Contrast-modulation flicker: dynamics and spatial resolution of the light adaptation process

Idiosyncratic preferences in transparent motion and binocular rivalry are dissociable

Previous studies revealed that there are idiosyncratic preferences to perceive certain motion directions in front during motion transparency depth rivalry (Mamassian & Wallace, 2010; Schütz, 2014). Meanwhile, other studies reported idiosyncratic preferences in binocular rivalry during the onset stage (Carter & Cavanagh, 2007; Stanley, Carter, & Forte, 2011). Here we investigated the relationship of idiosyncratic preferences in transparent motion and binocular rivalry. We presented two dot clouds that were moving in opposite directions. In the transparent motion condition, both dot clouds were presented to both eyes and participants had to report the dot cloud they perceived in front. In the binocular rivalry condition, the dot clouds were presented to different eyes and participants had to report the dominant dot cloud. There were strong idiosyncratic directional preferences in transparent motion and rather weak directional preferences in binocular rivalry. In general, binocular rivalry was dominated by biases in contrast polarity, whereas transparent motion was dominated by biases in motion direction. A circular correlation analysis showed no correlation between directional preferences in transparent motion and binocular rivalry. These findings show that idiosyncratic preferences in a visual feature can be dissociated at different stages of processing.

Binocular combination of luminance profiles

We develop and test a new two-dimensional model for binocular combination of the two eyes' luminance profiles. For first-order stimuli, the model assumes that one eye's luminance profile first goes through a luminance compressor, receives gain-control and gain-enhancement from the other eye, and then linearly combines the other eye's output profile. For second-order stimuli, rectification is added in the signal path of the model before the binocular combination site. Both the total contrast and luminance energies, weighted sums over both the space and spatial-frequency domains, were used in the interocular gain-control, while only the total contrast energy was used in the interocular gain-enhancement. To challenge the model, we performed a binocular brightness matching experiment over a large range of background and target luminances. The target stimulus was a dichoptic disc with a sharp edge that has an increment or decrement luminance from its background. The disk's interocular luminance ratio varied from trial to trial. To refine the model we tested three luminance compressors, five nested binocular combination models (including the Ding–Sperling and the DSKL models), and examined the presence or absence of total luminance energy in the model. We found that (1) installing a luminance compressor, either a logarithmic luminance function or luminance gain-control, (2) including both contrast and luminance energies, and (3) adding interocular gain-enhancement (the DSKL model) to a combined model significantly improved its performance. The combined model provides a systematic account of binocular luminance summation over a large range of luminance input levels. It gives a unified explanation of Fechner's paradox observed on a dark background, and a winner-take-all phenomenon observed on a light background. To further test the model, we conducted two additional experiments: luminance summation of discs with asymmetric contour information (Experiment 2), similar to Levelt (1965) and binocular combination of second-order contrast-modulated gratings (Experiment 3). We used the model obtained in Experiment 1 to predict the results of Experiments 2 and 3 and the results of our previous studies. Model simulations further refined the contrast space weight and contrast sensitivity functions that are installed in the model, and provide a reasonable account for rebalancing of imbalanced binocular vision by reducing the mean luminance in the dominant eye.

Encoding and estimation of first- and second-order binocular disparity in natural images

•

First- and second-order responses to natural binocular images are correlated.

•

Second-order mechanisms can improve the accuracy of disparity estimation.

•

Second-order mechanisms can extend the depth range of binocular stereopsis.

The first stage of processing of binocular information in the visual cortex is performed by mechanisms that are bandpass-tuned for spatial frequency and orientation. Psychophysical and physiological evidence have also demonstrated the existence of second-order mechanisms in binocular processing, which can encode disparities that are not directly accessible to first-order mechanisms. We compared the responses of first- and second-order binocular filters to natural images. We found that the responses of the second-order mechanisms are to some extent correlated with the responses of the first-order mechanisms, and that they can contribute to increasing both the accuracy, and depth range, of binocular stereopsis.

