Bifurcation study of a neural field competition model with an application to perceptual switching in motion integration

Perceptual multistability is a phenomenon in which alternate interpretations of a fixed stimulus are perceived intermittently. Although correlates between activity in specific cortical areas and perception have been found, the complex patterns of activity and the underlying mechanisms that gate multistable perception are little understood. Here, we present a neural field competition model in which competing states are represented in a continuous feature space. Bifurcation analysis is used to describe the different types of complex spatio-temporal dynamics produced by the model in terms of several parameters and for different inputs. The dynamics of the model was then compared to human perception investigated psychophysically during long presentations of an ambiguous, multistable motion pattern known as the barberpole illusion. In order to do this, the model is operated in a parameter range where known physiological response properties are reproduced whilst also working close to bifurcation. The model accounts for characteristic behaviour from the psychophysical experiments in terms of the type of switching observed and changes in the rate of switching with respect to contrast. In this way, the modelling study sheds light on the underlying mechanisms that drive perceptual switching in different contrast regimes. The general approach presented is applicable to a broad range of perceptual competition problems in which spatial interactions play a role.

Input-output transformation in the visuo-oculomotor loop: comparison of real-time optical imaging recordings in V1 to ocular following responses upon center-surround stimulation

In psychophysics and physiology, it is well established that lateral interactions are crucial mechanisms to constrain response normalization and contextual modulations. To study the cortical mechanisms involved in the contextual modulation of the behavioral contrast response function, we compared in behaving monkeys the Ocular Following Response (OFR) to V1 population activity measured using Optical Imaging of Voltage-Sensitive Dyes (VSD). If contrast response functions (CRF) to a simple local stimulus are similar in V1 and in the OFR, lateral interaction leads however to quite different modulation at those two levels. At the behavioural level, contrast response function is strongly suppressed by lateral interactions, and this suppression is stronger for higher contrasts. In V1, we showed a slow dynamic of facilitation for low contrasts integration and a fast suppression operating on high contrasts. These modulatory interactions influence differently the contrast response functions, interrupting the dynamic increase of contrast sensitivity in OFR, but not in V1 response. The temporal properties of those effects lead us to hypothesize that horizontal and feedback connectivity have differential effect on low and high contrasts integration in V1. V1 provides then an input to MT whose contextual dependency is not totally determined and must be refined before affecting the behavioural OFR.

Version and vergence eye movements in humans: open-loop dynamics determined by monocular rather than binocular image speed

We examined the velocity dependence of the vergence and version eye movements elicited by motion stimuli that were symmetric or asymmetric at the two eyes. Movements of both eyes were recorded with the scleral search coil technique. Vergence was computed as the difference in the positions of the two eyes (left-right) and version was computed as the average position of the two eyes ((left+right)/2). Subjects faced a large tangent screen onto which two identical random-dot patterns were back-projected. Each pattern was viewed by one eye only using crossed-polarizers and its position was controlled by X/Y mirror galvanometers. Viewing was always binocular and horizontal velocity steps (range, 5-240 deg/s) were applied to one (asymmetric stimulus) or both (symmetric stimulus) patterns approximately 50 ms after a centering saccade. With the symmetric stimulus, the motion at the two eyes could be either in the opposite direction (eliciting vergence responses) or in the same direction (eliciting version responses). The asymmetric stimuli elicited both vergence and version. In all cases, minimum response latencies were very short (<90 ms). Velocity tuning curves (based on the changes in vergence and version over the time period, 90-140 ms) were all sigmoidal and peaked when the monocular (i.e., retinal) image velocities were 30-60 deg/s. The vergence (version) responses to symmetric stimuli were linearly related to the vergence (version) responses to asymmetric stimuli when expressed in terms of the monocular rather than the binocular image velocities. We conclude that the dynamical limits for both vergence and version are imposed in the monocular visual pathways, before the inputs from the two eyes are combined.

Reversed short-latency ocular following

Using the scleral search coil technique to monitor eye movements, we recorded short-latency ocular following responses to displacement steps of large random-dot patterns. On half of the trials, the luminance of the dots and background were reversed during the step, a procedure that is known to reverse the direction of the perceived motion ("reverse phi"). Steps without luminance reversal induced small but consistent ocular following in the direction of the steps at ultra-short latency (<80 ms). Steps with luminance reversal induced small but consistent tracking at the same latency but in the direction opposite to the actual displacement. Tuning curves describing the dependence of initial ocular following on the amplitude of the displacement had a form approximating the derivative of a Gaussian and were well fit by Gabor functions, the cosine term being phase shifted approximately 180 degrees by the luminance reversal. This result is consistent with the idea that the initial ocular following is mediated, at least in part, by first-order (luminance) motion-energy detectors.

