Vernier Target Research Articles

Spatial localization of motion-defined and luminance-defined contours.

Thresholds for the vernier alignment of contours defined by luminance and coherent random-dot motion were measured. The luminance-defined contours were localized with a precision better than the receptor grain, while the motion-defined contours were localized more poorly than this limit. When motion-defined and luminance-defined targets were matched for dot density, vernier thresholds were equivalent at low densities. When the targets were also equated for perceived contrast, the vernier thresholds became equivalent at higher densities as well. These results suggest that the precision with which motion-defined contours are localized is contrast and sample limited. Next, the localization mechanism for motion-defined targets was investigated. Length summation limits were similar for motion-defined and luminance-defined targets, suggesting that these targets could be localized by a common mechanism. Vernier targets were then flanked by two additional bars. Motion-defined flanks interfered with the localization of motion-defined targets and luminance-defined flanks interfered with the localization of luminance-defined targets. However, motion-defined and luminance-defined bars did not interact to produce spatial interference. This result indicates that the mechanisms for localizing luminance-defined and motion-defined targets are independent. We suggest that parallel mechanisms govern the vernier localization of motion-defined and luminance-defined targets.

Fusional suppression in normal and stereoanomalous observers

Observers with normal stereopsis suppress some of the monocular information contained in each stereo half-image, a phenomenon we call fusional suppression. We measured vernier acuity for an ordinary vertical vernier test target, presented to one eye, that was paired stereoscopically with a vernier target with a large fixed offset, presented to the other eye. The size of the fixed offset and hence, the disparity of the upper target line, was varied parametrically. Vernier thresholds for the test target rose as a function of disparity, reaching a maximum at 20 min of disparity and then decreasing gradually as the disparity exceeded the limits of foveal fusion (40–60 min arc). In the two normal observers, fusional suppression was symmetrical; neither eye had good access to monocular information. In the Stereoanomalous observers, fusional suppression was not symmetrical. When they viewed the vernier test target with the stronger of their two eyes, their vernier thresholds were barely affected by the stereo half-image in the other eye and so were better than those of the normal observers measured in the same condition. When the Stereoanomalous observers viewed the test target with their weaker eye, their fusional suppression was similar in range and magnitude to the suppression found in normal observers. Amblyopic suppression in mild amblyopes may be a residual effect of normal fusional suppression, operating to suppress monocular signals in the weaker eye, without conferring the benefits of normal stereopsis and fusion.

Orientation, masking, and vernier acuity for line targets

In an attempt to uncover the properties of the psychophysical spatial mechanisms which optimally respond to the vernier offset between two abutting lines, we investigated the effects of one-dimensional band-limited spatial noise masks superimposed with the target, on vernier thresholds. Unidirectional vernier thresholds were measured in the presence of masks varying in orientation, spatial frequency content and luminance modulation. Because of the dependence of vernier thresholds on target visibility, the effects of these masks on target detection thresholds were also measured. In accordance with the results of Findlay [(1973) Nature, 241, 135–137] but contrary to an hypothesis that the direction of the vernier offset is mediated by the differential output of spatial filters of a single orientation, our results reveal a bimodal orientation tuning function for vernier acuity. We propose that, for offset line targets, the differential responses of at least two filters with orientations which straddle the target lines are combined to extract relative position information. The spatial frequency tuning characteristics of the optimal mechanisms for mediating vernier information are similar to those optimal for detecting the target lines themselves, except that they are tuned to a slightly higher spatial frequency and have a slightly narrower bandwidth. The spatial mechanisms most sensitive to the vernier offset and to target detection exhibit similar responses to increases in mask modulation. This finding suggests that these tasks are limited by the same source of noise and explains why under a variety of experimental manipulations, equally visible vernier targets result in similar vernier thresholds.