Contrast adaptation in the Limulus lateral eye

Luminance and contrast adaptation are neuronal mechanisms employed by the visual system to adjust our sensitivity to light. They are mediated by an assortment of cellular and network processes distributed across the retina and visual cortex. Both have been demonstrated in the eyes of many vertebrates, but only luminance adaptation has been shown in invertebrate eyes to date. Since the computational benefits of contrast adaptation should apply to all visual systems, we investigated whether this mechanism operates in horseshoe crab eyes, one of the best-understood neural networks in the animal kingdom. The spike trains of optic nerve fibers were recorded in response to light stimuli modulated randomly in time and delivered to single ommatidia or the whole eye. We found that the retina adapts to both the mean luminance and contrast of a white-noise stimulus, that luminance- and contrast-adaptive processes are largely independent, and that they originate within an ommatidium. Network interactions are not involved. A published computer model that simulates existing knowledge of the horseshoe crab eye did not show contrast adaptation, suggesting that a heretofore unknown mechanism may underlie the phenomenon. This mechanism does not appear to reside in photoreceptors because white-noise analysis of electroretinogram recordings did not show contrast adaptation. The likely site of origin is therefore the spike discharge mechanism of optic nerve fibers. The finding of contrast adaption in a retinal network as simple as the horseshoe crab eye underscores the broader importance of this image processing strategy to vision.

Binocular combination of second-order stimuli

Phase information is a fundamental aspect of visual stimuli. However, the nature of the binocular combination of stimuli defined by modulations in contrast, so-called second-order stimuli, is presently not clear. To address this issue, we measured binocular combination for first- (luminance modulated) and second-order (contrast modulated) stimuli using a binocular phase combination paradigm in seven normal adults. We found that the binocular perceived phase of second-order gratings depends on the interocular signal ratio as has been previously shown for their first order counterparts; the interocular signal ratios when the two eyes were balanced was close to 1 in both first- and second-order phase combinations. However, second-order combination is more linear than previously found for first-order combination. Furthermore, binocular combination of second-order stimuli was similar regardless of whether the carriers in the two eyes were correlated, anti-correlated, or uncorrelated. This suggests that, in normal adults, the binocular phase combination of second-order stimuli occurs after the monocular extracting of the second-order modulations. The sensory balance associated with this second-order combination can be obtained from binocular phase combination measurements.

Black-white asymmetry in visual perception

With eleven different types of stimuli that exercise a wide gamut of spatial and temporal visual processes, negative perturbations from mean luminance are found to be typically 25% more effective visually than positive perturbations of the same magnitude (range 8-67%). In Experiment 12, the magnitude of the black-white asymmetry is shown to be a saturating function of stimulus contrast. Experiment 13 shows black-white asymmetry primarily involves a nonlinearity in the visual representation of decrements. Black-white asymmetry in early visual processing produces even-harmonic distortion frequencies in all ordinary stimuli and in illusions such as the perceived asymmetry of optically perfect sine wave gratings. In stimuli intended to stimulate exclusively second-order processing in which motion or shape are defined not by luminance differences but by differences in texture contrast, the black-white asymmetry typically generates artifactual luminance (first-order) motion and shape components. Because black-white asymmetry pervades psychophysical and neurophysiological procedures that utilize spatial or temporal variations of luminance, it frequently needs to be considered in the design and evaluation of experiments that involve visual stimuli. Simple procedures to compensate for black-white asymmetry are proposed.

Visual adaptation and face perception

The appearance of faces can be strongly affected by the characteristics of faces viewed previously. These perceptual after-effects reflect processes of sensory adaptation that are found throughout the visual system, but which have been considered only relatively recently in the context of higher level perceptual judgements. In this review, we explore the consequences of adaptation for human face perception, and the implications of adaptation for understanding the neural-coding schemes underlying the visual representation of faces. The properties of face after-effects suggest that they, in part, reflect response changes at high and possibly face-specific levels of visual processing. Yet, the form of the after-effects and the norm-based codes that they point to show many parallels with the adaptations and functional organization that are thought to underlie the encoding of perceptual attributes like colour. The nature and basis for human colour vision have been studied extensively, and we draw on ideas and principles that have been developed to account for norms and normalization in colour vision to consider potential similarities and differences in the representation and adaptation of faces.

