Is the increased spatial uncertainty in the normal periphery due to spatial undersampling or uncalibrated disarray?

Identifying the Retinal Layers Linked to Human Contrast Sensitivity Via Deep Learning

Purpose

Luminance contrast is the fundamental building block of human spatial vision. Therefore contrast sensitivity, the reciprocal of contrast threshold required for target detection, has been a barometer of human visual function. Although retinal ganglion cells (RGCs) are known to be involved in contrast coding, it still remains unknown whether the retinal layers containing RGCs are linked to a person's contrast sensitivity (e.g., Pelli-Robson contrast sensitivity) and, if so, to what extent the retinal layers are related to behavioral contrast sensitivity. Thus the current study aims to identify the retinal layers and features critical for predicting a person's contrast sensitivity via deep learning.

Methods

Data were collected from 225 subjects including individuals with either glaucoma, age-related macular degeneration, or normal vision. A deep convolutional neural network trained to predict a person's Pelli-Robson contrast sensitivity from structural retinal images measured with optical coherence tomography was used. Then, activation maps that represent the critical features learned by the network for the output prediction were computed.

Results

The thickness of both ganglion cell and inner plexiform layers, reflecting RGC counts, were found to be significantly correlated with contrast sensitivity (r = 0.26 ∼ 0.58, Ps < 0.001 for different eccentricities). Importantly, the results showed that retinal layers containing RGCs were the critical features the network uses to predict a person's contrast sensitivity (an average R2 = 0.36 ± 0.10).

Conclusions

The findings confirmed the structure and function relationship for contrast sensitivity while highlighting the role of RGC density for human contrast sensitivity.

Global processing in amblyopia: a review

Amblyopia is a neurodevelopmental disorder of the visual system that is associated with disrupted binocular vision during early childhood. There is evidence that the effects of amblyopia extend beyond the primary visual cortex to regions of the dorsal and ventral extra-striate visual cortex involved in visual integration. Here, we review the current literature on global processing deficits in observers with either strabismic, anisometropic, or deprivation amblyopia. A range of global processing tasks have been used to investigate the extent of the cortical deficit in amblyopia including: global motion perception, global form perception, face perception, and biological motion. These tasks appear to be differentially affected by amblyopia. In general, observers with unilateral amblyopia appear to show deficits for local spatial processing and global tasks that require the segregation of signal from noise. In bilateral cases, the global processing deficits are exaggerated, and appear to extend to specialized perceptual systems such as those involved in face processing.

Distinct Contributions to Facial Emotion Perception of Foveated versus Nonfoveated Facial Features

Foveated stimuli receive visual processing that is quantitatively and qualitatively different from nonfoveated stimuli. At normal interpersonal distances, people move their eyes around another’s face so that certain features receive foveal processing; on any given fixation, other features therefore project extrafoveally. Yet little is known about the processing of extrafoveally presented facial features, how informative those extrafoveally presented features are for face perception (e.g., for assessing another’s emotion), or what processes extract task-relevant (e.g., emotion-related) cues from facial features that first appear outside the fovea, and how these processes are implemented in the brain.

Intrinsic position uncertainty explains detection and localization performance in peripheral vision

Efficient performance in visual detection tasks requires excluding signals from irrelevant spatial locations. Indeed, researchers have found that detection performance in many tasks involving multiple potential target locations can be explained by the uncertainty the added locations contribute to the task. A similar type of Location Uncertainty may arise within the visual system itself. Converging evidence from hyperacuity and crowding studies suggests that feature localization declines rapidly in peripheral vision. This decline should add inherent position uncertainty to detection tasks. The current study used a modified detection task to measure how intrinsic position uncertainty changes with eccentricity. Subjects judged whether a Gabor target appeared within a cued region of a noisy display. The eccentricity and size of the region varied across blocks. When subjects detected the target, they used a mouse to indicate its location. This allowed measurement of localization as well as detection errors. An ideal observer degraded with internal response noise and position noise (uncertainty) accounted for both the detection and localization performance of the subjects. The results suggest that position uncertainty grows linearly with visual eccentricity and is independent of target contrast. Intrinsic position uncertainty appears to be a critical factor limiting search and detection performance.