The development of vernier acuity in human infants

Vernier acuity, i.e. the detection of a small misalignment between lines, is about one order of magnitude finer than the resolution of periodic gratings in adult humans. This hyperacuity is generally attributed to cortical mechanisms, and the time-course of its development seems to differ from the development of grating resolution that probably is limited by retinal factors. We investigated 271 human infants and children between 2 months and 8 yr of age with essentially identical stimuli and experimental procedures. Vernier thresholds for Vernier targets were compared to grating resolution. The preferential looking experiments led to the following results: (i) Vernier acuity starts below grating resolution. (ii) Like grating resolution, Vernier acuity develops gradually, but more rapidly and longer; at the age of 5 yr performance becomes comparable to that of adults. (iii) Flanking borders without offset, added to the Vernier targets at various distances, did not affect thresholds consistently across distances and age groups.

Visual memory for vernier offsets

Human ability to perceive and remember precise spatial relationships was investigated in a vernier acuity task. An initial (“standard”) vernier stimulus with a variable offset was presented for 100 msec. After a delay of 1, 4, or 8 sec, another vernier target (the “variable” stimulus) followed, also for 100 msec. Observers compared the offsets of the two stimuli with each other. For very small offsets, discrimination between smaller and larger offsets was very precise, in the hyperacuity range. Thresholds increased linearly with the spatial offset of the standard stimulus, suggesting that the precision of the mechanism solving this spatial task scales with offset size. Control experiments suggested that this effect was not due to variations in retinal eccentricity. Thresholds also increased with increasing delay between the presentations of the two stimuli. By varying the delay, we directly measured the fading of the spatial memory trace.

Visual assessment of infants: vernier targets for the Catford drum.

Targets comprising a horizontal black line 5' thick offset by 1' were printed on strips to stick to the drums of the Catford Visual Acuity Apparatus. The 'vernier' targets so produced corresponded to the different sizes of Snellen letters from 6/6 to 2/60 when presented at 50 cm. Twenty-five children between the ages of 3 and 12 years with known amblyopia (mostly strabismic) were tested in a double blind trial to compare the visibility of the vernier targets with subjective Snellen acuity. All vernier results, both for better and amblyopic eye, were within one line of Snellen acuity. One hundred and twenty normal preverbal infants with normal eyes under the age of 2 1/2 years were tested with the vernier strips. Normal infants under the age of 6 months recorded a vision of 6/60-2/60; normal infants aged 6 to 12 months recorded 6/24-6/36, and infants between the ages of 1 and 2 1/2 years recorded 6/12-6/18.

Psychophysical measurement of eye drifts and tremor by dichoptic or monocular vernier acuity

If the two segments of a vernier target are presented to different eyes, i.e. dichoptically, thresholds are three to four times higher than with presentation to the same eye. This increase in thresholds is mainly due to uncorrelated movements of both eyes, such as tremor and drifts, that occur even under steady fixation. The psychophysically measured thresholds allow one to calculate an upper estimate for the amplitudes of uncorrelated eye movements during fixation. This estimate matches the best results from direct eye position recording, with the calculated mean amplitude of eye tremor corresponding to roughly one photoreceptor diameter. The combined amplitude of both correlated and uncorrelated eye movements was also measured by delaying one segment of the vernier relative to its partner under monocular or dichoptic conditions. Fixation proved to be relatively stable, and trained observers could sustain eye position within a few min arc.

The imprecision of stereopsis

In comparison to lateral judgments of distance, stereoscopic judgments are not precise. Although stereoacuity thresholds for targets presented in the fixation plane can equal the best thresholds for the monocular hyperacuities i.e. a few sec arc, the increment thresholds for disparity are substantially larger than the increment thresholds for lateral separation (width). We measured the minimum detectable change in the three-dimensional distance separating two features, one presented in the fixation plane and the other some distance in front of it, i.e. with a significant standing disparity between the two features. For briefly-presented targets (150 msec), the Weber fraction for disparity was 10–20% over the range from 1 to 20 min arc, while the Weber fraction for width was only 2–3% under comparable conditions. The disparity thresholds were substantially improved for a longer duration target (1000 msec), but they were still a factor of two worse than the monocular width thresholds. In a related experiment, the vernier acuity for a standard vernier target was profoundly degraded by pairing the offset upper line presented to one eye with a disparate Une in the other eye; the vernier threshold was elevated for disparities ranging from 3 to 30 min arc. This finding shows that the more precise monocular signals are actively suppressed in fused or partially-fused stereoscopic images.

