How many positions can we perceptually encode, one or many?

Here we show that our sensitivity for discriminating relative position across the visual field is limited. In experiment 1 we show that we are much worse at detecting a texture defined by the relative position of elements within an array than would be expected if we had access to multiple estimates of relative position across the visual field. In experiment 2 we show that human performance is impaired for positional judgments when there is uncertainty as to which of a number of possible elements is misaligned. This impairment is greater than one would expect from an ideal observer model and greater than that found for a comparable task involving orientation. It is consistent with positional thresholds being determined by only one estimate of relative position. In experiment 3 we estimate the number of suprathreshold positional signals that can be pooled at the same time across the visual field using a standard summation variance paradigm. The results suggest that the human visual system is limited to one estimate of position, but additional estimates can be built up serially over time; however, this process is slow and probably cognitive in nature. These experiments taken as a whole suggest that only one estimate of relative position (i.e. relative to a predefined reference) at a time is accessible at the perceptual level.

Summation of concentric orientation structure: seeing the Glass or the window?

Rotational Glass patterns are discriminable from noise at substantially lower signal-to-noise levels than translational patterns, a finding that has been attributed to the operation of concentrically tuned units in cortical area V4 (Wilson, Wilkinson, & Asaad, Vis. Res. 37 (17) (1997) 2325; Wilson & Wilkinson, Vis. Res. 38 (19) (1998) 2933). Under experimental conditions similar to Wilson et al. we found this advantage to be largely contingent on the pattern being viewed through a circular aperture. Because rotation of a random dot set cannot lead to the presence of unmatched dots at the boundary of a circular aperture, the integrity of low spatial frequency information at the boundary reliably indicates the presence of rotational, but not translational, structure. When we removed this cue, either using a square aperture or surrounding a round aperture with noise dots, none of the nine subjects tested showed any statistically significant advantage for rotational Glass patterns (although at least two did take longer to master the task with translational compared to rotational patterns). We go on to show generally similar patterns of global integration for both rotational and translational patterns. We conclude that this paradigm presently offers no concrete psychophysical evidence for specialised concentric orientation detectors.

Snakes and ladders: the role of temporal modulation in visual contour integration.

We investigated temporal aspects of the cortical mechanisms supporting visual contour integration by measuring observers' efficiency at detecting fragmented contours, composed of Gabor micropatterns, embedded in a field of distractor elements. Gabors consisted of a static Gaussian enveloping a sinusoidal carrier which was temporally modulated by motion or counter-phase flicker. The elements forming the path could be oriented either parallel ('snakes') or perpendicular to the contour orientation ('ladders'). Sensitivity to contour structure (estimated by measuring the maximum tolerable element orientation jitter supporting contour detection) was increased when the elements were drifting or flickering. Snakes were more detectable than ladders under all conditions. The increase in sensitivity conferred by drifting carriers was present even when the elements in the same stimulus were drifting at a range of speeds spanning almost three octaves. These results lend further support to the notion that the contour integration system receives separate transient and sustained input.

Contour interaction in amblyopia: scale selection.

It has been known for some time that visual acuity in amblyopia is higher for single letters than for letters in a row (termed crowding). Early work showed that this could not be accounted for on the basis of the destructive interaction of adjacent contours (termed contour interaction), which was shown to be, in resolution units, normal in amblyopia. We have re-examined this issue using a letter stimulus that is modulated about a mean light level. This allows an examination of the effects of contrast polarity and spatial filtering within the contour interaction paradigm. We show that the majority of strabismic amblyopes that we investigated exhibit an anomalous contour interaction that, in some cases, was dependent on the contrast polarity of the flanking stimuli. Furthermore, we show that while amblyopes do select the optimum scale of analysis for unflanked stimuli, they do not select the optimum scale of analysis for flanked stimuli. For reasons that may have to do with their poorer shape discrimination, they select a non-optimal scale to process flanked stimuli.

Information limit on the spatial integration of local orientation signals.

