Are judgements of circularity local or global?

Development of radial frequency pattern perception in macaque monkeys

Infant primates see poorly, and most perceptual functions mature steadily beyond early infancy. Behavioral studies on human and macaque infants show that global form perception, as measured by the ability to integrate contour information into a coherent percept, improves dramatically throughout the first several years after birth. However, it is unknown when sensitivity to curvature and shape emerges in early life or how it develops. We studied the development of shape sensitivity in 18 macaques, aged 2 months to 10 years. Using radial frequency stimuli, circular targets whose radii are modulated sinusoidally, we tested monkeys' ability to radial frequency stimuli from circles as a function of the depth and frequency of sinusoidal modulation. We implemented a new four-choice oddity task and compared the resulting data with that from a traditional two-alternative forced choice task. We found that radial frequency pattern perception was measurable at the youngest age tested (2 months). Behavioral performance at all radial frequencies improved with age. Performance was better for higher radial frequencies, suggesting the developing visual system prioritizes processing of fine visual details that are ecologically relevant. By using two complementary methods, we were able to capture a comprehensive developmental trajectory for shape perception.

Lateral inhibition between banks of orientation selective channels predicts shape context effects: A tilt-illusion field

The perceived shapes of almost circular paths are modified by concentrically placed context paths. These induced changes have previously been attributed to curvature masking. This paper shows that, instead, they can be explained by the impacts of local tilt illusions. First, the tilt-illusion was measured over the full range of orientation differences between short test and context lines and it was shown that the resulting function can be predicted by a model based on a vectorial population response of a bank of orientation selective channels, provided lateral inhibition between channels with the same orientation selectivity and adjacent receptive fields was postulated. Subsequently, it was demonstrated that, if the perceived shape of a test path were modified to accommodate the predicted local tilt-illusion, then this could account for previously reported changes in the detectability of a path sinusoidally modulated in radius. Further, we measured points of subjective vertical in test lines and points of subjective circularity in test paths when surrounded by modulated context paths. The tilt required to null the tilt-illusion approximated the maximum orientation difference from circular measured in the modulated paths at their point of subjective circularity, supporting the proposal that the illusory shape change is due to local changes in the position of the path arising from a response to local tilt illusions induced by the orientation context. An important corollary to this result is that such effects will generalize to all paths which are adjacent.

Gaze patterns during presentation of fixed and random phase radial frequency patterns

Radial frequency (RF) patterns, circles which have had their radius modulated as a function of their polar angle, have been used in the examination of the integration of contour information around closed contour patterns. Typically, these patterns have been presented in a random orientation from trial-to-trial in order to maintain spatial uncertainty as to the location of the deformation on the pattern, as it may affect observer strategy and performance. However, the effect of fixed and random orientation (phase) on observer gaze strategies used to discriminate RF patterns has not been directly tested. This study compared fixation patterns across four conditions: fixed phase single cycle; random phase single cycle; fixed phase three cycle; and random phase three cycle RF3 patterns. The results showed that observers fixated on the known location of deformation for the fixed phase single cycle condition but used a more central fixation for the other three conditions. This strategy had a significant effect on observer thresholds for the fixed phase single cycle condition, with greater adherence to the strategy resulting in lower thresholds. It was also found that for the single cycle patterns observers tended to fixate on different locations on the pattern: on the maximum orientation difference from circular for the fixed phase pattern; and on the point of maximum curvature for the random phase pattern. These differences in gaze patterns are likely driven by the underlying local or global processing of the fixed or random phase single cycle patterns, respectively.

Simple Vision Function Tests that Distinguish Eyes with Early to Intermediate Age-related Macular Degeneration

PURPOSE

To present and compare baseline vision findings in eyes with early age-related macular degeneration (E-AMD), intermediate AMD (I-AMD), and age-similar participants with normal aging changes to the retina (No-AMD).

METHODS

Two hundred and thirty-seven eyes of 125 individuals (66.4% female, mean age 75.3 years) were tested monocularly using several simple, rapid psychophysical tests: high contrast visual acuity, low contrast visual acuity at reduced luminance, contrast sensitivity, shape discrimination hyperacuity, colour vision, reading rate, and glare recovery. Retinal status was determined using colour fundus photographs that were graded according to the Beckman Initiative for Macular Research Classification Committee scale. Logistic regression analyses with generalized estimating equations were used to assess the association between each vision variable and AMD category, while taking into account the correlation between the two eyes.