Double dissociation between first- and second-order processing

To study the difference of sensitivity to luminance- (LM) and contrast-modulated (CM) stimuli, we compared LM and CM detection thresholds in LM- and CM-noise conditions. The results showed a double dissociation (no or little inter-attribute interaction) between the processing of these stimuli, which implies that both stimuli must be processed, at least at some point, by separate mechanisms and that both stimuli are not merged after a rectification process. A second experiment showed that the internal equivalent noise limiting the CM sensitivity was greater than the one limiting the carrier sensitivity, which suggests that the internal noise occurring before the rectification process is not limiting the CM sensitivity. These results support the hypothesis that a suboptimal rectification process partially explains the difference of LM and CM sensitivity.

Short-latency disparity vergence eye movements: a response to disparity energy

Vergence eye movements were elicited in human subjects by applying disparities to square-wave gratings lacking the fundamental ("missing fundamental", mf). Using a dichoptic arrangement, subjects viewed gratings that were identical at the two eyes except for a phase difference of 1/4 wavelength so that, based on the nearest-neighbor matches, the features and the 4n+1 harmonics (5th, 9th, etc.) all had binocular disparities of one sign, whereas the 4n-1 harmonics (3rd, 7th, etc.) all had disparities of the opposite sign. Further, the amplitude of the ith harmonic was proportional to 1/i. Using the electromagnetic search coil technique to record the positions of both eyes indicated that the earliest vergence eye movements elicited by these disparity stimuli had ultra-short latencies (minimum, <65 ms) and were always in the direction of the most prominent harmonic, the 3rd, but their magnitudes fell short of those elicited when the same disparities were applied to pure sinusoids whose spatial frequency and contrast matched those of the 3rd harmonic. This shortfall was evident in both the horizontal vergence responses recorded with vertical grating stimuli and the vertical vergence responses recorded with horizontal grating stimuli. When the next most prominent harmonic, the 5th, was removed from the mf stimulus (creating the "mf-5" stimulus) the vertical vergence responses showed almost no shortfall-indicating that it had been almost entirely due to that 5th harmonic-but the horizontal vergence responses still showed a small shortfall, at least with higher contrast stimuli. This small shortfall might represent a very minor contribution from higher harmonics and/or distortion products and/or a feature-based mechanism. We conclude that the earliest disparity vergence responses-especially vertical-were strongly dependent on the major Fourier components of the binocular images, consistent with early spatial filtering of the monocular visual inputs prior to their binocular combination as in the disparity-energy model of complex cells in striate cortex [Ohzawa, I., DeAngelis, G. C., & Freeman, R. D. (1990). Stereoscopic depth discrimination in the visual cortex: neurons ideally suited as disparity detectors. Science, 249, 1037-1041].

Initial ocular following in humans: a response to first-order motion energy

Visual motion is sensed by low-level (energy-based) and high-level (feature-based) mechanisms. Ocular following responses (OFR) were elicited in humans by applying horizontal motion to vertical square-wave gratings lacking the fundamental ("missing fundamental stimulus"). Motion consisted of successive 1/4-wavelength steps, so the features and 4n+1 harmonics (where n=integer) shifted forwards, whereas the 4n-1 harmonics--including the strongest Fourier component (the 3rd harmonic)--shifted backwards (spatial aliasing). Initial OFR, recorded with the electromagnetic search coil technique, were always in the direction of the 3rd harmonic, e.g., leftward steps resulted in rightward OFR. Thus, the earliest OFR were strongly dependent on the motion of the major Fourier component, consistent with early spatio-temporal filtering prior to motion detection, as in the well-known energy model of motion analysis.