Relation of spatial and temporal frequencies to vernier acuity

Vernier thresholds were measured with a pair of vertical sinusoidal gratings of one and a half cycles as targets. The amplitude was weighted by a one-dimensional Gaussian and contrast was set one log unit above contrast threshold. The vernier thresholds were estimated with the method of constant stimuli. Temporal frequency effects were introduced by movement of the vernier targets. It was found that vernier thresholds expressed in phase angle were unchanged in the effective range of spatial frequencies provided that the temporal frequency and the visibility were unchanged, and that thresholds deteriorated by increasing the temporal frequency. It is suggested that the detection of relative phase may be involved in the discrimination of vernier offsets and that it may be mediated by a sustained unit. Three possible types of mechanisms, edge-localization processes, orientation-selective units and phase-sensitive units, were considered in relation to vernier acuity.

Dichoptic hyperacuity: the precision of nonius alignment.

The alignment of nonius targets can be judged with the same precision as the alignment of vernier targets for some target configurations. We measured dichoptic and monocular hyperacuity thresholds as a function of the separation between the target lines. At separations above a critical value (30-60 arcmin), monocular and dichoptic thresholds were identical and increased as a power function of line separation. At smaller separations, the dichoptic thresholds were 0.6-0.7 arcmin, independent of separation, and significantly higher than the comparable monocular thresholds. The dichoptic results can be modeled as the sum of two sources of noise: (1) intrinsic positional uncertainty, which depends on line separation and is common to both dichoptic and monocular judgments, and (2) disjunctive fluctuations in convergence. It seems likely that the mechanism that limits the precision of vernier acuity has its locus at a point in the visual pathways after the signals from the two eyes have been combined.

Positional acuity without monocular cues.

The accuracy with which human observers can determine the spatial location of a shape boundary was measured by vernier alignment. The vernier targets were presented as random-dot stereograms, with varying amounts of camouflage in the monocular image. Camouflage decreased vernier acuity, but when the camouflage was broken by stereoscopic disparity, acuity was improved. In the limiting case when the shape boundaries were defined by disparity information alone, vernier thresholds (75% correct, binary forced-choice) were in the region of 40 s visual angle. This is poor acuity in comparison to vernier thresholds with monocular contour, but if the limited resolution acuity for stereopsis is taken into account, cyclopean and monocular positional acuities can be considered quite similar in relation to their respective resolution limits.

Evoked potentials elicited by brief vernier offsets: Estimating vernier thresholds and properties of the neural substrate

The characteristics of the neural generator producing an evoked potential in response to the brief presentation of a vernier offset was investigated in three experiments. In the first study, averaged evoked potentials (EPs) recorded in response to a single vernier offset stimulus consisting of a horizontal line which changed from colinearity to noncolinearity for 100 msec every 1.5 sec were compared to responses elicited by other vernier configurations consisting of: (1) stimuli with multiple offsets; (2) stimuli presented in different orientations; (3) targets with different offset features; and (4) with the simple displacement of a colinear line. The results showed that a single vernier offset elicited a robust response if the offset was located in the central zone (1°) of the target. Other features of the target configuration were unimportant. Displacement of a colinear line over the same range without an offset evoked little, if any, response. In the second study, EPs were recorded in response to a single offset target which varied in magnitude from 21 to 82 sec of visual angle on different trials. The latency and amplitude of the EP response varied systematically with the amplitude of the vernier offset. Plots of EP amplitude against log of the offset magnitude were linear over the range of offsets employed. Straight lines fitted to the data and extrapolated to zero amplitude provided estimates of vernier threshold. These estimates agreed closely with psychophysical measures taken with the same targets and confirm the initial observations by Levi et al. (1983). In the third experiment, irrelevant contours were added to the vernier target in various spatial and temporal configurations. The addition of stationary, contiguous contours to the vernier target reduced the amplitude of the EP response when the contours were within 4–8 min of the offset, producing progressively less EP attenuation with increasing distance from the offset. However, brief presentation of the irrelevant contour (e.g. a single line passing through the offset) with an onset asynchrony relative to the vernier offset stimulus appropriate to assure simultaneity of the line-elicited EP and the offset-elicited EP yielded an enhanced response, i.e. to two responses added algebraically. The long latency of the offset evoked response and the summation results of the EPs generated by an offset and by a briefly presented linear contour suggests independence of the neural generators producing the response to these two targets.