RESULTS

Three vision measures (contrast sensitivity [CS], shape discrimination hyperacuity [SDH], and colour discrimination [DesatCCS]) were significantly and independently associated with intermediate AMD. Relative Risk Ratios (RRR), 95% Confidence Intervals (in parentheses), beta coefficients, and significance (p) for the I-AMD vs. No-AMD model are: CS: RRR = 6.5 (1.91-22.0), beta = 1.87, p < .01; SDH: RRR = 2.34 (1.24-4.44), beta = 0.85, p < .001; DesatCCS: RRR = 1.43 (1.22-1.68), beta = 0.36, p < .001. Performance on these measures was significantly poorer for participants with I-AMD vs. No-AMD.

CONCLUSIONS

Simple screening tests distinguish eyes with intermediate AMD from eyes with less severe AMD or normal aging changes. This suggests that these vision measures may be significant predictors of which participants will go on to develop advanced AMD.

Visual Function in Eyes with Intermediate AMD with and without Retinal Pigment Abnormalities

SIGNIFICANCE

In intermediate AMD, a simple, clinically feasible vision test of sensitivity to radial deformation is significantly more impaired in eyes with hyperpigmentation than in eyes with large drusen but normal retinal pigmentation, consistent with the former's increased risk of progression to advanced AMD. This ongoing longitudinal study will determine whether this vision measure is predictive of progression to advanced AMD.

PURPOSE

This study aimed to determine whether simple, clinically feasible psychophysical measures distinguish between two levels of intermediate AMD that differ in their risk of progression to advanced AMD: eyes with large macular drusen and retinal pigment abnormalities versus eyes with large macular drusen without pigment abnormalities. Abnormal pigmentation in the presence of large drusen is associated with a higher risk of development of advanced AMD.

METHODS

Each eye of 39 individuals with the same form of intermediate AMD in both eyes was tested monocularly on a battery of vision tests. The measures (photopic optotype contrast sensitivity, discrimination of desaturated colors, and sensitivity to radial deformation [shape discrimination hyperacuity]) were compared for both dominant and nondominant eyes. ANOVA with eye (dominant or nondominant) as a within-subject factor and retinal status (pigmentary abnormalities present or absent from the macula) as a between-subject factor was used to determine statistical significance.

RESULTS

Sensitivity to radial deformation was significantly reduced in eyes with large drusen and pigment changes compared with eyes with large drusen and normal retinal pigmentation (-0.40 ± 0.04 vs. -0.61 ± 0.02, respectively; F = 13.31, P = .001).

CONCLUSIONS

In the presence of large macular drusen, performance on a shape discrimination task is related to the presence versus absence of abnormal retinal pigmentation, being poorer in the higher-risk group, supportive of the measure's potential to predict progression to advanced AMD.

Impact of microsaccades on visual shape processing

Sensitivity to subtle changes in the shape of visual objects has been attributed to the existence of global pooling mechanisms that integrate local form information across space. Although global pooling is typically demonstrated under steady fixation, other work suggests prolonged fixation can lead to a collapse of global structure. Here, we ask whether small ballistic eye movements that naturally occur during periods of fixation affect the global processing of radial frequency (RF) patterns-closed contours created by sinusoidally modulating the radius of a circle. Observers were asked to discriminate the shapes of circular patterns and RF-modulated patterns while fixational eye movements were recorded binocularly at 500 Hz. Microsaccades were detected using a velocity-based algorithm, allowing trials to be sorted according to the relative timing of stimulus and microsaccade onset. Results revealed clear perisaccadic changes in shape discrimination thresholds. Performance was impaired when microsaccades occurred close to stimulus onset, but facilitated when they occurred shortly afterward. In contrast, global integration of shape was unaffected by the timing of microsaccades. These findings suggest that microsaccades alter the discrimination sensitivity to briefly presented shapes but do not disrupt the spatial pooling of local form signals.NEW & NOTEWORTHY Microsaccades cause rapid displacement of visual images during fixation and dramatically alter the perception of basic image features. However, their effect on more complex aspects of visual processing is not well understood. Here, we demonstrate a dissociation in the impact of microsaccades on shape perception. Although overall shape discrimination performance is modulated around the time of microsaccades, the pooling efficiency of global mechanisms that combine local form information across space remains unaffected.