[Eccentricity-dependent influence of amodal completion on visual search]

Does amodal completion occur homogeneously across the visual field? Rensink and Enns (1998) found that visual search for efficiently-detected fragments became inefficient when observers perceived the fragments as a partially-occluded version of a distractor due to a rapid completion process. We examined the effect of target eccentricity in Rensink and Enns's tasks and a few additional tasks by magnifying the stimuli in the peripheral visual field to compensate for the loss of spatial resolution (M-scaling; Rovamo & Virsu, 1979). We found that amodal completion disrupted the efficient search for the salient fragments (i.e., target) even when the target was presented at high eccentricity (within 17 deg). In addition, the configuration effect of the fragments, which produced amodal completion, increased with eccentricity while the same target was detected efficiently at the lowest eccentricity. This eccentricity effect is different from a previously-reported eccentricity effect where M-scaling was effective (Carrasco & Frieder, 1997). These findings indicate that the visual system has a basis for rapid completion across the visual field, but the stimulus representations constructed through amodal completion have eccentricity-dependent properties.

Efficient integration across spatial frequencies for letter identification in foveal and peripheral vision

Objects in natural scenes are spatially broadband; in contrast, feature detectors in the early stages of visual processing are narrowly tuned in spatial frequency. Earlier studies of feature integration using gratings suggested that integration across spatial frequencies is suboptimal. Here we re-examined this conclusion using a letter identification task at the fovea and at 10 deg in the lower visual field. We found that integration across narrow-band (1-octave) spatial frequency components of letter stimuli is optimal in the fovea. Surprisingly, this optimality is preserved in the periphery, even though feature integration is known to be deficient in the periphery from studies of other form-vision tasks such as crowding. A model that is otherwise a white-noise ideal observer except for a limited spatial resolution defined by the human contrast sensitivity function and using internal templates slightly wider in bandwidth than the stimuli is able to account for the human data. Our findings suggest that deficiency in feature integration found in peripheral vision is not across spatial frequencies.

The nature of letter crowding as revealed by first- and second-order classification images

Visual crowding refers to the marked inability to identify an otherwise perfectly identifiable object when it is flanked by other objects. Crowding places a significant limit on form vision in the visual periphery; its mechanism is, however, unknown. Building on the method of signal-clamped classification images (Tjan & Nandy, 2006), we developed a series of first- and second-order classification-image techniques to investigate the nature of crowding without presupposing any model of crowding. Using an "o" versus "x" letter-identification task, we found that (1) crowding significantly reduced the contrast of first-order classification images, although it did not alter the shape of the classification images; (2) response errors during crowding were strongly correlated with the spatial structures of the flankers that resembled those of the erroneously perceived targets; (3) crowding had no systematic effect on intrinsic spatial uncertainty of an observer nor did it suppress feature detection; and (4) analysis of the second-order classification images revealed that crowding reduced the amount of valid features used by the visual system and, at the same time, increased the amount of invalid features used. Our findings strongly support the feature-mislocalization or source-confusion hypothesis as one of the proximal contributors of crowding. Our data also agree with the inappropriate feature-integration account with the requirement that feature integration be a competitive process. However, the feature-masking account and a front-end version of the spatial attention account of crowding are not supported by our data.

Classification images with uncertainty

Classification image and other similar noise-driven linear methods have found increasingly wider applications in revealing psychophysical receptive field structures or perceptual templates. These techniques are relatively easy to deploy, and the results are simple to interpret. However, being a linear technique, the utility of the classification-image method is believed to be limited. Uncertainty about the target stimuli on the part of an observer will result in a classification image that is the superposition of all possible templates for all the possible signals. In the context of a well-established uncertainty model, which pools the outputs of a large set of linear frontends with a max operator, we show analytically, in simulations, and with human experiments that the effect of intrinsic uncertainty can be limited or even eliminated by presenting a signal at a relatively high contrast in a classification-image experiment. We further argue that the subimages from different stimulus-response categories should not be combined, as is conventionally done. We show that when the signal contrast is high, the subimages from the error trials contain a clear high-contrast image that is negatively correlated with the perceptual template associated with the presented signal, relatively unaffected by uncertainty. The subimages also contain a "haze" that is of a much lower contrast and is positively correlated with the superposition of all the templates associated with the erroneous response. In the case of spatial uncertainty, we show that the spatial extent of the uncertainty can be estimated from the classification subimages. We link intrinsic uncertainty to invariance and suggest that this signal-clamped classification-image method will find general applications in uncovering the underlying representations of high-level neural and psychophysical mechanisms.