Channel-based models of human spatial vision require that the output of spatial filters be pooled across space. This pooling yields global estimates of local feature attributes such as orientation that are useful in situations in which that attribute may be locally variable, as is the case for visual texture. The spatial characteristics of orientation summation are considered in the study. By assessing the effect of orientation variability on observers' ability to estimate the mean orientation of spatially unstructured textures, one can determine both the internal noise on each orientation sample and the number of samples being pooled. By a combination of fixing and covarying the size of textured regions and the number of elements constituting them, one can then assess the effects of the texture's size, density, and numerosity (the number of elements present) on the internal noise and the sampling density. Results indicate that internal noise shows a primary dependence on texture density but that, counterintuitively, subjects rely on a sample size approximately equal to a fixed power of the number of samples present, regardless of their spatial arrangement. Orientation pooling is entirely flexible with respect to the position of input features.

Local and global visual grouping: tuning for spatial frequency and contrast.

Glass patterns are visual textures composed of a field of dot pairs (dipoles) whose orientations are determined by a simple geometrical transformation, such as a rotation. Detection of structure in these patterns requires the observer to perform local grouping (to find dipoles) and global grouping to combine their orientations into a percept of overall shape. We estimated the spatial frequency tuning of these grouping processes by measuring signal-to-noise detection thresholds for Glass patterns composed of spatially narrow-band elements. Local tuning was probed by varying the spatial frequency difference between the two elements comprising each dipole. Global tuning was estimated using dipoles containing one spatial frequency and then estimating masking as a function of the spatial frequency of randomly positioned noise elements. We report that the tuning of local grouping is band-pass (ie, it is responsive to a narrow range of spatial frequencies), but that tuning of global grouping is broad and low-pass (ie, it integrates across a broader range of lower spatial frequencies). Control experiments examined how the contrast and visibility of elements might contribute to these findings. Local grouping proved to be more resistant to local contrast variation than global grouping. We conclude that local grouping is consistent with the use of simple-oriented filtering mechanisms. Global grouping seems to depend more on the visibility of elements that can be affected by both spatial frequency and contrast.

Contour interaction in fovea and periphery.

It has been known for some time that both foveal and peripheral visual acuity are higher for single letters than for letters in a row. Early work showed that this was due to the destructive interaction of adjacent contours (termed contour interaction). It has been assumed to have a neural basis, and a number of competing explanations have been advanced that implicate either high-level or low-level stages of visual processing. Our previous results for foveal vision suggested a much simpler explanation, one determined primarily by the physics of the stimulus rather than the physiology of the visual system. We show that, under conditions of contour interaction or crowding, the most relevant physical spatial-frequency band of the letter is displaced to higher spatial frequencies and that foveal vision tracks this change in spatial scale. In the periphery, however, beyond 5 degrees, the physical explanation is not sufficient. Here we show that there are genuine physiological lateral spatial interactions, which are due to changes in the spatial scale of analysis.

Sensitivity to contrast modulation depends on carrier spatial frequency and orientation.

We consider how the detection of second-order contrast structure depends on the orientation and spatial frequency of first-order luminance structure. For patterns composed of a bandpass noise carrier multiplied by a contrast envelope function, we show that sensitivity to the envelope varies in proportion to the spatial frequency of the carrier. For oriented carriers at low spatial-frequencies, detection of the contrast envelope is easier when the envelope and carrier are perpendicular, but this dependency diminishes as the spatial frequency of the carrier increases. These differences are not attributable to either the detection of side-bands, or the presence of spurious contrast structure in unmodulated carrier images. A final experiment measured envelope detection in the presence of noise masks. Results indicate that orientationally and spatially-band pass filtering precedes the detection of second-order structure.

The foveal 'crowding' effect: physics or physiology?

It has been known for some time that both foveal and peripheral visual acuity is higher for single letters than for letters in a row. Early work showed that this was due to the destructive interaction of adjacent contours (termed 'crowding' or contour interaction). It has been assumed to have a neural basis and a number of competing explanations have been advanced which implicate either high-level or low-level stages of visual processing. Our results suggest a much simpler explanation, one primarily determined by the physics of the stimulus rather than the physiology of the visual system. We show that, under conditions of contour interaction or 'crowding', the most relevant physical spatial frequency band of the letter is displaced to higher spatial frequencies and that foveal vision tracks this change in spatial scale.

The role of relative motion computation in 'direction repulsion'.