Eccentricity Effect of Deformation Detection for Radial Frequency Patterns With Their Centers at Fixation Point

We measured the eccentricity effect of deformation thresholds of circular contours for two types of the radial frequency (RF) patterns with their centers at the fixation point: constant circular contour frequency (CCF) RF patterns and constant RF magnified (retino-cortical scaling) RF patterns. We varied the eccentricity by changing the mean radius of the RF patterns while keeping the centers of the RF patterns at the fixation point. Our peripheral stimulus presentation was distinguished from previous studies which have simply translated RF patterns at different locations in the visual field. Sensitivity for such shape discrimination fell off as the moderate and high CCF patterns were presented on more eccentric sites but did not as the low CCF patterns. However, sensitivity held constant as the magnified RF patterns were presented on more eccentric sites, indicating that the eccentricity effects observed for the high and moderate CCF patterns were neutralized by retinocortical mapping. Notably, sensitivity for the magnified RF patterns with large radii (4°–16°) presented in the peripheral field revealed a similar RF dependence observed for RF patterns with small radii (0.25°–1.0°) presented at the fovea in previous studies.

Sensitivity to curvature deformations along closed contours

Human observers are exquisitely sensitive to curvature deformations along a circular closed contour (Wilkinson, Wilson, & Habak, 1998; Hess, Wang, & Dakin, 1999; Loffler, Wilson, & Wilkinson, 2003). Such remarkable sensitivity has been attributed to the curvature encoding scheme used by V4 neurons, which typically are assumed to be equally sensitive to curvature at all polar angles (Pasupathy & Connor, 2001, 2002; Carlson, Rasquinha, Zhang, & Connor, 2011). To test the assumption that detection thresholds for curvature deformations are invariant across polar angles, we used a novel stimulus class we call Difference of Gaussian (DoG) contours that allowed us to independently manipulate the amplitude, angular frequency, and polar angle of curvature of a closed-contour shape while measuring contour-curvature thresholds. Our results demonstrate that (a) detection thresholds were higher when observers were uncertain about the location of the curvature deformation, but on average, thresholds did not vary significantly across 24 polar angles; (b) the direction and magnitude of the oblique effect varies across individuals; (c) there is a strong association between detecting a contour deformation and identifying its location; (d) curvature detectors may serve as labeled lines.

Good Visual Performance Despite Reduced Optical Quality during the First Month of Orthokeratology Lens Wear

Purpose: To measure changes in visual performances and optical quality in myopic children during the first month of wearing orthokeratology lens, and to reveal the association between those two.Methods: Thirty-five myopic children participated in this study. Visual performances were evaluated with visual acuity and shape discrimination threshold (SDT) for radial frequency patterns. Placido disc-based corneal topography for central 4 mm and 6 mm zones was collected and decomposed by Fourier analysis into the spherical, asymmetric, and regular astigmatic components. Root-mean-square of third-order, fourth-order, and total higher-order aberrations (HOA) were extracted for the 4 mm and 6 mm zones. All examinations were conducted at baseline, 1-week, and 1-month after lens dispensing. The changing trends over time and association between SDT and optical quality were analysed with linear-mixed model.Results: All subjects' uncorrected visual acuity improved to 0.1 logMAR or better at 1-week and 1-month lens wear (P < .01). SDT did not change significantly from the baseline at 1-week and 1-month after lens wear (P > .05). For the two zones with diameters of 4 mm and 6 mm, the spherical component decreased significantly at 1-week (P < .01) and remained stable thereafter (P < .01); the asymmetric component increased significantly at 1-week (P < .01) and remained high at 1-month (P < .01); and the regular astigmatism did not show any significant change throughout (P > .05). At the two zones with diameters of 4 mm and 6 mm, the third-order, fourth-order, and total HOA increased significantly over time (P < .05). Change of SDT did not correlate with impairments in optical quality (P > .05 for all parameters).Conclusions: While corneal optical quality decreased steadily during the first month following lens wearing, the visual acuity and shape discrimination sensitivity assessed by SDT remained very satisfactory.