Amblyopic processing of positional information. Part II: Sensitivity to phase distortion.

Amblyopic sensitivities to spatial distortions of compound gratings and checker-board textures were studied. Iso-energy target signals were used by employing phase modulations which leave the stimulus power spectra unaltered. The non-amblyopic eyes of the 6 amplyopes tested showed supranormal sensitivities at 1 s exposure duration for both types of patterns. At 125 ms the amblyopic eyes were found virtually blind to the texture distortions while performance improved with prolonging the presentation time to 1 s. Comparable results were obtained with compound gratings. However, the correlation between amblyopic acuities and texture discrimination was higher than that between acuities and grating performance. This is probably due to the fact that both (misaligned) vernier targets and the texture are more 'natural' stimuli in the sense that they contain a broad range of spatial frequency components at many different orientations. Differences in behaviour between strabismic and anisometropic amblyopes did not occur. This suggests that the results depend upon defects of foveal visual function.

Vernier acuity, crowding and amblyopia

When a vernier target is flanked by a pair of optimally positioned flanks, offset discrimination is strongly degraded. Spatial interference with vernier acuity was studied in each eye of observers with unilateral amblyopia associated with strabismus, anisometropia or both, and were compared to the functions obtained in the normal periphery (Levi et al., 1985). The results showed that: (1) For both strabismic and anisometropic amblyopes, as in normal central and peripheral vision, the extent of spatial interference was proportional to the unflanked vernier threshold. (2) For anisometropic amblyopes, grating and vernier acuity are affected similarly. (3) For strabismic amblyopes, like the normal periphery, vernier and grating acuity are decoupled, with vernier falling off faster than grating acuity. (4) The preferred eyes of strabismic but not anisometropic amblyopes have poorer vernier acuity than the normal controls. A conceptual framework for amblyopia based upon spatial filtering and spatial sampling is discussed.

Selectivity of the evoked potential for vernier offset

Hyperacuity thresholds of a few arc seconds can be achieved psychophysically for a variety of spatial localization tasks. The present experiments show that evoked potentials can be elicited in response to the introduction of vernier offsets, but not by the introduction of other cues to hyperacuity such as bisection or relative pattern motion, although each of these cues is equally salient psychophysically. Moreover, vernier acuity measurements and the evoked potentials elicited in response to vernier offsets are strongly degraded by the introduction of flanking stimuli 2–4 min from the vernier target. This suggests that the hyperacuity VEP is a cortical correlate of a very specific type of hyperacuity, that produced by vernier offsets (colinearity failure).

Vernier acuity, crowding and cortical magnification

When a vernier target is flanked by optimally positioned lines, foveal vernier discrimination is strongly degraded (Westheimer and Hauske, 1975). We confirmed this observation (Experiment I) and have mapped out a 2 dimensional “perceptive field” for crowding in the fovea using a 2 dot target (Experiment II). Crowding was also measured in peripheral vision, using either small flanking dots as masks (Experiment III), or using repetitive vernier gratings (Experiment IV). The results showed that when scaled in proportion to recent estimates of the cortical magnification factor, vernier acuity is as good in the periphery as it is centrally. Both centrally and peripherally, there appears to be a psychophysical processing module which we term a “perceptive hypercolumn”. At all eccentricities vernier thresholds were found to be approximately 1/40 of the size of a perceptive hypercolumn and were elevated if interfering contours are present in the same (or adjacent) hypercolumns.

