A visual nonlinearity fed by single cones

An intensive nonlinearity in the visual system can produce distortion products, or difference frequency gratings, when observers view two high contrast, high spatial frequency interference fringes of slightly different frequency or orientation added together at the retina. These distortion products are visible even when the two fringes imaged on the retina are above the resolution limit. Our experiments take advantage of this nonlinearity to measure the spatial filtering in the visual system following the formation of the retinal image, but preceding the site of the nonlinearity. The point spread function corresponding to this spatial filter is so small that it can be entirely explained by light integration within the apertures of foveal and parafoveal cones. The small size of this point spread function implies that (1) laser interferometry avoids contrast losses inherent in the eye's optics at spatial frequencies as high as 130 c/deg, (2) retinal scatter causes negligible image degradation in the fovea and parafoveal retina, (3) eye movements have little or no effect on contrast sensitivity to the distortion product and (4) that there is no neural spatial summation in the visual system prior to the site of the nonlinearity. Distortion products could also be observed when a bright interference fringe was briefly flashed on the fovea and a test interference fringe was viewed through the resulting afterimage. Measurements of the point spread function at stages in the visual system that precede the generation of this distortion product were similar to those obtained with simultaneous presentation of the two fringes, implying that the aftereffect of light adaptation is extremely local, no larger than the dimensions of single cones.

A three channel model of temporal frequency perception

This paper derives the constraints on a set of channels that would be consistent with the results of several experiments on the temporal properties of the visual system, and it describes a specific set of channels that meet these constraints. Data on simultaneous detection and discrimination require a minimum of three channels. Temporal frequency discrimination at and above threshold constrain the bandwidths and locations of the channels. The shape of the temporal modulation sensitivity function constrains their sensitivities. The functions that meet these constraints are similar to those derived from masking data, and they can account for data on flicker matching, notch losses in modulation sensitivity, and changes of perceived temporal frequency with changes of modulation depth.

Visual mechanisms of spatial disorientation in Alzheimer's disease

Impaired optic flow perception may contribute to the visuospatial disorientation of Alzheimer's disease (AD). We find that 36% of AD patients have elevated perceptual thresholds for left/right outward radial optic flow discrimination. This impairment is related to independent visual motion processing deficits affecting the perception of left/right motion-defined boundaries and in/out radial motion. Elevated optic flow thresholds in AD are correlated with greater difficulty in the Road Map test of visuospatial function (r = -0.5) and in on-the-road driving tests (r = -0.83). When local motion cues are removed from optic flow, subjects must rely on the global pattern of motion. This reveals global pattern perceptual deficits that affect most AD patients (85%) and some normal elderly subjects (21%). This deficit might combine with impaired local motion processing to undermine the alternative perceptual strategies for visuospatial orientation. The greater prevalence of global pattern deficits suggests that it might precede local motion processing impairments, possibly relating to the sequence of early hippocampal and later posterior cortical damage that is typical of AD.

Enhanced motion aftereffect for complex motions

We measured the magnitude of the motion after effect (MAE) elicited by gratings viewed through four spatial apertures symmetrically positioned around fixation. The gratings were identical except for their orientations, which were varied to form patterns of global motion corresponding to radiation, rotation or translation. MAE magnitude was estimated by three methods: the duration of the MAE; the contrast required to null the MAE and the threshold elevation for detecting an abrupt jump. All three techniques showed that MAEs for radiation and rotation were greater than those for translation. The greater adaptability of radiation and rotation over translation also was observed in areas of the display where no adapting stimulus had been presented. We also found that adaptation to motion in one direction had equal effects on sensitivity to motion in the same and opposite directions.

Radial motion looks faster

Current models of motion perception depend on unidirectional motion-sensitive mechanisms that provide local inputs for complex pattern motion, such as optic flow. To test the generality of such models, we asked observers to compare the speed of radial gratings with the translational speed of vertical gratings. The speed of the radial gratings was consistently overestimated by 20-60% relative to that of translating gratings that were identical in all other respects. The speed bias was not associated with a general spatial or temporal processing bias, nor with the high relative speed of points about the center of expansion/contraction. The bias increased non-linearly with the size of sectors of the radiating pattern exposed. As the motion of the two patterns was locally identical but judged differently, the apparent speed of both kinds of motion cannot be served by any mechanism, nor described by any model, that is based entirely on local motion signals. We speculate that the greater apparent speed of the radial motion has to do with apparent motion in depth.