The processing of compound radial frequency patterns

Radial frequency (RF) patterns can be combined to construct complex shapes. Previous studies have suggested that such complex shapes may be encoded by multiple, narrowly-tuned RF shape channels. To test this hypothesis, thresholds were measured for detection and discrimination of various combinations of two RF components. Results show evidence of summation: sensitivity for the compounds was better than that for the components, with little effect of the components' relative phase. If both RF components are processed separately at the point of detection, they would combine by probability summation (PS), resulting in only a small increase in sensitivity for the compound compared to the components. Summation exceeding the prediction of PS suggests a form of additive summation (AS) by a common mechanism. Data were compared to predictions of winner-take-all, where only the strongest component contributes to detection, a single channel AS model, and multi-channel PS and AS models. The multi-channel PS and AS models were modelled under both Fixed and Matched Attention Window scenarios, the former assuming a single internal noise source for both components and compounds or different internal noise sources for components and compounds respectively. The winner-take-all and single channel models could be rejected. Of the remaining models, the best performing one was an AS model with a Fixed Attention Window, consistent with detection being mediated by channels that are efficiently combined and limited by a single source of noise for both components and compounds.

Evaluating spatiotemporal interactions between shapes

Spatiotemporal interactions between stimuli can alter the perceived curvature along the outline of a shape (Habak, Wilkinson, Zakher, & Wilson, 2004; Habak, Wilkinson, & Wilson, 2006). To better understand these interactions, we used a forward and backward masking paradigm with radial frequency (RF) contours while measuring RF detection thresholds. In Experiment 1, we presented a mask alongside a target contour and altered the stimulus onset asynchrony between this target-mask pair and a temporal mask. We found that a temporal mask increased thresholds when it preceded the target-mask stimulus by 130-180 ms but decreased thresholds when it followed the target-stimulus mask by 180 ms. Furthermore, Experiment 2 demonstrated that the effects of temporal and spatial masks are approximately additive. We discuss these findings in relation to theories of transient and sustained channels in vision.

Scotopic contour and shape discrimination using radial frequency patterns

Radial frequency (RF) patterns are valuable tools for investigations of contour integration and shape discrimination. Under photopic conditions, healthy observers can detect deformations from circularity in RF patterns as small as 3 seconds of arc. Such fine discrimination may be facilitated by cortical curvature detectors or global shape-detecting mechanisms that favor a closed contour. Rods make up 95% of photoreceptors in the retina, but we know very little about how spatial information is processed by rod-mediated pathways. We measured scotopic radial deformation discrimination using both full and partly occluded RF pattern stimuli. We found radial deformation thresholds of around 2–3 minutes of arc for stimuli with a wide range of radii and RFs. When parts of the stimulus were occluded, scotopic thresholds improved up to the point that three or four cycles of modulation were visible; no further improvement occurred with the addition of more visible cycles. When only one to three cycles were visible, an increase in curvature per cycle became important, allowing observers to detect smaller deformations from circularity. Our results indicate that the scotopic radial deformation thresholds for the stimuli tested are not dependent on global circularity cues but are instead mediated by local curvature cues.

Phase-selective masking with radial frequency contours

Sensitivity to changes in the shape of a closed-contour figure is affected by surrounding figures (Vision Research 44 (2004) 2815-2823). We examined how between-contour masking depends on radial frequency. Experiment 1 replicated previous studies that found that masking between adjacent radial frequency (RF) patterns was greatest when the two shapes were phase aligned, and that the magnitude of masking declined approximately linearly with increasing phase offsets. In addition, we found that the effect of phase offset on masking was very similar for RFs ranging from 3 to 8, a result that suggests that sensitivity to phase decreases with increasing radial frequency. Experiment 2 tested this idea and found that phase discrimination threshold for single cycles of curvature was approximately proportional to radial frequency. Experiment 3 showed that both curvature maxima and minima contribute to phase dependent masking between RF contours. Together, Experiments 1-3 demonstrate that the strength of phase-dependent masking does not depend on RF, but is related to sensitivity for phase shifts in isolated contours, and is affected by both positive and negative curvature extrema. We discuss these results in relation to properties of curvature sensitive neurons.