Spatial resolution for feature binding is impaired in peripheral and amblyopic vision

We measured spatial resolution for discriminating targets that differed from nearby distractors in either color or orientation or their conjunction. In the fovea of normal human observers, whenever both attributes are big enough to be individually visible, their conjunction is also visible. In the periphery, the two attributes may be visible, but their conjunction may be invisible. We found a similar impairment in resolving conjunctions for the fovea of deprived eyes of humans with abnormal visual development (amblyopia). These results are quantitatively explained by a model of primary visual cortex (V1) in which orientation and color maps are imperfectly co-registered topographically. Our results in persons with amblyopia indicate that the ability of the fovea to compensate for this poor co-registration is consolidated by visual experience during postnatal development.

Haphazard neural connections underlie the visual deficits of cats with strabismic or deprivation amblyopia

Identification of the neural basis of the visual deficits experienced by humans with amblyopia, particularly when associated with strabismus (strabismic amblyopia), has proved to be difficult in part because of the inability to observe directly the neural changes at various levels of the human visual pathway. Much of our knowledge has necessarily been obtained on the basis of sophisticated psychophysical studies as well as from electrophysiological explorations on the visual pathways in animal models of amblyopia. This study combines these two approaches to the problem by employing similar psychophysical probes of performance on animal models of two forms of amblyopia (deprivation and strabismic) to those employed earlier on human amblyopes (Hess & Field, 1994, Vis. Res., 34, 13397-13406). The tests explore two competing explanations for the visual deficits, namely an evenly distributed loss of neural connections (undersampling) with the amblyopic eye as opposed to disordered connections with this eye (neural disarray). Unexpectedly, the results in animal models of deprivation amblyopia were not in accord with expectations based upon an even distribution of lost connections with the amblyopic eye. However, the results were similar to those observed in a strabismic amblyopic animal and to strabismic amblyopic humans. We suggest that deprivation amblyopia may be accompanied by an uneven loss of connections that results in effective neural disarray. By contrast, amblyopia associated with strabismus might arise from neural disarray of a different origin such as an alteration of intrinsic cortical connections.

Identification of facial images in peripheral vision

Contrast sensitivity for face identification was measured as a function of image size to find out whether foveal and peripheral performance would become equivalent by magnification. Size scaling was not sufficient for this task, but when the data was scaled both in size and contrast dimensions, there was no significant eccentricity-dependent variation in the data, i.e. for equivalent performance both the size and contrast needed to increase in the periphery. By utilising spatial noise added to the images we found that in periphery information was utilised less efficiently and peripheral inferiority arose completely from lower efficiency, not from increased internal noise.

Detecting disorder in spatial vision

In normal foveal vision, visual space is accurately mapped from retina to cortex. However, the normal periphery, and the central field of strabismic amblyopes have elevated position discrimination thresholds, which have often been ascribed to increased 'intrinsic' spatial disorder. In the present study we evaluated the sensitivity of the human visual system (both normal and amblyopic) to spatial disorder, and asked whether there is increased 'intrinsic' topographical disorder in the amblyopic visual system. Specifically, we measured thresholds for detecting disorder (two-dimensional Gaussian position perturbations) either in a horizontal string of N equally spaced samples (Gabor patches), or in a ring of equally spaced samples over a wide range of feature separations. We also estimated both the 'equivalent intrinsic spatial disorder' and sampling efficiency using an equivalent noise approach. Our results suggest that both thresholds for detecting disorder, and equivalent intrinsic disorder depend strongly on separation, and are modestly increased in strabismic amblyopes. Strabismic amblyopes also show markedly reduced sampling efficiency. However, neither amblyopic nor peripheral vision performs like ideal or human observers with added separation-independent positional noise. Rather, the strong separation dependence suggests that the 'equivalent intrinsic disorder' may not reflect topographic disorder at all, but rather may reflect an abnormality in the amblyopes' Weber relationship.

Vernier and contrast discrimination in central and peripheral vision

The present paper asks whether Vernier offset discrimination is limited by the observer's sensitivity to local contrast change in both central and peripheral vision. To answer this question we compared Vernier discrimination and contrast discrimination thresholds (specified in the same units) for a pair of narrow ribbons of cosine gratings. Because the ribbons are narrow, both the offset information (for Vernier discrimination) and the contrast information (for contrast discrimination) are highly localized. We found that when the stimuli are narrow ribbons, the local contrast cue is the limiting factor in Vernier discrimination. However, our results also show that integration of information along the length of the gratings (the ribbon width) is: (i) different for Vernier and contrast discrimination, and (ii) for Vernier discrimination the integration of information along the length of the gratings differs qualitatively in central and peripheral vision. For narrow ribbons, the peripheral 'template' for ribbon Vernier acuity is not as well matched to the stimulus (in two-dimensional spatial frequency space) as the foveal 'template'.