Short-latency ocular following in humans: sensitivity to binocular disparity

We show that the initial ocular following responses elicited by motion of a large pattern are modestly attenuated when that pattern is shifted out of the plane of fixation by altering its binocular disparity. If the motion is applied to only restricted regions of the pattern, however, then altering the disparity of those regions severely attenuates their ability to generate ocular following. This sensitivity of the ocular tracking mechanism to local binocular disparity would help the observer who moves through a cluttered 3-D world to stabilize objects in the plane of fixation and ignore all others.

Spatial scale of motion segmentation from speed cues

For the accurate perception of multiple, potentially overlapping, surfaces or objects, the visual system must distinguish different local motion vectors and selectively integrate similar motion vectors over space to segment the retinal image properly. We recently showed that large differences in speed are required to yield a percept of motion transparency. In the present study, to investigate the spatial scale of motion segmentation from speed cues alone, we measured the speed-segmentation threshold (the minimum speed difference required for 75% performance accuracy) for 'corrugated' random-dot patterns, i.e. patterns in which dots with two different speeds were alternately placed in adjacent bars of variable width. In a first experiment, we found that, at large bar widths, a smaller speed difference was required to segment and perceive the corrugated pattern of moving dots, while at small bar-widths, a larger speed difference was required to segment the two speeds and perceive two transparent surfaces of moving dots. Both the perceptual and segmentation performance transitions occurred at a bar width of around 0.4 degrees. In a second experiment, speed-segmentation thresholds were found to increase sharply when dots with different speeds were paired within a local pooling area. The critical pairing distance was about 0.2 degrees in the fovea and increased linearly with stimulus eccentricity. However, across the range of eccentricities tested (up to 15 degrees ), the critical pairing distance did not change much and remained close to the receptive field size of neurons within the primate primary visual cortex. In a third experiment, increasing dot density changed the relationship between speed-segmentation thresholds and bar width. Thresholds decreased for large bar widths, but increased for small bar widths. All of these results are well fit by a simple stochastic model, which estimates the probabilities of having identical or different motion vectors within a local pooling area whose size is the same as that of primate V1 neurons. Altogether, these results demonstrate that speed-based segmentation can function well, even at small spatial scales (i.e. high-spatial frequencies of spatial corrugation) and thereby emphasizes the critical role of a local pooling process early in the cortical motion-processing pathway.

Temporal dynamics of motion integration for the initiation of tracking eye movements at ultra-short latencies

The perceived direction of a grating moving behind an elongated aperture is biased towards the aperture's long axis. This "barber pole" illusion is a consequence of integrating one-dimensional (1D) or grating and two-dimensional (2D) or terminator motion signals. In humans, we recorded the ocular following responses to this stimulus. Tracking was always initiated at ultra-short latencies (approximately 85 ms) in the direction of grating motion. With elongated apertures, a later component was initiated 15-20 ms later in the direction of the terminator motion signals along the aperture's long axis. Amplitude of the later component was dependent upon the aperture's aspect ratio. Mean tracking direction at the end of the trial (135-175 ms after stimulus onset) was between the directions of the vector sum computed by integrating either terminator motion signals only or both grating and terminator motion signals. Introducing an elongated mask at the center of the "barber pole" did not affect the latency difference between early and later components, indicating that this latency shift was not due to foveal versus peripheral locations of 1D and 2D motion signals. Increasing the size of the foveal mask up to 90% of the stimulus area selectively reduced the strength of the grating motion signals and, consequently, the amplitude of the early component. Conversely, reducing the contrast of, or indenting the aperture's edges, selectively reduced the strength of terminator motion signals and, consequently, the amplitude of the later component. Latencies were never affected by these manipulations. These results tease apart an early component of tracking responses, driven by the grating motion signals and a later component, driven by the line-endings moving at the intersection between grating and aperture's borders. These results support the hypothesis of a parallel processing of 1D and 2D motion signals with different temporal dynamics.