Creating Noisy Stimuli

A method for creating a variety of pseudo-random ‘noisy’ stimuli that possess several useful statistical and phenomenal features for psychophysical experimentation is outlined. These stimuli are derived from a pseudo-periodic function known as multidimensional noise. This class of function has the desirable property that it is periodic, defined on a fixed domain, is roughly symmetric, and is stochastic, yet consistent and repeatable. The stimuli that can be created from these functions have a controllable amount of complexity and self-similarity properties that are further useful when generating naturalistic looking objects and surfaces for investigation. The paper addresses the creation and manipulation of stimuli with the use of noise, including an overview of this particular implementation. Stimuli derived from these procedures have been used successfully in several shape and surface perception experiments and are presented here for use by others and further discussion as to their utility.

When "Bouba" equals "Kiki": Cultural commonalities and cultural differences in sound-shape correspondences

It has been suggested that the Bouba/Kiki effect, in which meaningless speech sounds are systematically mapped onto rounded or angular shapes, reflects a universal crossmodal correspondence between audition and vision. Here, radial frequency (RF) patterns were adapted in order to compare the Bouba/Kiki effect in Eastern and Western participants demonstrating different perceptual styles. Three attributes of the RF patterns were manipulated: The frequency, amplitude, and spikiness of the sinusoidal modulations along the circumference of a circle. By testing participants in the US and Taiwan, both cultural commonalities and differences in sound-shape correspondence were revealed. RF patterns were more likely to be matched with “Kiki” than with “Bouba” when the frequency, amplitude, and spikiness increased. The responses from both groups of participants had a similar weighting on frequency; nevertheless, the North Americans had a higher weighting on amplitude, but a lower weighting on spikiness, than their Taiwanese counterparts. These novel results regarding cultural differences suggest that the Bouba/Kiki effect is partly tuned by differing perceptual experience. In addition, using the RF patterns in the Bouba/Kiki effect provides a “mid-level” linkage between visual and auditory processing, and a future understanding of sound-shape correspondences based on the mechanism of visual pattern processing.

Rejecting probability summation for radial frequency patterns, not so Quick!

Radial frequency (RF) patterns are used to assess how the visual system processes shape. They are thought to be detected globally. This is supported by studies that have found summation for RF patterns to be greater than what is possible if the parts were being independently detected and performance only then improved with an increasing number of cycles by probability summation between them. However, the model of probability summation employed in these previous studies was based on High Threshold Theory (HTT), rather than Signal Detection Theory (SDT). We conducted rating scale experiments to investigate the receiver operating characteristics. We find these are of the curved form predicted by SDT, rather than the straight lines predicted by HTT. This means that to test probability summation we must use a model based on SDT. We conducted a set of summation experiments finding that thresholds decrease as the number of modulated cycles increases at approximately the same rate as previously found. As this could be consistent with either additive or probability summation, we performed maximum-likelihood fitting of a set of summation models (Matlab code provided in our Supplementary material) and assessed the fits using cross validation. We find we are not able to distinguish whether the responses to the parts of an RF pattern are combined by additive or probability summation, because the predictions are too similar. We present similar results for summation between separate RF patterns, suggesting that the summation process there may be the same as that within a single RF.

Radial Frequency Analysis of Contour Shapes in the Visual Cortex

Cumulative psychophysical evidence suggests that the shape of closed contours is analysed by means of their radial frequency components (RFC). However, neurophysiological evidence for RFC-based representations is still missing. We investigated the representation of radial frequency in the human visual cortex with functional magnetic resonance imaging. We parametrically varied the radial frequency, amplitude and local curvature of contour shapes. The stimuli evoked clear responses across visual areas in the univariate analysis, but the response magnitude did not depend on radial frequency or local curvature. Searchlight-based, multivariate representational similarity analysis revealed RFC specific response patterns in areas V2d, V3d, V3AB, and IPS0. Interestingly, RFC-specific representations were not found in hV4 or LO, traditionally associated with visual shape analysis. The modulation amplitude of the shapes did not affect the responses in any visual area. Local curvature, SF-spectrum and contrast energy related representations were found across visual areas but without similar specificity for visual area that was found for RFC. The results suggest that the radial frequency of a closed contour is one of the cortical shape analysis dimensions, represented in the early and mid-level visual areas.