Strabismic amblyopia. Part 2. Neural processing

This is the second of a two-part survey of current literature concerning strabismic amblyopia. The aim of this review is to bring the optometric community up to date on the status of scientific research into strabismic amblyopia. Part 1 in this series discussed research into strabismic amblyopia from the viewpoint of psychophysical experiments, which investigate both spatial and temporal behavioural deficits accompanying strabismic amblyopia. These include deficits in contrast sensitivity, spatial localisation, fixation, ocular motility, accommodation, crowding, attention, motion perception and temporal processing. Part 2 concerns neural processing in regards to strabismic amblyopia. It discusses current understanding of more fundamental aspects of central processing of visual information and in particular current theories regarding neural sites and mechanisms involved in amblyopia.

Relationship between acuity for gratings and for tumbling-E letters in peripheral vision

Earlier studies have reported that grating resolution is sampling-limited in peripheral vision but that letter acuity is generally poorer than grating acuity. These results suggest that peripheral resolution of objects with rich Fourier spectra may be limited by some factor other than neural sampling. To examine this suggestion we formulated and tested the hypothesis that letter acuity in the periphery is sampling-limited, just as it is for extended and truncated gratings. We tested this hypothesis with improved methodology to avoid the confounding factors of target similarity, alphabet size, individual variation, peripheral refractive error, and stimulus size. Acuity was measured for an orientation-discrimination task (horizontal versus vertical) for a three-bar resolution target and for a block-E letter in which all strokes have the same length. We confirmed previous reports in the literature that acuity for these targets is worse than for extended sinusoidal gratings. To account for these results quantitatively, we used difference-spectrum analysis to identify those frequency components of the targets that might form a basis for performing the visual discrimination task. We find that discrimination performance for the three-bar targets and the block-E letters can be accounted for by a sampling-limited model, provided that the limited number of cycles that are present in the characteristic frequency of the stimulus is taken into account. Quantitative differences in acuity for discriminating other letter pairs (e.g., right versus left letters E or characters with short central strokes) could not be attributed to undersampling of either the characteristic frequency or the frequency of maximum energy in the difference spectrum. These results suggest additional tests of the sampling theory of visual resolution, which are the subject of a companion paper.

Sampling limits and critical bandwidth for letter discrimination in peripheral vision

We develop and test two functional hypotheses based on the sampling theory of visual resolution that might account for letter acuity in peripheral vision. First, a letter smaller than the acuity limit provides insufficient veridical energy for performing the task, and, second, the available veridical energy is masked by increased amounts of visible but aliased energy. These two hypotheses make opposite predictions about the effect of low-pass filtering on letter acuity, which we tested experimentally by using filtered letters from the tumbling-E alphabet. Our results reject the masking hypothesis in favor of the energy insufficiency hypothesis. Additional experiments in which high-pass-filtered letters were used permitted the isolation of a critical band of spatial frequencies, which is necessary and sufficient for achieving maximum visual acuity. This critical band varied with the particular pair of letters to be discriminated but was in the range 0.9-2.2 cycles per letter.

Position jitter and undersampling in pattern perception

The present paper addresses whether topographical jitter or undersampling might limit pattern perception in foveal, peripheral and strabismic amblyopic vision. In the first experiment, we measured contrast thresholds for detecting and identifying the orientation (up, down, left, right) of E-like patterns comprised of Gabor samples. We found that detection and identification thresholds were both degraded in peripheral and amblyopic vision; however, the orientation identification/detection threshold ratio was approximately the same in foveal, peripheral and amblyopic vision. This result is somewhat surprising, because we anticipated that a high degree of uncalibrated topographical jitter in peripheral and amblyopic vision would have affected orientation identification to a greater extent than detection. In the second experiment, we investigated the tolerance of human and model observers to perturbation of the positions of the samples defining the pattern when its contrast was suprathreshold, by measuring a 'jitter threshold' (the amount of jitter required to reduce performance from near perfect to 62.5% correct). The results and modeling of our jitter experiments suggest that pattern identification is highly robust to positional jitter. The positional tolerance of foveal, peripheral and amblyopic vision is equal to about half the separation of the features and the close similarity between the three visual systems argues against extreme topographical jitter. The effects of jitter on human performance are consistent with the predictions of a 'template' model. In the third experiment we determined what fraction of the 17 Gabor samples are needed to reliably identify the orientation of the E-patterns by measuring a 'sample threshold' (the proportion of samples required for 62.5% correct performance). In foveal vision, human observers are highly efficient requiring only about half the samples for reliable pattern identification. Relative to an ideal observer model, humans perform this task with 85% efficiency. In contrast, in both peripheral vision and strabismic amblyopia more samples are required. The increased number of features required in peripheral vision and strabismic amblyopia suggests that in these visual systems, the stimulus is underrepresented at the stage of feature integration.