The use of different cues in vernier acuity

The roles of the various cues in the traditional vernier target are examined. We conclude that there are at least two mechanisms by which vernier acuities of the order of 5 sec arc may be obtained. The two cues are the overall slope of the target, and the relative positional differences. By using vernier targets that are degraded in two different ways, we can demonstrate each mechanism.

On the failure of spatiotemporal interpolation: A filtering model

A vernier target moving discontinuously between discrete spatial stations is seen as having a spatial offset if its component bars are presented at spatially aligning stations with a temporal delay (the interpolation effect). In agreement with previous work, we find that the threshold for detecting this virtual spatial offset is the same as that for detecting an explicit spatial offset, provided that certain spatial and temporal constraints are met. Interpolation is a completely efficient process provided that the spatial interval between stations in the movement trajectory is less than 3–4 min arc, but thereafter it shows a gradual decline in efficiency. This paper presents a model of the decline in efficiency which arises, we suggest, not because of a failure of sampling to represent the original stimulus, but because of a progressive mismatch between the sampled signal and the bandwidth of the spatial filters involved in interpolation. Our model is compared with the constant velocity model of Fahle & Poggio [ Proc. R. Soc. Lond. B 213, 451–477 (1981)].

Exposure duration affects the sensitivity of vernier acuity to target motion

Threshold vernier acuity was measured under different conditions of target movement and exposure duration. In the case of a simple two-line vernier target, image motion up to about 3 deg/sec had little effect upon threshold for a briefly exposed (150 msec) target, which is relatively poor even for a stationary stimulus, but produced a decrement in acuity for a continuously exposed stimulus. This finding was repeated in a second experiment, which used a centroid cue to vernier offset, and which compared the effects of horizontal and vertical target orientation. It is suggested that image motion and reduced exposure duration restrict the proportion of the light spread function that can be usefully sampled by the neural networks responsible for hyperacuity.

Visual hyperacuity:spatiotemporal interpolation in human vision.

Stroboscopic presentation of a moving object can be interpolated by our visual system into the perception of continuous motion. The precision of this interpolation process has been explored by measuring the vernier discrimination threshold for targets displayed stroboscopically at a sequence of stations. The vernier targets, moving at constant velocity, were presented either with a spatial offset or with a temporal offset or with both. The main results are: (1) vernier acuity for spatial offset is rather invariant over a wide range of velocities and separations between the stations (see Westheimer & McKee 1975); (2) vernier acuity for temporal offset depends on spatial separation and velocity. At each separation there is an optimal velocity such that the strobe interval is roughly constant at about 30 ms; optimal acuity decreases with increasing separation; (3) blur of the vernier pattern decreases acuity for spatial offsets, but improves acuity for temporal offsets (at high velocities and large separations); (4) a temporal offset exactly compensates the equivalent (at the given velocity) spatial offset only for a small separation and optimal velocity; otherwise the spatial offset dominates. A theoretical analysis of the interpolation problem suggests a computational scheme based on the assumption of constant velocity motion. This assumption reflects a constraint satisfied in normal vision over the short times and small distances normally relevant for the interpolation process. A reasonable implementation of this scheme only requires a set of independent, direction selective spatiotemporal channels, that is receptive fields with the different sizes and temporal properties revealed by psychophysical experiments. It is concluded that sophisticated mechanisms are not required to account for the main properties of vernier acuity with moving targets. It is furthermore suggested that the spatiotemporal channels of human vision may be the interpolation filters themselves. Possible neurophysiological implications are briefly discussed.