The role of the foreshortening cue in the perception of 3D object slant

Slant is the degree to which a surface recedes or slopes away from the observer about the horizontal axis. The perception of surface slant may be derived from static monocular cues, including linear perspective and foreshortening, applied to single shapes or to multi-element textures. It is still unclear the extent to which color vision can use these cues to determine slant in the absence of achromatic contrast. Although previous demonstrations have shown that some pictures and images may lose their depth when presented at isoluminance, this has not been tested systematically using stimuli within the spatio-temporal passband of color vision. Here we test whether the foreshortening cue from surface compression (change in the ratio of width to length) can induce slant perception for single shapes for both color and luminance vision. We use radial frequency patterns with narrowband spatio-temporal properties. In the first experiment, both a manual task (lever rotation) and a visual task (line rotation) are used as metrics to measure the perception of slant for achromatic, red-green isoluminant and S-cone isolating stimuli. In the second experiment, we measure slant discrimination thresholds as a function of depicted slant in a 2AFC paradigm and find similar thresholds for chromatic and achromatic stimuli. We conclude that both color and luminance vision can use the foreshortening of a single surface to perceive slant, with performances similar to those obtained using other strong cues for slant, such as texture. This has implications for the role of color in monocular 3D vision, and the cortical organization used in 3D object perception.

Handheld shape discrimination hyperacuity test on a mobile device for remote monitoring of visual function in maculopathy

PURPOSE

Frequency monitoring of age-related macular degeneration (AMD) and diabetic retinopathy (DR) is crucial for timely intervention. This study evaluated a handheld shape discrimination hyperacuity (hSDH) test iPhone app designed for visual function self-monitoring in patients with AMD and DR.

METHODS

One hundred subjects (27 visually normal, 37 with AMD, and 36 with DR) were included based on clinical documentation and visual acuity of 20/100 or better. The hSDH test was implemented on the iOS platform. A cross-sectional study was conducted to compare the hSDH test with a previously established desktop SDH (dSDH) test and to assess the effect of disease severity on the hSDH test. A user survey was also conducted to assess the usability of the hSDH test on the mobile device.

RESULTS

The hSDH test and dSDH test were highly correlated (r = 0.88, P < 0.0001). Bland-Altman analysis indicated no significant difference in hSDH and dSDH measurements. One-way ANOVA indicated that the mean hSDH measurement of the eyes with advanced AMD (n = 16) or with severe to very severe nonproliferative DR (NPDR) (n = 12) was significantly worse than that of the eyes with intermediate AMD (n = 11) or with mild to moderate NPDR (n = 11) (P < 0.0001). Ninety-eight percent of 46 patients (10 with AMD and 36 with DR) who completed the usability survey reported that the hSDH test was easy to use.

CONCLUSIONS

This study demonstrated that the hSDH test on a mobile device is comparable to PC-based testing methods. As a mobile app, it is intuitive to use, readily accessible, and sensitive to the severity of maculopathy. It has the potential to provide patients having maculopathy with a new tool to monitor their vision at home.

Set-size effects for sampled shapes: experiments and model

The location of imperfections or heterogeneities in shapes and contours often correlates with points of interest in a visual scene. Investigating the detection of such heterogeneities provides clues as to the mechanisms processing simple shapes and contours. We determined set-size effects (e.g., sensitivity to single target detection as distractor number increases) for sampled contours to investigate how the visual system combines information across space. Stimuli were shapes sampled by oriented Gabor patches: circles and high-amplitude RF4 and RF8 radial frequency patterns with Gabor orientations tangential to the shape. Subjects had to detect a deviation in orientation of one element ("heterogeneity"). Heterogeneity detection sensitivity was measured for a range (7-40) of equally spaced (2.3-0.4°) elements. In a second condition, performance was measured when elements sampled a part of the shapes. We either varied partial contour length for a fixed (7) set-size, co-varying inter-element spacing, or set-size for a fixed spacing (0.7°), co-varying partial contour length. Surprisingly, set-size effects (poorer performance with more elements) are rarely seen. Set-size effects only occur for shapes containing concavities (RF4 and RF8) and when spacing is fixed. When elements are regularly spaced, detection performance improves with set-size for all shapes. When set-size is fixed and spacing varied, performance improves with decreasing spacing. Thus, when an increase in set-size and a decrease in spacing co-occur, the effect of spacing dominates, suggesting that inter-element spacing, not set-size, is the critical parameter for sampled shapes. We propose a model for the processing of simple shapes based on V4 curvature units with late noise, incorporating spacing, average shape curvature, and the number of segments with constant sign of curvature contained in the shape, which accurately accounts for our experimental results, making testable predictions for a variety of simple shapes.