Recognition of band-pass filtered hand-written numerals in foveal and peripheral vision

The purpose of the present study was to find out what differences between foveal and peripheral pattern recognition remain unexplained by the inhomogeneities of retinal sampling and the optics of the eye. We measured contrast thresholds for pattern recognition at different eccentricities. The effects of retinal sampling were homogenised by using M-scaling of the stimuli, and the effects of the optics of the eye were by-passed either by using strong external noise (signal-to-noise ratio is not affected by optical attenuation) or by computing retinal image contrast by means of the optical modulation transfer function. The stimuli were hand-written numerals filtered to two-octave bands of various centre object spatial frequencies (c/object). The results were described as contrast thresholds and recognition efficiency. At all eccentricities, lowest contrast thresholds and highest recognition efficiencies were found at medium object spatial frequencies. At high object spatial frequencies the peripheral retinal contrast thresholds and recognition efficiencies were nearly as good as at the fovea, but at low object spatial frequencies most of the data showed superiority of the fovea to the periphery. Therefore, at high object spatial frequencies peripheral recognition performance could be explained relatively well by the retinal sampling gradient, or equivalently by the cortical magnification factor, together with the effects of the optics of the eye. Some eccentricity dependent deterioration of recognition at low object spatial frequencies remained unexplained.

Feature integration in pattern perception

The human visual system is able to effortlessly integrate local features to form our rich perception of patterns, despite the fact that visual information is discretely sampled by the retina and cortex. By using a novel perturbation technique, we show that the mechanisms by which features are integrated into coherent percepts are scale-invariant and nonlinear (phase and contrast polarity independent). They appear to operate by assigning position labels or "place tags" to each feature. Specifically, in the first series of experiments, we show that the positional tolerance of these place tags in foveal, and peripheral vision is about half the separation of the features, suggesting that the neural mechanisms that bind features into forms are quite robust to topographical jitter. In the second series of experiment, we asked how many stimulus samples are required for pattern identification by human and ideal observers. In human foveal vision, only about half the features are needed for reliable pattern interpolation. In this regard, human vision is quite efficient (ratio of ideal to real approximately 0.75). Peripheral vision, on the other hand is rather inefficient, requiring more features, suggesting that the stimulus may be relatively underrepresented at the stage of feature integration.

Vernier acuity with non-simultaneous targets: the cortical magnification factor estimated by psychophysics

The eccentricity at which peripheral thresholds double their foveal value (E2) may relate to the visual system's anatomical organization. Using a variety of experimental approaches, previous estimates of E2 for vernier acuity have ranged from less than 0.1 deg to greater than 15.0 deg. This broad range of values seems to challenge the usefulness of E2 for determining visual topography. We explain that the varying contributions from at least two different regimes, spatial filter and local sign, may explain the broad range of E2 values found previously. We attempt to limit responses to the local sign regime, where it may be possible to determine the psychophysical analog to the gradient of the cortical spatial grain. In our experiments we measure how vernier task performance falls off with eccentricity. We hypothesize that if the vernier features are adequately separated in time, they will fall outside of the spatial filter's temporal integration span and the local sign regime would then predominate for precise positional processing. Using an interstimulus interval ranging from 20 to 200 msec between the two vernier features, we estimate that vernier thresholds in the local sign regime double at about 0.8 +/- 0.2 deg eccentricity, which is similar to anatomical estimates of the eccentricity at which the linear spacing of human cortical units doubles.

Localization of a peripheral patch: the role of blur and spatial frequency

Peripheral vision serves to direct our attention and fixation to objects of interest. This requires that the visual system be capable of accurately localizing peripherally presented targets having different spatial structures. The question we address is "to what extent does stimulus spatial structure influence the precision of peripheral localization?" To address this issue, we measured the precision of spatial localization (with reference to a foveal target) for a single Gaussian or Gabor patch briefly presented in the periphery. For both stimuli, we find that when the standard deviation of the stimulus envelope (SD) is less than 1/5 the stimulus eccentricity, localization thresholds are independent of SD and are approximately 1/50 of eccentricity. For larger values of SD, localization thresholds increase linearly with increasing SD, and are approximately 1/5 of SD. The results hold over a range of eccentricities (from 2.5 to 10 deg) and stimulus contrasts (from near detection threshold to 80%). In addition, for Gabor patches, the results are independent of frequency, phase and orientation of the carrier.