Sensitivity to contrast modulation: the spatial frequency dependence of second-order vision

We consider the overall shape of the second-order modulation sensitivity function (MSF). Because second-order modulations of local contrast or orientation require a carrier signal, it is necessary to evaluate modulation sensitivity against a variety of carriers before reaching a general conclusion about second-order sensitivity. Here we present second-order sensitivity functions for new carrier types (low pass (1/f) noise, and high pass noise) and demonstrate that, when first-order artefacts have been accounted for, the shape of the resulting MSFs are similar to one another and to those for white and broad band noise. They are all low pass with a likely upper frequency limit in the range 10-20 c/deg, suggesting that detection of second-order stimuli is relatively insensitive to the structure of the carrier signal. This result contrasts strongly with that found for (first-order) luminance modulations of the same noise types. Here the noise acts as mask and each noise type masks most those frequencies that are dominant in its spectrum. Thus the shape of second-order MSFs are largely independent of the spectrum of their noise carrier, but first-order CSFs depend on the spectrum of an additive noise mask. This provides further evidence for the separation of first- and second-order vision and characterises second-order vision as a low pass mechanism.

Electrical coupling between mammalian cones

BACKGROUND

Cone photoreceptors are noisy because of random fluctuations of photon absorption, signaling molecules, and ion channels. However, each cone's noise is independent of the others, whereas their signals are partially shared. Therefore, electrically coupling the synaptic terminals prior to forward transmission and subsequent nonlinear processing can appreciably reduce noise relative to the signal. This signal-processing strategy has been demonstrated in lower vertebrates with rather coarse vision, but its occurrence in mammals with fine acuity has been doubted (even though gap junctions are present) because coupling would blur the neural image.

RESULTS

In ground squirrel retina, whose triangular cone lattice resembles the human fovea, paired electrical recordings from adjacent cones demonstrated electrical coupling with an average conductance of approximately 320 pS. Blur caused by this degree of coupling had a space constant of approximately 0.5 cone diameters. Psychophysical measurements employing laser interferometry to bypass the eye's optics suggest that human foveal cones experience a similar degree of neural blur and that it is invariant with light intensity. This neural blur is narrower than the eye's optical blur, and we calculate that it should improve the signal-to-noise ratio at the cone terminal by about 77%.

CONCLUSIONS

We conclude that the gap junctions observed between mammalian cones, including those in the human fovea, represent genuine electrical coupling. Because the space constant of the resulting neural blur is less than that of the optical blur, the signal-to-noise ratio can be markedly improved before the nonlinear stages with little compromise to visual acuity.

Chromatic light adaptation measured using functional magnetic resonance imaging

Sensitivity changes, beginning at the first stages of visual transduction, permit neurons with modest dynamic range to respond to contrast variations across an enormous range of mean illumination. We have used functional magnetic resonance imaging (fMRI) to investigate how these sensitivity changes are controlled within the visual pathways. We measured responses in human visual area V1 to a constant-amplitude, contrast-reversing probe presented on a range of mean backgrounds. We found that signals from probes initiated in the L and M cones were affected by backgrounds that changed the mean absorption rates in the L and M cones, but not by background changes seen only by the S cones. Similarly, signals from S cone-initiated probes were altered by background changes in the S cones, but not by background changes in the L and M cones. Performance in psychophysical tests under similar conditions closely mirrored the changes in V1 fMRI signals. We compare our data with simulations of the visual pathway from photon catch rates to cortical blood-oxygen level-dependent signals and show that the quantitative fMRI signals are consistent with a simple model of mean-field adaptation based on Naka-Rushton (Naka and Rushton, 1966) adaptation mechanisms within cone photoreceptor classes.

Color from invisible patterns

Human pattern resolution is limited by optical blurring as well as neural filtering by a cascade of retinal and cortical sites with progressively lower resolution limits. Curiously, pattern structure can influence perceived color: a high-contrast, monochromatic (single wavelength) pattern appears desaturated (closer to white) relative to a uniform field of the same wavelength. Here we show that this desaturation is evident even when the pattern's frequency is too high for conscious perception, implicating a nonlinear process--namely light adaptation--at the level of single cone photoreceptors. We propose a neural mechanism in which fast, involuntary eye movements serve to shift control over perception between two competing cone populations, each operating at different levels of adaptation.