Detecting shapes in noise: tuning characteristics of global shape mechanisms

The proportion of signal elements embedded in noise needed to detect a signal is a standard tool for investigating motion perception. This paradigm was applied to the shape domain to determine how local information is pooled into a global percept. Stimulus arrays consisted of oriented Gabor elements that sampled the circumference of concentric radial frequency (RF) patterns. Individual Gabors were oriented tangentially to the shape (signal) or randomly (noise). In different conditions, signal elements were located randomly within the entire array or constrained to fall along one of the concentric contours. Coherence thresholds were measured for RF patterns with various frequencies (number of corners) and amplitudes (“sharpness” of corners). Coherence thresholds (about 10% = 15 elements) were lowest for circular shapes. Manipulating shape frequency or amplitude showed a range where thresholds remain unaffected (frequency ≤ RF4; amplitude ≤ 0.05). Increasing either parameter caused thresholds to rise. Compared to circles, thresholds increased by approximately four times for RF13 and five times for amplitudes of 0.3. Confining the signals to individual contours significantly reduced the number of elements needed to reach threshold (between 4 and 6), independent of the total number of elements on the contour or contour shape. Finally, adding external noise to the orientation of the elements had a greater effect on detection thresholds than adding noise to their position. These results provide evidence for a series of highly sensitive, shape-specific analysers which sum information globally but only from within specific annuli. These global mechanisms are tuned to position and orientation of local elements from which they pool information. The overall performance for arrays of elements can be explained by the sensitivity of multiple, independent concentric shape detectors rather than a single detector integrating information widely across space (e.g. Glass pattern detector).

Detecting global form: separate processes required for Glass and radial frequency patterns

Global processing of form information has been studied extensively using both Glass and radial frequency (RF) patterns. Models, with common early stages, have been proposed for the detection of properties of both pattern types but human performance has not been examined to determine whether the two pattern types interact in the manner this would suggest. The experiments here investigated whether low RF patterns and concentric Glass patterns, which are thought to tap the same level of processing in form-vision, are detected by a common mechanism. Six observers participated in two series of masking experiments. First: sensitivity to the presence of either coherent structure, or contour deformation, was assessed. The computational model predicted that detection of one pattern would be masked by the other. Second: a further experiment examined position coding. The model predicted that localizing the center of form in a Glass pattern would be affected by the presence of an RF pattern: sensitivity to a change of location should be reduced and the apparent location should be drawn toward the center of the masking pattern. However, the results observed in all experiments were inconsistent with the interaction predicted by the models, suggesting that separate neural mechanisms for global processing of signal are required to process these two patterns, and also indicating that the models need to be altered to preclude the interactions that were predicted but not obtained.

Global shape processing involves a hierarchy of integration stages

Radial Frequency (RF) patterns can be used to study the processing of familiar shapes, e.g. triangles and squares. Opinion is divided over whether the mechanisms that detect these shapes integrate local orientation and position information directly, or whether local orientations and positions are first combined to represent extended features, such as curves, and that it is local curvatures that the shape mechanism integrates. The latter view incorporates an intermediate processing stage, the former does not. To differentiate between these hypotheses we studied the processing of micro-patch sampled RF patterns as a function of the luminance polarity of successive elements on the contour path. Our first study measures shape after effects involving suprathreshold amplitude RF shapes and shows that alternating the luminance polarity of successive micro-patch elements disrupts adaptation of the global shape. Our second study shows that polarity alternations also disrupt sensitivity to threshold-amplitude RF patterns. These results suggest that neighbouring points of the contour shape are integrated into extended features by a polarity selective mechanism, prior to global shape processing, consistent with the view that for both threshold amplitude and suprathreshold amplitude patterns, global processing of RF shapes involves an intermediate stage of processing.

Global shape processing: which parts form the whole?