Limitations on position coding imposed by undersampling and univariance

Position judgements, which are exquisitely precise in the fovea, are markedly degraded in the periphery. In a recent article [Hess & Field (1993) Vision Research, 33, 2663-2670] argue that the poor representation of positional information in peripheral vision is a consequence of uncalibrated spatial disorder of cortical connections rather than due to undersampling of the retinal image. Specifically, Hess and Field argued that if positional uncertainty is due to undersampling, then because of univariance, there should be an associated contrast uncertainty. In this report we show that the univariance model is limited in its generality since: (1) the Hess and Field data in which contrast and position discrimination are decoupled do not preclude undersampling with large univariant filters: (2) aliasing can decouple position from contrast; (3) undersampling or noise at a second stage of processing can lead to selective losses of position information without any degradation of contrast information.

Uncalibrated distortions vs undersampling

In a recent paper of ours [Hess & Field (1993). Vision Research, 33, 2663-2670], we claim that there was a predictable relationship between position errors and contrast errors for an undersampled system. In this paper we re-state our main points. We feel that the response to that paper by Levi and Klein in the accompanying article does not require us to produce changes in our original position. We believe that the data support the notion that the principal causes of the positional errors in the normal periphery and the in the amblyopic visual system are due to uncalibrated distortions in the local signs of visual neurons. We believe that undersampling plays a major role in producing positional errors only in the far periphery at, or very near, the acuity limit. We maintain that our initial studies provide strong evidence that undersampling is insufficient as an explanation for the positional errors in the periphery of normals (Hess & Field, 1993) or the central field of amblyopes [Hess & Field (1994). Vision Research, 34, 3397-3406.

Amblyopic quasi-blindness for image structure

Human amblyopes display reduced contrast sensitivities, suffer from perceptual distortion, and their letter acuities are worse than is predicted from grating visibility. We sought the origin of these dysfunctions by measuring normal and amblyopic sensitivities to various forms of well-defined image distortion, namely band-limited phase quantization, phase quantization with additional amplitude modulation, and grey-scale modification. Our results prove the existence of an amblyopic quasi-blindness to image structure, that cannot be explained in terms of contrast detection. We discuss these findings within the computational scheme of image decomposition into local amplitude and local phase values. they are consistent with the assumption of amblyopic eyes beings impaired in processing local phase but having the local amplitude (or "energy", possibly at reduced gain) at their disposal. Phrased in physiological terms, we propose a scheme of complex-cells-only vision in amblyopia. We also provide a demonstration of how amblyopic eyes may see the test stimuli and natural images by generating local amplitude and phase representations at limited phase resolution.

Angle judgement: is the whole the sum of its parts?

This study concerns whether the discrimination of a geometric angle depends on the orientations of its bounding lines or on angle size. In Experiment 1, thresholds for angle discrimination were measured in three observers for angles ranging from 15 to 180 deg, oriented either vertically or obliquely. Angle discrimination thresholds were found to depend primarily on angle size for most of the range of angles (angle-dependent, or Weber's law regime). However, in a small region near 90 deg (orientation-dependent regime) angle discrimination depends on the orientations of the bounding lines. When our data in the angle-dependent regime were fitted with a power function, the exponents were close to or < 0.5, suggesting that a step-increment approach was used to calculate angle. In Experiment 2, orientation discrimination thresholds for lines corresponding to the bounding lines of the vertically and obliquely oriented 15, 90 and 165 deg angles were measured. Confirming previous studies, a strong meridional anisotropy in line orientation discrimination was found for all three observers. The orientation discrimination thresholds were then used to predict the discrimination thresholds for the corresponding angles based on a simple statistical model. The predicted angle discrimination thresholds were worse than those measured empirically except for the titled 90 deg angles. This result indicates that angle discrimination thresholds are not limited by the same noise as orientation discrimination for most angles except for the tilted 90 deg angle, where the limiting factor may be the precision in determining the orientations of the bounding lines. In Experiment 3, we show that angle discrimination is quite robust to small amounts of orientation jitter, suggesting that angle judgments are made at a level beyond the early filter representation.