Cellular basis for the response to second-order motion cues in Y retinal ganglion cells

We perceive motion when presented with spatiotemporal changes in contrast (second-order cue). This requires linear signals to be rectified and then summed in temporal order to compute direction. Although both operations have been attributed to cortex, rectification might occur in retina, prior to the ganglion cell. Here we show that the Y ganglion cell does indeed respond to spatiotemporal contrast modulations of a second-order motion stimulus. Responses in an OFF ganglion cell are caused by an EPSP/IPSP sequence evoked from within the dendritic field; in ON cells inhibition is indirect. Inhibitory effects, which are blocked by tetrodotoxin, clamp the response near resting potential thus preventing saturation. Apparently the computation for second-order motion can be initiated by Y cells and completed by cortical cells that sum outputs of multiple Y cells in a directionally selective manner.

Retinal contrast losses and visual resolution with obliquely incident light

To determine whether vision with obliquely incident light is degraded by contrast losses originating in the retina, laser interference fringe patterns were produced on the retina for various directions of incidence of the two interfering beams. Contrast-modulation flicker [Vision Res. 38, 985 (1998)] was used as a psychophysical measure of contrast at the level of the photoreceptors. Fringe contrast was shown to be maximal when the interfering beams were equal in perceived brightness, not in physical intensity. The effective fringe contrast was slightly reduced with oblique incidence for high spatial frequencies, but the reduction was too slight to be an important factor in visual resolution. The loss was similar whether the incident beams were displaced from the pupil center in a direction parallel or perpendicular to the grating bars.

Sensitive calibration and measurement procedures based on the amplification principle in motion perception

We compare two types of sampled motion stimuli: ordinary periodic displays with modulation amplitude m(o=e) that translate 90 degrees between successive frames and amplifier sandwich displays. In sandwich displays, even-numbered frames are of one type, odd-numbered frames are of the same or different type, and (1) both types have the same period, (2) translate in a consistent direction 90 degrees between frames, and (3) even frames have modulation amplitude m(e), odd frames have modulation amplitude m(o). In both first-order motion (van Santen, J.P.H. & Sperling, G. (1984). Temporal covariance model of human motion perception. Journal of the Optical Society of America A, 1, 451-73) and second-order motion (Werkhoven, P., Sperling, G., & Chubb, C. (1993). Motion perception between dissimilar gratings: a single channel theory. Vision Research, 33, 463-85) the motion strength of amplifier sandwich displays is proportional to the product m(o)m(e) for a wide range of m(e). By setting m(e) to a large value, an amplifier sandwich stimulus with a very small value of m(o) can still produce visible motion. The amplification factor is the ratio of two threshold modulation amplitudes: ordinary circumflexm(o=e) over amplified circumflexm(o), circumflexm(o=e)/circumflexm(o). We find amplification factors of up to about 8x. Light adaptation and contrast gain control in early visual processing distort the representations of visual stimuli so that inputs to subsequent perceptual processes contain undesired distortion products or 'impurities'. Motion amplification is used to measure and thence to reduce these unwanted components in a stimulus to a small fraction of their threshold. Such stimuli are certifiably pure in the sense that the residual impurity is less than a specified value. Six applications are considered: (1) removing (first-order) luminance contamination from moving (second-order) texture gratings; (2) removing luminance contamination from moving chromatic gratings to produce pure isoluminant gratings; (3) removing distortion products in luminance-modulated (first-order) gratings - by iterative application, all significant distortion products can be removed; (4) removing second-order texture contamination from third-order motion displays; (5) removing feature bias from third-order motion displays; (6) and the same general principles are applied to texture-slant discrimination in which x,y spatial coordinates replace the x,t motion coordinates. In all applicable domains, the amplification principle provides a powerful assay method for the precise measurement of very weak stimuli, and thereby a means of producing visual displays of certifiable purity.