Serial spatial filters in vision

Observers viewing two superimposed laser interference fringes of nearly equal spatial frequency see an illusory grating of low spatial frequency, even when the spatial frequency of the fringes exceeds the resolution limit. This grating is a product of nonlinear distortion within the visual system [MacLeod, Williams and Makous (1992) Vision Research, 32, 347-363]. By separately manipulating the spatial frequencies of the interference fringes and the distortion gratings, we decomposed the contrast sensitivity function into two serial components separated by the nonlinear process. Losses in the optics of the eye were avoided by use of laser interferometry. Spatial summation preceding the nonlinear stage was restricted to the light-collecting area of individual cones and was directly proportional to the diameters of cone inner segments at three retinal eccentricities; this suggests that light is trapped within cones at the level of their inner segments. Even 30 degrees from the fovea, the nonlinear stage precedes the site where separate signals from individual cones are no longer maintained; this leads us to suggest that the nonlinear process lies within the retina. In addition, spatial antagonism precedes the nonlinear stage; this places the nonlinear process at a site following the outer segments of the cones. Dichoptic presentation of the interference fringes failed to produce illusory gratings; that is, the nonlinearities within the binocular pathway do not produce distortions like those produced by the monocular nonlinearity.

Light capture by human cones

1. The variation in visual efficiency of light with varying pupillary entry (the Stiles-Crawford effect) was measured to determine the proportion of light incident on the cones that escapes them without recovery by other cones. 2. The variation in detectability of interference fringes with varying pupillary entry of the interfering beams was measured to determine the proportion of incident light that was recaptured by cones in the dark stripes after escaping cones in the bright stripes of the fringes. 3. By exclusion, these observations determine the variation, with varying pupillary entry, in the proportion of incident light that was captured and absorbed by the first cones it entered. 4. Some 70-90% of the light absorbed by the cones when it passes through the centre of the pupil, is entirely lost to the visual system if it passes instead through the margin of the (dilated) pupil. 5. Over half the light that cones absorb when the light enters the margin of the pupil is light that has previously passed through other cones. 6. If the spread of recaptured light is assumed to be Gaussian, its standard deviation is at most one minute of visual angle. 7. Such recaptured light makes a previously unknown contribution to the various Stiles-Crawford effects.

Psychophysical evidence for a functional hierarchy of motion processing mechanisms

Current models of motion perception typically describe mechanisms that operate locally to extract direction and speed information. To deal with the movement of self or objects with respect to the environment, higher-level receptive fields are presumably assembled from the outputs of such local analyzers. We find that the apparent speed of gratings viewed through four spatial apertures depends on the interaction of motion directions among the apertures, even when the motion within each aperture is identical except for direction. Specifically, local motion consistent with a global pattern of radial motion appears 32% faster than that consistent with translational or rotational motion. The enhancement of speed is not reflected in detection thresholds and persists in spite of instructions to fixate a single local aperture and ignore the global configuration. We also find that a two-dimensional pattern of motion is necessary to elicit the effect and that motion contrast alone does not produce the enhancement. These results implicate at least two serial stages of motion-information processing: a mechanism to code the local direction and speed of motion, followed by a global mechanism that integrates such signals to represent meaningful patterns of movement, depending on the configuration of the local motions.

Modeling pedestal experiments with amplitude instead of contrast

To provide a comprehensive quantitative model of contrast discrimination, we measured contrast discrimination functions at four mean luminances, four spatial frequencies, three phase relations between test and pedestal gratings, and two temporal frequencies for the test grating. The results confirm previous findings that the shape of the contrast discrimination function varies with three of these variables but is independent of luminance when each discrimination threshold is divided by the detection threshold for the test grating presented alone. The data in this 5-dimensional space can be described quantitatively if expressed in amplitudes instead of contrasts. The resulting model of visual amplitude sensitivity has seven parameters that are specific to a particular observer and are tied to identifiable visual properties. The "pedestal effect" and tests with the pedestal and test gratings out-of-phase can be explained by subthreshold summation but not stimulus uncertainty.

Zero frequency masking and a model of contrast sensitivity

Stimulating the visual system tends to desensitize it to certain stimulus properties. Such desensitization is usually called adaptation or masking, but the distinction between the two is unclear. Nonspecific desensitization by light is usually regarded as adaptation, whereas pattern-specific desensitization is typically considered masking. Here we unify the treatment of such desensitizing phenomena by handling both in the spatial frequency domain. The amount of adapting light in a stimulus is represented in the spatial frequency domain by the component at zero frequency. To determine whether such adapting light acts like other components in the spatial frequency domain, we compared the effect of masking by the zero frequency component with the effects of masking by components at other frequencies. We show that the zero frequency component acts like other masking components, decreasing sensitivity to nearby test frequencies and thereby producing the insensitivity to low spatial frequencies that gives the contrast sensitivity curve its band-pass shape at high light levels. Treating light adaptation as masking by the zero frequency component leads to a general model that describes visual sensitivity to test gratings of varying spatial frequency at varying mean luminance, in the presence (or absence) of masking gratings of varying spatial frequency. Individual components of the model provide insight into visual processing at the system level.