When two sets of intermixed dots move in different directions the perceived direction of each is considerably shifted [Marshak & Sekuler (1979). Science, 205, 1399-1401; Mather & Moulden, (1980). Quarterly Journal of Experimental Psychology, 32, 325-333)]. This phenomenon has been attributed to 'repulsive' interactions between channels tuned to different directions of motion. However, we report that it is not only the relative direction, but also the density and speed of the sets, which determines the magnitude of the apparent shift. These results are difficult to reconcile with the notion of 'repulsive' interactions, and we describe an alternative, functionally motivated explanation. In the natural environment, observed motion results from objects moving over background surfaces that may themselves be mobile. Disentanglement of motion signals therefore necessitates a computation of relative motion. We propose that the phenomenon of 'direction repulsion' results from a deliberate adjustment of observed motion to compensate for an inferred source of 'background' motion. A simple scheme to do this subtracts the weighted vector-sum of all motion signals from observed motion. This relative motion computation quantitatively predicts the observed effects of the density of dot sets on perceived direction. The effects of speed cannot be reconciled with the scheme as it stands, but this could be due to the model's failure to consider the effect of temporal frequency on the effective contrast of the sets.

The interaction of first- and second-order cues to orientation.

The visual system is sensitive to orientation information defined both by first-order (luminance) and by second-order (texture) cues. We consider how these orientation cues are computed and how they affect one another. We measured the perceived orientation of the first and second-order components of Gabor patches (the carrier and envelope, respectively) and report a dependence of the perceived orientation of each on the orientation of the other, and on the spatial frequency of the carrier. Fixing the carrier orientation near that of the envelope interferes with envelope orientation judgements. This interference is reduced by adding a small (subthreshold) rotation to the carrier indicating that the site of interference is early. When the gross relative orientation of carrier and envelope is varied, the carrier appears systematically tilted towards the envelope. However, provided envelope and carrier are separated by more than approximately 10 degrees, the perceived envelope orientation appears tilted away from the carrier. The size of these effects increases with decreasing carrier spatial frequency, and with increasing exposure duration. When the envelope and carrier are both non parallel and non-perpendicular Fourier energy is distributed asymmetrically across orientation. We demonstrate that, for a channel-based orientation code, this asymmetry induces a shift in mean orientation that is sufficient to explain illusory tilting of carriers. The illusory tilting of the envelope, as a function of carrier orientation and spatial frequency, demonstrates that human ability to demodulate contrast information is far from ideal and cannot be explained by existing two-stage filter-rectify-filter models. We propose that illusory tilting of the envelope is due to selective connectivity between first- and second-stage filters whose purpose is to dissociate the type of image structure producing each class of cue.

Contour integration and scale combination processes in visual edge detection.

Contours in the natural visual environment consist mainly of edges which are spatially broad-band and whose (cosinusoidal) components have arrival phases close to +/-90 deg. Because early visual processing is thought to be based on a local Fourier description, the representation of edges requires two forms of filter combination: scale integration (filter combination across spatial frequency) and contour integration (filter combination across space). In order to determine how these two types of combination fit together, we determined spatial-frequency tuning for the detection of contours composed of broadband edge elements, alternating with narrow-band Gabor elements. A contour integration system operating independently at a number of spatial scales should be able to ignore the distracting influence of edge structure in such patterns. However, subjects cannot ignore edge structure indicating that local phase-alignment across spatial scale is coded prior to, or concurrent with, contour integration. Moreover, unlike contours composed of Gabors, the bandwidth of local elements is important for edge integration; the coding of element bandwidth seems to be dependent on the phase alignment of features across spatial frequency.

Contour integration in the peripheral field.

Contour integration was measured in the normal peripheral field to determine if an explanation based solely on the known peripheral positional uncertainty was sufficient to explain performance. The task involved the detection of paths composed of micropatterns with correlated carrier orientations embedded in a field of similar micropatterns of random position and orientation (Field, D. J., Hayes A., & Hess, R. F. (1993). Vision Research, 33, 173-193). The intrinsic positional uncertainty for each eccentric locus was measured with the same stimulus and it did not account for levels of peripheral performance. We show that peripheral performance on this task does not get worse with eccentricity beyond about 10 degrees and that these results can be modeled by simple filtering without any subsequent cellular linking interactions.

Orientation variance as a quantifier of structure in texture.