Lorazepam-induced modifications of saccadic and smooth-pursuit eye movements in humans: attentional and motor factors

In a placebo-controlled, double-blind study, we measured the effects of low dose lorazepam on attentional and motor factors involved in saccadic and smooth pursuit eye movements. We manipulated the temporal interval between the extinction of the central fixation target and the appearance of a second eccentric target (gap/overlap step paradigm). The second target was either stationary (saccade trial) or moving in a direction opposite to the step (pursuit trial). Gap/overlap effects on the latency of saccadic and smooth pursuit eye movements were measured before and after oral intake of either lorazepam or placebo. Pharmacological effects on the dynamics and the accuracy of both types of eye movements were also investigated. In 14 healthy volunteers, we found that the temporal interval between fixation target offset and eccentric target onset modulates the latency of saccadic and smooth pursuit eye movements in a similar way. As compared to placebo, lorazepam significantly increased the latency of both types of eye movements, but did not modify the gap/overlap effect. Moreover, lorazepam significantly decreased the peak velocity of the first saccade towards the eccentric stationary target, as well as the gain of tracking towards the eccentric moving target. However, the overall accuracy of both behaviors was not significantly affected, indicating that systematic errors in foveating or tracking were detected and corrected by appropriate corrective or catch-up saccades, respectively. Results are discussed in terms of shared/different mechanisms for saccadic and pursuit systems in primates.

Motion perception during saccadic eye movements

During rapid eye movements, motion of the stationary world is generally not perceived despite displacement of the whole image on the retina. Here we report that during saccades, human observers sensed visual motion of patterns with low spatial frequency. The effect was greatest when the stimulus was spatiotemporally optimal for motion detection by the magnocellular pathway. Adaptation experiments demonstrated dependence of this intrasaccadic motion percept on activation of direction-selective mechanisms. Even two-dimensional complex motion percepts requiring spatial integration of early motion signals were observed during saccades. These results indicate that the magnocellular pathway functions during saccades, and that only spatiotemporal limitations of visual motion perception are important in suppressing awareness of intrasaccadic motion signals.

Speed tuning of motion segmentation and discrimination

Motion transparency requires that the visual system distinguish different motion vectors and selectively integrate similar motion vectors over space into the perception of multiple surfaces moving through or over each other. Using large-field (7 degrees x 7 degrees) displays containing two populations of random-dots moving in the same (horizontal) direction but at different speeds, we examined speed-based segmentation by measuring the speed difference above which observers can perceive two moving surfaces. We systematically investigated this 'speed-segmentation' threshold as a function of speed and stimulus duration, and found that it increases sharply for speeds above approximately 8 degrees/s. In addition, speed-segmentation thresholds decrease with stimulus duration out to approximately 200 ms. In contrast, under matched conditions, speed-discrimination thresholds stay low at least out to 16 degrees/s and decrease with increasing stimulus duration at a faster rate than for speed segmentation. Thus, motion segmentation and motion discrimination exhibit different speed selectivity and different temporal integration characteristics. Results are discussed in terms of the speed preferences of different neuronal populations within the primate visual cortex.

Radial optic flow induces vergence eye movements with ultra-short latencies

An observer moving forwards through the environment experiences a radial pattern of image motion on each retina. Such patterns of optic flow are a potential source of information about the observer's rate of progress, direction of heading and time to reach objects that lie ahead. As the viewing distance changes there must be changes in the vergence angle between the two eyes so that both foveas remain aligned on the object of interest in the scene ahead. Here we show that radial optic flow can elicit appropriately directed (horizontal) vergence eye movements with ultra-short latencies (roughly 80 ms) in human subjects. Centrifugal flow, signalling forwards motion, increases the vergence angle, whereas centripetal flow decreases the vergence angle. These vergence eye movements are still evident when the observer's view of the flow pattern is restricted to the temporal hemifield of one eye, indicating that these responses do not result from anisotropies in motion processing but from a mechanism that senses the radial pattern of flow. We hypothesize that flow-induced vergence is but one of a family of rapid ocular reflexes, mediated by the medial superior temporal cortex, compensating for translational disturbance of the observer.

Vergence eye movements in response to binocular disparity without depth perception

Primates use vergence eye movements to align their two eyes on the same object and can correct misalignments by sensing the difference in the positions of the two retinal images of the object (binocular disparity). When large random-dot patterns are viewed dichoptically and small binocular misalignments are suddenly imposed (disparity steps), corrective vergence eye movements are elicited at ultrashort latencies. Here we show that the same steps applied to dense anticorrelated patterns, in which each black dot in one eye is matched to a white dot in the other eye, initiate vergence responses that are very similar, except that they are in the opposite direction. This sensitivity to the disparity of anticorrelated patterns is shared by many disparity-selective neurons in cortical area V1, despite the fact that human subjects fail to perceive depth in such stimuli. These data indicate that the vergence eye movements initiated at ultrashort latencies result solely from locally matched binocular features, and derive their visual input from an early stage of cortical processing before the level at which depth percepts are elaborated.