What does second-order vision see in an image?

The human visual system is sensitive to both first-order variations in luminance and second-order variations in local contrast and texture. Although there is some debate about the nature of second-order vision and its relationship to first-order processing, there is now a body of results showing that they are processed separately. However, the amount, and nature, of second-order structure present in the natural environment is unclear. This is an important question because, if natural scenes contain little second-order structure in addition to first-order signals, the notion of a separate second-order system would lack ecological validity. Two models of second-order vision were applied to a number of well-calibrated natural images. Both models consisted of a first stage of oriented spatial filters followed by a rectifying nonlinearity and then a second set of filters. The models differed in terms of the connectivity between first-stage and second-stage filters. Output images taken from the models indicate that natural images do contain useful second-order structure. Specifically, the models reveal variations in texture and features defined by such variations. Areas of high contrast (but not necessarily high luminance) are also highlighted by the models. Second-order structure--as revealed by the models--did not correlate with the first-order profile of the images, suggesting that the two types of image 'content' may be statistically independent.

Spatial and temporal properties of light adaptation in the rod system

Little is known about the mechanism that regulates the sensitivity of rod system at its normal operating light levels. Two experiments are reported in this paper. First, we searched for nonlinear distortion products in rod vision that could be generated from any local adaptation process, using a sensitive experimental procedure that has demonstrated local adaptation in cone vision. No local adaptation was evident in the rod system, even at near saturating light levels. Second, to investigate the dynamics of light adaptation in the rod system we presented a uniform flickering background, sinusoidally modulated in time, and measured increment thresholds for brief test flashes that were superimposed on this background at different times during the sinusoidal flicker cycle. At frequencies less than 5-6 Hz, the rod increment threshold follows the background modulation, with a slight phase advance. When the background is modulated faster than 5-6 Hz, the increment threshold remains the same regardless of when the test flash occurred during the background cycle. Thus the rod system sensitivity, unlike that of the cone system, can only change slowly, and is set by a space-integrated signal rather than independently for different rods.

The temporal properties of first- and second-order vision

Vision is sensitive to first-order modulations of luminance and second-order modulations of image contrast. There is now a body of evidence that the two types of modulation are detected by separate mechanisms. Some previous experiments on motion detection have suggested that the second-order system is quite sluggish compared to the first-order system. Here we derive temporal properties of first- and second-order vision at threshold from studies of temporal integration and two-pulse summation. Three types of modulation were tested: luminance gratings alone, luminance modulations added to dynamic visual noise, and contrast modulations of dynamic noise. Data from the two-pulse summation experiment were used to derive impulse response functions for the three types of stimulus. These were then used to predict performance in the temporal integration experiment. Temporal frequency response functions were obtained as the Fourier transform of impulse responses derived from data averaged across two observers. The response to noise-free luminance gratings of 2 c/deg was bi-phasic and transient in the time domain, and bandpass in the frequency domain. The addition of dynamic noise caused the response to become mono-phasic, sustained and low-pass. The response to contrast modulated noise (second-order) was also mono-phasic, sustained and low-pass, with only a slightly longer integration time than in the first-order case. The ultimate roll-off at high frequencies was about the same as for the first-order case. We conclude that second-order vision may not be as sluggish as previously thought.

Variance of high contrast textures is sensed using negative half-wave rectification

A rectifying transformation is required to sense variations in texture contrast. Various theoretical and practical considerations have inclined researchers to suppose that this rectification is full-wave, rather than half-wave. In the studies reported here, observers are asked to judge which of two texture patches has higher texture variance. Textures are composed of small squares, with each square being painted with one of nine different luminances. Different texture variances are achieved by manipulating the histograms of the texture patches to be compared. When the nine luminances range linearly from 0 to 160 cd/m(2), the transformation mediating judgments of texture variance takes the form of a negative half-wave rectifier: texture variance judgments are determined exclusively by the frequencies of luminances below mean luminance in the textures being compared. However, when the nine luminances range linearly from 60 to 100 cd/m(2), two of three observers use a full-wave rectifying transformation in making texture variance judgments; the third observer continued to use a negative half-wave rectifier. The unexpectedly asymmetric roles played by low versus high luminances in texture variance judgments suggest that the off-center system may play a dominant role in human perception of texture contrast.

