nonlinear stage for non-Fourier motion stimuli) or on the changes in the relative locations of spatial primitives in the image. Both approaches have been successful in accounting for detection of simple translational displacements, but we examined how such models coped with more demanding stimuli. We examined direction discrimination using two-flash random Gabor kinematograms which selectively reveal Fourier and non-Fourier motion mechanisms. In addition to target elements, multiple distractor elements were added, either static or randomly moving. It was found that detection of Fourier motion was relatively unaffected by the distractors unless they were of orthogonal orientation. Detection of non-Fourier motion was possible, but with a slightly higher error rate, even with many distractors and was not at all affected by orthogonal distractors. The results for distractors of the same orientation as targets are in better agreement with predictions of energy than with edge-matching models. The differing effects of orthogonal distractors further strengthen the proposed dichotomy of quasi-linear and nonlinear motion mechanisms, but indicate that the latter operates on a more complex representation than a simple contrast envelope.

Nonlinear preprocessing in short-range motion

The phenomenon of non-Fourier motion (visually perceived motion that cannot be explained simply on the basis of the autocorrelation structure of the visual stimulus) is well recognized, and is generally considered to be due to nonlinear preprocessing of the visual stimulus prior to a stage of standard motion analysis. We devised a sequence of novel visual stimuli in which the availability of a motion stimulus depends on the nature of the nonlinear preprocessing: an nth order stimulus Pn will generate a perception of motion if it is preprocessed by a nonlinearity of polynomial order n or greater, but not if preprocessed by a nonlinearity of polynomial order less than n. We found that unambiguous motion direction was perceived for P2, P3, and P4, but not for higher-order stimuli, and we measured the contrast thresholds for direction discrimination with superimposed noise. We found that an asymmetric compressive nonlinearity can, in a unified fashion, account for these results, while a purely quadratic nonlinearity or a rectification of the form T(p) = magnitude of p cannot. We compared velocity discrimination judgements for second-order non-Fourier stimuli (P2) with standard drifting gratings. Although velocity comparisons were veridical, uncertainties were greater for the non-Fourier stimuli. This could be reproduced by substituting a Fourier grating with superimposed noise for the non-Fourier grating. These findings are consistent with a single pathway which processes both Fourier and non-Fourier short-range motion, and are discussed in the context of other investigations which have been interpreted as demonstrating separate pathways.

Optical blur and the perception of global coherent motion in random dot cinematograms

We evaluated the effect of +3.25 dioptres of optical blur on the discrimination of motion direction in random dot cinematograms. Dot displacement between frames varied from 2.1 to 63' of visual angle while the temporal interval was held constant. Optical blur worsened discrimination in three normal subjects at displacements below 16', but improved discrimination at displacements of 21' or more. In a second experiment, two subjects viewed equivalent velocity stimuli constructed with different combinations of temporal interval and spatial displacement. Results showed that the effect of blur was specific to displacement and not velocity. Furthermore, varying the dot density of the display showed that the effect of blur correlated with dot displacement and not the probability of dot mismatches. Since optical blur attenuates high spatial frequencies, this suggests that high spatial frequencies are important for motion perception when dot displacements are less than 16' to 21', but reduce motion perception at larger dot displacements. The use of random dot cinematograms in populations must take into account stimulus displacement and optical causes of reduced spatial acuity.

Motion detection is limited by element density not spatial frequency

Two-frame random-element kinematograms were used to study the matching algorithm employed by the visual system to keep track of moving elements. Previous data have shown that the maximum spatial displacement detectable (dmax) for random-dot kinematogram stimuli increases both with increasing dot size and with decreasing centre frequency for spatially band-pass kinematograms. Both of these findings could be explained by either (i) a matching algorithm sensitive to the number of false targets in the display (informational limit) or (ii) spatial-frequency tuned sensors hardwired for detecting displacements of a constant proportion of their preferred frequency (phase-based limit). The present experiment was designed to differentiate between these alternative explanations. The stimuli were band-pass filtered (difference-of-Gaussian) random-dot patterns. The combination of six dot densities and three filter sizes produced 18 experimental conditions and allowed independent control of the spectral content and filtered-element density of the stimuli. When the dot density was high, dmax was larger for the coarse-filtered stimuli, as predicted by both theories. There was also a critical dot density for each filter size, above which dmax was constant but below which dmax rose sharply. This critical density was higher for fine-filtered stimuli such that at the lowest dot density of 0.025%, dmax was constant for all filter sizes. In support of the informational limit model, dmax was found to be directly proportional to the two-dimensional spacing of filtered elements. In contrast, dmax varied from 0.6 to 8.5 cycles of the stimulus peak frequency, suggesting that a phase-based model of motion detection cannot account for the results.