Spatiotemporal separability in contrast sensitivity

Contrast sensitivity functions were measured in two ways: by counterphase modulation; and by in-phase modulation, in which the luminance of every point of a spatial grating was sinusoidally modulated in phase with one another. Contrast sensitivity functions measured by counterphase modulated gratings show spatiotemporal interactions that represent bandpass filtering. Contrast sensitivity functions measured by in-phase modulation are even more sharply bandpass in the spatial frequency domain, but they are spatiotemporally decoupled, i.e. the effects of spatial and temporal variables are separable. This difference can be explained by the composition of the frequency components of the counterphase and the in-phase modulated gratings and by masking between components. The results suggest that the intrinsic filters are low-pass exponentials, that they are spatiotemporally separable, and that the spatiotemporal interaction of counterphase gratings is best described as masking by the zero spatiotemporal frequency component of the test gratings.

Methylazoxymethanol acetate: effect of postnatal injection on brain amines and behavior

The antimitotic drug, methylazoxymethanol acetate (MAMA), was injected into newborn rats during the first four days of life. At 48 days of age, these rats weighed one-third less than controls, as did the cerebella of their brains, but the rest of their brains weighed only 7% less than those of controls. The cerebella structures of the drug-injected rats was highly disorganized. Purkinje cells were scattered haphazardly in the granular layer instead of forming a monolayer. More foldings and short folia were found in the cerebella of drugged animals. In spite of these large morphological differences, the total amounts of norepinephrine and serotonin in the cerebella of the drugged rats were not different from those of the control rats. Behavioral effects of postnatal injection of MAMA include retarded development of the righting reflex,i.e., the drugged pups took longer time to right themselves when placed on their backs during the first nine days after birth; and scondly, MAMA reduced locomotor activity measured 45 days after birth.

Implicit masking constrained by spatial inhomogeneities

Human contrast sensitivities to gratings were measured within windows of 3, 9.1 and 61.5 deg at spatial differences down to the nominal frequency of 0 c/deg (i.e., a uniform field), and the resulting curves were related to the Fourier spectra of the corresponding windows and of spatial inhomogeneities in the visual pathway. The data show that sensitivity approaches an asymptote about 1.5 log units below peak sensitivity as spatial frequency decreases, the so-called low frequency cut. Computations show that the fundamentals of the test files used here were detected and not their harmonics, and control experiments suggest that the edges of the gratings did not affect detection of the gratings. Most of the low frequency cut could be attributed to masking by the harmonics of the windows within which the gratings were introduced. The added contribution of the inhomogeneities in the retinal distribution of cones accounts for the remainder of the low frequency cut observed with the two smaller windows, and adding the effects of the inhomogeneities to the distribution of parvocellular ganglion cells accounts for the remainder of the low frequency attenuation with the largest field. Therefore, the attenuation of sensitivity to low frequencies that gives the contrast sensitivity curve its bandpass shape can be attributed entirely to implicit masking, i.e., to masking by the Fourier spectrum of the window within the test grating is presented, after further spreading by retinal inhomogeneities.

Undetected gray strips displace perceived edges nonlinearly

The luminance profile of a contour affects its perceived location. We measured the relationship between luminance profile and perceived location of an edge by interposing a thin uniform strip of variable luminance between the black and the white sides of a sharp edge and having observers make Vernier adjustments of an uncomplicated sharp edge so that the two edges appeared to be aligned. The perceived location of the contour depended on the luminance of the strip even when the strip itself was too thin to be seen. The largest visual angle at which a strip was still invisible was approximately 1.4'. Although the relation between perceived location and luminance was nonlinear, the relation approached linearity as the strip thickness decreased. A model with no free parameters, involving three stages of spatial filtering and an interposed nonlinearity, described the data from strips that could not be seen. With a strip thickness of 1.4', the model halved both errors of prediction and residual variance over those based on the assumption of linearity.

Changes of visual sensitivity caused by on- and off-transients

The effects of abrupt increases and decreases of light in one part of the retina on sensitivity in an adjacent part of the retina were studied under low scotopic conditions near absolute threshold. The basic finding is that a brief annular surround decreases sensitivity to test spots occurring near the time of its onset or its offset, but that the surround increases sensitivity to test spots occurring the first few hundred milliseconds following its offset. If the annulus is presented in one eye and the test flash to the other, annulus onset reduces sensitivity, but annulus offset has almost no effect on thresholds in the contralateral eye. In fully dark-adapted observers, absolute sensitivity is somewhat greater when the test flashes are preceded by a flashed surround than when they are presented alone. These results challenge the idea that sensitivity to these stimuli is limited by an irreducible level of noise in the dark and under dim illumination.