Spatial alignment across gaps: contributions of orientation and spatial scale

To assess the contributions of orientation and spatial scale to the processing of relative-position information for broadband spatial targets, we measure misalignment thresholds for dots separated by as much as 6 deg, in the presence of one-dimensional spatial noise. For all the dot separations, thresholds for misalignment are raised most when the mask is oriented at approximately 20 deg to either side of true alignment. This bimodal orientation tuning function appears to be fundamental to the alignment judgment, including abutting vernier acuity for equally visible lines [Vision Res. 33, 1619 (1993)]. With increasing dot separation the spatial frequency at which peak masking occurs becomes progressively lower, a finding that suggests that the spatial mechanisms important for processing this information become larger. However, the rate of increase in size of these putative mechanisms is insufficient to account for the increase in relative-position thresholds for increasingly separated stimuli (i.e., Weber's law for alignment). In addition, oriented masks placed between two target lines lead to threshold elevation, revealing that the collection of positional information between target features may be important for optimal processing of misalignment thresholds. The findings of this study suggest that, although shifts in spatial scale of the underlying low-level oriented mechanisms may contribute to increased misalignment thresholds with increasing separation, additional factors, such as positional uncertainty associated with eccentricity per se, are limiting.

Assessment of vernier acuity development using the "equivalent intrinsic blur" paradigm

Vernier acuity in human infants is more than two orders of magnitude poorer than in adults and does not appear to reach adult levels until well beyond the first postnatal year. One source of these developmental differences in vernier acuity may be the presence of levels of intrinsic blur that are higher in infants than in adults. We investigated this hypothesis by measuring vernier acuity in 3-month-olds, 5-month-olds, and adults using stimuli blurred by two-dimensional Gaussian filters. Experiment 1 showed that more stimulus blur is required to degrade vernier acuity in infants than in adults. From these data we estimated that the level of equivalent intrinsic blur for this vernier acuity task decreased by approx. 1.5 log units between 3 months of age and adulthood. These results also suggested that this reduction of equivalent intrinsic blur can account entirely for the improvement in vernier acuity between 3 and 5 months postnatal. However, the large further improvement which occurs between 5 months of age and adulthood cannot be explained solely by equivalent intrinsic blur. In Expt 2, we measured vernier acuity in 3-month-olds and adults using a non-blurred stimulus with the same luminance contrast as the most-blurred stimulus used in Expt 1. Infants' and adults' thresholds were degraded slightly, relative to the non-blurred stimulus from Expt 1, but still were significantly better than the most blurred condition of Expt 1. This suggests that the results from the first experiment were not due simply to the reduction in overall luminance contrast which occurs when stimuli are blurred.

Metric for separation discrimination by the human visual system

It is now clear that models of positional coding for elements sufficiently separated to permit individual identification require not only a first stage of linear filtering but also a second stage of representation that is preceded by a rectifying type of nonlinearity. To address the issue of the metric of this second stage we measure separation discrimination for Gabor stimuli of different sizes and of different peak spatial frequencies and separation, with and without different types of lateral distractors. Our results show that there is only a weak dependence of separation discrimination on the spatial frequency of equidetectable, spatially narrow-band stimuli; however, carrier spatial frequency can affect the influence that lateral distractors have on separation judgments. We conclude that (1) the second-stage representation is a space-size one consistent with the fact that there are scaled distributions of energy detectors of different sizes and (2) the influence of distractor elements suggests a spatial-frequency influence either at the second-stage representation or at a site beyond this second stage.

Is the spatial deficit in strabismic amblyopia due to loss of cells or an uncalibrated disarray of cells?

We examine two competing explanations for the spatial localization deficit in human strabismic amblyopia, namely neural undersampling and uncalibrated neural disarray. An undersampling hypothesis would predict an associated deficit for contrast discrimination for which we find no evidence in strabismic amblyopia. A neural disarray hypothesis would predict an associated deficit in the degree to which stimuli appear spatially distorted. We find evidence for such a deficit in strabismic amblyopia. We propose that the spatial deficit in strabismic amblyopia is due to a filter-based distortion which is unable to be re-calibrated by higher visual centres.