Spatial phase differences can drive apparent motion

Can shape differences drive apparent motion? Results from previous research are equivocal. Much of the confusion may be due to the use of relatively complex stimuli: letters or geometric shapes, comprising many spatial frequencies, phases, orientations, and contrasts. We focus on relatively simple stimuli: Gaussian damped f+nf compound sinewave gratings. We examine whether relative phase differences, which are critical for shape perception, can drive apparent motion. We find that some, but not all, phase differences can drive apparent motion. Specifically, stimuli that are easily discriminable and perceptually dissimilar can affect the solution of the correspondence problem. In this case, observers consistently perceive stimuli in one frame moving to the position of perceptually similar stimuli in the next frame. This general result holds over a wide range of spatial frequencies, orientations, and contrasts. Implications for theories of motion processing are discussed.

Temporal filtering enhances direction discrimination in random-dot patterns

In conventional presentations of random-dot kinematograms, two frames of random dots are presented in temporal sequence, separated by a blank inter-stimulus interval, and a coherent offset in spatial position is added to dots in one frame relative to dots in the other frame. Direction discrimination performance is limited temporally to inter-stimulus intervals below about 100 msec (Tmax). Experiments are described in which temporal smoothing was applied to the onset and offset of each frame in the kinematogram. Tmax was found to increase in proportion with the time constant of the temporal smoothing function. An explanation based on contrast-dependent responses in simple motion detectors cannot accommodate the results. Instead, the increase in Tmax with temporal smoothing, and analogous increase in spatial limit (Dmax) with spatial blurring, can be related to the spatiotemporal frequency content of the stimulus. Random-dot kinematograms can be viewed as continuously drifting patterns that have been discretely sampled at regular spatiotemporal intervals. Sampling introduces artefacts (alias signals), which become more intrusive as sampling rate declines (i.e. inter-stimulus interval or spatial displacement increases) and consequently limit discrimination performance. Temporal smoothing or spatial blurring extends performance because it removes alias signals generated by high spatiotemporal frequencies in the pattern. Computational modelling to estimate the Fourier energy available in random-dot kinematograms confirmed that the sampling account can predict the proportional increase in Tmax and Dmax limits as filter time or space constant increases.

Motion detection in interleaved random dot patterns: evidence for a rectifying nonlinearity preceding motion analysis

Three experiments examined direction discrimination in temporally interleaved random dot patterns. The stimulus consisted of two or more uncorrelated random patterns presented in a repeating temporal sequence, so that each pattern appeared only once every n frames, separated by uncorrelated patterns. Each pattern shifted either leftward or rightward at each re-appearance (all patterns shifted in the same direction in any one presentation). Subjects could specify shift direction correctly even when eight different patterns were interleaved, provided that the duration of each frame was brief. An explanation based on responses in first-order motion energy detectors tuned to low spatiotemporal frequencies (effectively summating the interleaved patterns over time) was tested using a stimulus in which each pattern inverted in contrast mid-way through each frame. Contrary to predictions based on temporal summation, performance with contrast-inverting patterns was only slightly lower than with non-inverting patterns. An alternative explanation was examined, based on responses in motion detectors that full-wave rectify image contrast before extracting motion energy. Computed responses from such detectors successfully predicted psychophysical performance with interleaved random patterns. Implications for models of motion analysis are discussed.

Attentional tracking in the perception of apparent motion: evidence from sequential blanking displays

Perception of sequential blanking displays was studied in a series of three experiments investigating factors that influence whether "shadow motion" or "item motion" is seen in a display. In addition to the duration of the blanking interval (BI) itself, three other such factors were identified: the eccentricity at which the display is viewed, the spacing of items in the display, and the type of motion that subjects are instructed to try to see. It is argued that these and other previously reported results are explicable without the need to invoke any kind of visual integration period. Instead, they are interpreted in terms of a first-order system of automatic luminance detectors and a second-order tracking system involving both voluntary and involuntary attention. The relationship of these findings to other recent work in apparent motion and visual attention and to other bistable motion displays is discussed.

Linear and non-linear filtering in stereopsis

To better understand the spatial filtering operations underlying stereopsis, and their relationship to those underlying monocular localization of the same stimuli, we examined the dependence of stereoacuity on carrier and envelope size of Gabor patches. For stimuli of broad spatial bandwidth, stereoacuity depends on the carrier spatial frequency whereas for stimuli of narrow bandwidth, stereoacuity depends on the modulation frequency. The dependence of stereoacuity on the separation of the reference elements differs for stimuli of broad and narrow spatial frequency bandwidths. These relationships suggests that stereopsis has access to two different types of information from the early filters which we term, linear and non-linear. This distinction is important not only for understanding the relationship between monocular and stereoscopic localization, but also for understanding the different filter operations underlying stereopsis.

Dependence on stimulus onset asynchrony in apparent motion: evidence for two mechanisms

The detection of the direction of motion was measured as a function of the spatial and temporal offset for a kinematogram stimulus presented in two-frame apparent motion. The stimulus was made up of Gabor function micro-patterns randomly distributed across the stimulus field. We show that for short stimulus onset asynchronies (SOA) performance can be predicted from the spatio-temporal Fourier power spectrum of the stimulus, whereas for long SOAs the pattern of performance is qualitatively different from such a prediction. The dependence of motion perception on SOA exhibits an abrupt change from one mode of behaviour to the other. These findings are suggestive of the operation of distinct mechanisms, one "quasi-linear" and one "nonlinear", which can be separated by temporal parameters.