I consider how structure is derived from texture containing changes in orientation over space, and propose that multi-local orientation variance (the average orientation variance across a series of discrete images locales) is an estimate of the degree of organization that is useful both for spatial scale selection and for discriminating structure from noise. The oriented textures used in this paper are Glass patterns, which contain structure at a narrow range of scales. The effect of adding noise to Glass patterns, on a structure versus noise task (Maloney et al., 1987), is compared to discrimination based on orientation variance and template matching (i.e. having prior knowledge of the target's orientation structure). At all but very low densities, the variance model accounts well for human data. Next, both models' estimates of tolerable orientation variance are shown to be broadly consistent with human discrimination of texture from noise. However, neither model can account for subjects' lower tolerance to noise for translational patterns than other (e.g. rotational) patterns. Finally, to investigate how well these structural measures preserve local orientation discontinuities, I show that the presence of a patch of unstructured dots embedded in a Glass pattern produces a change in multi-local orientation variance that is sufficient to account for human detection (Hel Or and Zucker, 1989). Together, these data suggest that simple orientation statistics could drive a range of 'texture tasks', although the dependency of noise resistance on the pattern type (rotation, translation, etc.) remains to be accounted for.

Are judgements of circularity local or global?

We assessed, in a task where subjects had to detect smooth deviations from circularity, whether the underlying mechanisms were localised in space to the size of the individual perturbations or whether they computed global shape. By manipulating the phase, the number of cycles of modulation and the spatial arrangement of the perturbations we argue that although either aspect can be detected, performance is ultimately limited by a global shape detecting mechanism. We show that this global mechanism receives input from spatially coarse, crossed orientationally tuned filters whose peak position in orientation depends on the overall shape to be detected.

Spatial-frequency tuning of visual contour integration.

We examine the mechanism that subserves visual contour detection and particularly its tuning for the spatial frequency of contour components. We measured the detection of contours composed of Gabor micropatterns within a field of randomly oriented distractor elements. Distractors were randomly assigned one of two spatial frequencies, and elements lying along the contour alternated between these values. We report that the degree of tolerable spatial-frequency difference between successive contour elements is inversely proportional to the orientation difference between them. Spatial-frequency tuning (half-width at half-height) for straight contours is approximately 1.3 octaves but, for contours with a 30 degrees difference between successive elements, drops to approximately 0.7 octaves. Integration of curved contours operates at a narrower bandwidth. Much orientation information in natural images arises from edges, and we propose that this narrowing of tuning is related to the reduction in interscale support that accompanies increasing edge curvature.

The spatial region of integration for visual symmetry detection.

Symmetry is a complex image property that is exploited by a sufficiently wide range of species to indicate that it is detected using simple visual mechanisms. These mechanisms rely on measurements made close to the axis of symmetry. We investigated the size and shape of this integration region (IR) by measuring human detection of spatially band-pass symmetrical patches embedded in noise. Resistance to disruption of symmetry (in the form of random phase noise) improves with increasing patch size, and then asymptotes when the embedded region fills the IR. The size of the IR is shown to vary in inverse proportion to spatial frequency; i.e. symmetry detection exhibits scale invariance. The IR is shown to have rigid dimensions, elongated in the direction of the axis of symmetry, with an aspect ratio of ca. 2:1. These results are consistent with a central role for spatial filtering in symmetry detection.

The role of "contrast enhancement" in the detection and appearance of visual contours.

We test the proposition that the appearance and detection of visual contours is based on an increase in the perceived contrast of contour elements. First we show that detection of contours is quite possible in the presence of very high levels of variability in contrast. Second we show that inclusion in a contour does not induce Gabor patches to appear to be of higher contrast than patches outside of a contour. These results suggest that, contrary to a number of current models, contrast or its assumed physiological correlate (the mean firing rate of early cortical neurons) is not the determining information for identifying the contour.

Absence of contour linking in peripheral vision.

Human foveal vision is subserved initially by groups of spatial, temporal and orientational 'filters', the outputs of which are combined to define perceptual objects. Although a great deal is known about the filtering properties of individual cortical cells, relatively little is known about the nature of this 'linking' process. One recent approach has shown that the process can be thought of in terms of an association field whose strength is determined conjointly by the orientation and distance of the object. Here we describe a fundamental difference in this feature-linking process in central and peripheral parts of the visual field, which provides insight into the ways that foveal and peripheral visual perception differ. In the fovea, performance can be explained only by intercellular linking operations whereas in the periphery intracellular filtering will suffice. This difference represents a substantial economy in cortical neuronal processing of peripheral visual information and may allow a recent theory of intercellular binding to be tested.