Differential Velocity Detection in Motion Parallax Fields

Processing of motion parallax relies on the ability of the visual system to segregate locally different motion signals and integrate them over space and time in order to reconstruct a 3-D structure. In a series of experiments, we evaluated the thresholds for differential motion detection and their dependences upon the spatial structure of the optic-flow field.

Visual stimuli were large moving random-dot displays (80 deg × 60 deg). Each dot was randomly attributed one of two velocities whose difference ranged between 0% and 80% of their average velocity, which ranged between 2 and 64 deg s−1. Stimulus duration was from 130 to 1040 ms. Subjects were instructed to stare at a central fixation mark and had to decide whether the display specified one or two surfaces. At a duration of 130 ms, subjects needed more than 40% difference between the two velocities to reach a 75%-correct detection criterion. Thresholds reached a minimum value of about 20% at a duration of 500 ms. Thresholds always increased with the average velocity and were not affected when a static form segregation cue was added to the displays. They were always larger than thresholds for velocity discrimination in successive displays (about 10% at 260 ms). We finally investigated the spatial properties of differential velocity detection. The visual field was divided into horizontal stripes of equal widths. Adjacent bars alternately contained random dots moving with one of two velocities. Thresholds for differential velocity detection increased monotonically when the bandwidth decreased, up to an asymptotic value, equal to those observed with a transparent display.

Ocular responses to motion parallax stimuli: the role of perceptual and attentional factors

When human subjects are presented with visual displays consisting of random dots moving sideways at different velocities, they perceive transparent surfaces, moving in the same direction but located at different distances from themselves. They perceive depth from motion parallax, without any additional cues to depth, such as relative size, occlusion or binocular disparity. Simultaneously, large-field visual motion triggers compensatory eye movements which tend to offset such motion, in order to stabilize the visual image of the environment. In a series of experiments, we investigated how such reflexive eye movements are controlled by motion parallax displays, that is, in a situation where a complete stabilization of the visual image is never possible. Results show that optokinetic nystagmus, and not merely active visual pursuit of singular elements, is triggered by such displays. Prior to the detection of depth from motion parallax, eye tracking velocity is equal to the average velocity of the visual image. After detection, eye tracking velocity spontaneously matches the slowest velocity in the visual field, but can be controlled by attentional factors. Finally, for a visual stimulation containing more than three velocities, subjects are no longer able to perceptually dissociate between different surfaces in depth, and eye tracking velocity remains equal to the average velocity of the visual image. These data suggest that, in the presence of flow fields containing motion parallax, optokinetic eye movements are modulated by perceptual and attentional factors.

Optokinetic Oculomotor Responses and the Perception of Depth from Motion Parallax Cues

In a series of experiments we studied the relationships between the characteristics of optokinetic oculomotor responses triggered spontaneously by large-field visual motion and the perception of depth from motion parallax cues. Random-dot dynamic displays were projected at 60 Hz frame rate. Oculomotor behaviour was monitored with an infrared device. Subjects were asked to identify the spatial structure specified by optical motion and their responses were recorded with a mouse device. Results were as follows: (1) In all cases optokinetic responses are triggered when subjects are presented with visual displays specifying either a single surface, many surfaces or a cloud of dots receding in depth. (2) The velocity of slow phases of the optokinetic nystagmus changes from matching the average velocity of a display in early phases after the onset of a stimulation to slowing down to the slowest velocity in the display, for a small number of surfaces specified by motion parallax cues. (3) Structure-from-motion is correctly detected by subjects with long detection times (between 1 and 2 s). The comparison between the slow build-up of depth perception and the slow decrease of eye pursuit velocity provides further support for the hypothesis that the control of optokinetic eye movements and the perception of depth from visual motion share common pathways up to higher cortical levels of visual processing.

A role for stereoscopic depth cues in the rapid visual stabilization of the eyes

Primates have visual tracking systems that help stabilize the eyes on the surroundings by responding to retinal image motion at ultra-short latencies. However, as the observer moves through the environment, the image motion on the retina depends on the three-dimensional structure of the scene. We report here that the very earliest of these tracking responses is elicited only by objects moving in the immediate vicinity of the plane of fixation: objects nearer or farther are ignored. This selectivity is achieved by means of a stereoscopic depth mechanism which uses the fact that the two eyes have differing viewpoints, so only objects in the plane of fixation have images that occupy corresponding positions on the two retinae. Such behaviour is readily explained by the known binocular properties of some motion-selective neurons in the visual cortex. Some (stereoanomalous) subjects showed highly specific tracking deficits as though lacking one subtype of these neurons.