Discrimination of position and contrast in amblyopic and peripheral vision

Many computational models of normal vernier acuity make predictions based on the just-noticeable contrast difference. Recently, Hu, Klein and Carney [(1993) Vision Research, 33, 1241-1258] compared vernier acuity and contrast discrimination (jnd) in normal foveal viewing using cosine gratings. In the jnd stimulus the test grating was added in-phase to the (sinusoidal) pedestal, whereas in the vernier stimulus the same test grating was added with an approx. 90 deg phase shift to the pedestal. In the present experiments, we measured thresholds for discriminating changes in relative position and changes in relative contrast for abutting, horizontal cosine gratings in a group of amblyopes using the Hu et al., test-pedestal approach. The approach here is to ask whether the reduced vernier acuity of amblyopes can be understood on the basis of reduced contrast sensitivity or contrast discrimination. Our results show that (i) abutting cosine vernier acuity is strongly dependent on stimulus contrast. (ii) In both anisometropic and strabismic amblyopes, abutting cosine vernier discrimination thresholds are elevated at all contrast levels, even after accounting for reduced target visibility, or contrast discrimination. (iii) For both strabismic and anisometropic amblyopes, the vernier Weber fraction is markedly degraded, while the contrast Weber fraction is normal or nearly so. (iv) In anisometropic amblyopes the elevated vernier thresholds are consistent with the observers' reduced cutoff spatial frequency, i.e. the loss can be accounted for on the basis of a shift in spatial scale. (v) In strabismic amblyopes and in the normal periphery, there appears to be an extra loss, which can not be accounted for by either reduced contrast sensitivity and contrast discrimination or by a shift in spatial scale. (vi) This extra loss cannot be quantitatively mimicked by "undersampling" the stimulus. (vii) Surprisingly, in some strabismics, and in the periphery, at relatively high spatial frequencies, vernier thresholds appear to lose their contrast dependence, suggesting the possibility that there may be qualitative differences between the normal fovea and these degraded visual systems. (viii) This contrast saturation can be mimicked by "undersampling" the target, or by introducing strips of mean luminance between the two vernier gratings, thus mimicking a "scotoma". Taken together with the preceding paper, our results suggest that the extra loss in position acuity of strabismic amblyopes and the normal periphery may be a consequence of noise at a second stage of processing, which selectively degrades position but not contrast discrimination.

Amblyopic and peripheral vernier acuity: a test-pedestal approach

This manuscript is concerned with three visual systems with degraded spatial vision: (i) anisometropic amblyopia; (ii) strabismic amblyopia; and (iii) the normal periphery. The question we ask here, is whether the poor positional acuity of each of these visual systems can be understood on the basis of reduced sensitivity to the local contrast information in the stimulus. To answer this question, we use a "test-pedestal" approach to position acuity. In the first experiment we measure our observers' thresholds for detecting both the pedestal stimuli (edges and lines) and the test or cue stimuli (lines and dipoles). This approach also provides an estimate of the size of the spatial pooling (integration) region for the local contrast cue. In experiments two and three, we measure line and edge vernier acuity as a function of contrast, and compare the losses to those found for the detection of the respective offset cues. The local contrast hypothesis predicts similar losses in vernier acuity and in "cue" detection in amblyopic or peripheral vision. Moreover, the precise form of the contrast response function can provide insights into the nature of the loss, and places constraints on the likely models for amblyopic or peripheral vision. Our results suggest that the loss in vernier acuity of our anisometropic amblyopes can be understood on the basis of the reduced local contrast sensitivity and by increased spatial pooling. In strabismic amblyopes and in the normal periphery, there appears to be an extra loss, which cannot be accounted for by either reduced local contrast sensitivity or by increased spatial pooling. Additional experiments and computational modeling suggest that the "extra" loss is not due to spatial undersampling or additive positional jitter, but rather results from positional noise at a "second" stage.

Topological disorder in peripheral vision

One of the most striking properties of the mammalian visual system is that it is only the central part of the visual field, the fovea, where vision is most acute. The superiority of the fovea is particularly evident in tasks requiring accurate spatial localization. It is currently thought that peripheral spatial uncertainty is a simple consequence of the decreased sampling grain of the peripheral field. We show that the topological fidelity of the afferent projection declines with eccentricity away from the fovea and that it is this rather than the sampling grain that underlies the poorer performance of the periphery in tasks involving spatial localization. The combination of normal sampling and a disordered topology results in the periphery having good sensitivity for detection but poor sensitivity for object recognition.

The coding of spatial position by the human visual system: effects of spatial scale and retinal eccentricity

In this study we investigate the nature of the computations that underlie the encoding of spatial position by the human visual system. Specifically, we explore the relationship between alignment accuracy and retinal eccentricity for stimuli where local luminance, local contrast, and orientation cues do not underlie performance. Spatial scale is especially important for such a comparison because of the well documented spatial inhomogeneity of the human visual field. The results suggest that the relationship between spatial localization and eccentricity is invariant with spatial scale if accuracy and eccentricity are expressed in terms of the stimulus envelope size. We show that the photoreceptor disarray does not determine the limit to performance for this task, the limit is post-receptoral and can be modelled in terms of a positional uncertainty within the early filters located before the response envelope has been extracted. This uncertainty varies with eccentricity in a similar way within each spatial array.