Texture luminance judgments are approximately veridical

This paper investigates intensity coding in human vision. Specifically, we address the following question: how do different luminances influence the perceived total luminance of a composite image? We investigate this question using a paradigm in which the observer attempts to judge, with feedback, which of two texture patches has higher total luminance. All patches are composed of nine luminances, ranging linearly from 0 (black) to a maximum luminance (white: 160 cd/m(2) in one condition; 20.2 cd/m(2) in another condition). Luminance histograms of the patches being compared are experimentally varied to derive, for each luminance nu, the impact exerted by texture elements (texels) of luminance nu on texture luminance judgments. We find that impact is approximately proportional to texel luminance; That is, a texture element exerts, on average, an impact on texture brightness (i.e. perceived texture luminance) that is proportional to its (the texel's) luminance. The only exception occurs for texels of maximal luminance, which surprisingly exert an impact that is slightly, but significantly, less than that exerted by texels of the next lower luminance. We conclude that visual intensity coding for purposes of assessing overall luminance of inhomogeneous patches is approximately veridical. In particular, texture luminance judgments are not mediated by a significant, compressive nonlinearity.

Does early non-linearity account for second-order motion?

A contrast-modulated (CM) pattern is formed when a modulating or envelope function imposes local contrast variations on a higher-frequency carrier. Motion may be seen when the envelope drifts across a stationary carrier and this has been attributed to a second-order pathway for motion. However, an early compressive response to luminance (e.g. in the photoreceptors) would introduce a distortion product at the modulating frequency. We used a nulling method to measure the distortion product, and then asked whether this early distortion could account for perception of second-order motion. The first stimulus sequence consisted of alternate frames of CM (100% modulation) and luminance-modulated (LM) patterns. Carriers were either 2-D binary noise (4 x 4 min arc dots) or a 4 c/deg grating, both modulated at 0.6 c/deg. The carrier was stationary while the phase of the modulating signal (LM alternating with CM) stepped successively through 90 degrees to the left or right. Motion was seen in a direction opposite to the phase stepping, consistent with early compressive distortion that induces an out-of-phase LM component into the CM stimulus. We measured distortion amplitude by adding LM to the CM frames to null the perceived motion. Distortion increased as the square of carrier contrast, as predicted by the compressive transducer. It also increased with modulation drift rate, implying that the transducer is time-dependent, not static. Thus early compressive non-linearity does induce first-order artefacts into second-order stimuli. Nevertheless this does not account for second-order motion, since perceived motion of second-order sequences (CM in every frame) could in general not be nulled by adding LM components. We conclude that two pathways for motion do exist.

Local nonlinearity in S-cones and their estimated light-collecting apertures

When an high frequency grating of high retinal contrast is presented intermittently by modulating its contrast at constant average luminance, observers experience uniform field flicker, even if the grating is too fine to be resolved. For long and middle wavelength cones, this contrast-modulation flicker can be seen for fringe periods as small as the diameter of a cone [MacLeod & He (1993). Nature, 361, 256-258], implying no substantial neural spatial integration prior to the nonlinear site. We now report that the short-wavelength cone system, despite its greater spatial integration than the other cone systems, can generate contrast-modulation flicker at spatial frequencies as high as 50 cycles/deg, a value comparable with that of the other cone systems in the same retinal area. Spatial resolution at the nonlinear site is in all cases apparently limited by the size of the cones. Likewise, little temporal filtering (in the range up to 18 Hz) precedes the S-cone nonlinearity. This suggests that the reduced S-cone system sensitivity for rapid flicker is due to postreceptoral limitations.