Research suggests that detection of low-frequency radial frequency (RF) patterns involves global shape processing and that points of maximum curvature (corners) contribute more than points of minimum curvature (sides). However, this has only been tested with stimuli presented at the threshold of discriminability from a circle. We used RF pattern adaptation to (a) examine whether a supra-threshold RF pattern is processed as a global shape and (b) determine what the critical features are for representing its shape. We measured the perceived amplitude shift of an RF test pattern after prolonged exposure either to a higher amplitude pattern or to various combinations of its parts (concave maxima, convex maxima, inflections). We found greater shifts in perceived amplitude after adaptation to a "whole" pattern than after adaptation to its component parts, which alternated to produce equal net contrast. Furthermore, when adapting to specific parts of the shape in isolation, we found that each part generated a similar magnitude aftereffect. Although the whole is clearly greater than the sum of the parts, we find that concave maxima, convex maxima, and inflections contribute equally to global shape processing, a fact that is only apparent when using a supra-threshold appearance-based task.

Course of development of global hyperacuity over lifespan

PURPOSE

Global visual integration is fundamental to shape and face recognition. Although the maturation of local visual function, such as resolution acuity, has been well documented, less is known about the changes in global visual function during development and with aging.

METHODS

Two hundred thirty-six normal subjects, ranging in age from 0.25- to 78-years old, participated in the study. Global hyperacuity (detection threshold for radial deformation) was obtained from 300 eyes using either a computerized testing or a chart testing protocol and spatial forced choice (preferential looking for <2.6-year old, pointing for young children, or verbal response for older children and adults). Resolution acuity was also measured. The developmental courses for global hyperacuity and resolution acuity were fit to a 3-segment curve to capture the initial rapid development, followed by a period of stable, adult-level visual function and, finally, the decline in visual function with aging.

RESULTS

Curve fitting revealed that global hyperacuity was 0.25 logMAR at 0.25 years of age, and improved rapidly to -0.56 logMAR at 5.4 years of age but did not reach the mean adult level (-0.86 logMAR) until 21 years of age. Global hyperacuity started to deteriorate from 55 years of age at the rate of 0.035 logMAR per decade. In comparison, resolution acuity reached 0.0 logMAR at 5 years of age, and reached the adult level of -0.1 logMAR at 11 years of age. Resolution acuity also started to decrease from 55 years of age at the rate of 0.058 logMAR per decade.

CONCLUSIONS

Similar to vernier alignment acuity, global hyperacuity improves rapidly during infancy and early childhood but takes longer to reach the adult level than resolution acuity. The delayed maturation of global hyperacuity suggests that further development to refine neural circuitry at the cortical level takes place in the second decade of life.

Radial frequency adaptation suggests polar-based coding of local shape cues

The study of shape processing in the human visual system has frequently employed radial frequency (RF) patterns as conveniently manipulable stimuli. This study uses an adaptation paradigm to investigate how local shape information is sampled in the processing of RF contour shapes. Experiment 1 measured thresholds for detecting a fixed mean radius RF contour following adaptation to RF patterns which, in separate conditions, varied in mean radius and radial frequency. Results reveal that, adaptation is strongly tuned for RF over a range of pattern radii, but is not tuned for the number of cycles of radial modulation per visual degree of contour length; a characteristic that changes with both radius and radial frequency. Experiment 2 manipulated the polar angle separation on the fronto-parallel plane between curvature features on a fixed RF by foreshortening the pattern appearance (consistent with a rotation in depth) and shows that RF shape processing is tuned for fronto-parallel separation angles between curvature features. Results were near identical when a stereo rotation cue was added to the perspective modified RF. In the second part of Experiment 2 we showed that RF shape adaptation is also tuned for the polar angular extent of the curvature represented by the lobe at that angle. Collectively, our results indicate that the polar angle at which local curvature features appear, in addition to the angular extent of the curvature feature at that location, are both critical parameters for coding specific RF shapes.

Neural Coding of Global Form in the Human Visual Cortex

Extensive psychophysical and computational work proposes that the perception of coherent and meaningful structures in natural images relies on neural processes that convert information about local edges in primary visual cortex to complex object features represented in the temporal cortex. However, the neural basis of these mid-level vision mechanisms in the human brain remains largely unknown. Here, we examine functional MRI (fMRI) selectivity for global forms in the human visual pathways using sensitive multivariate analysis methods that take advantage of information across brain activation patterns. We use Glass patterns, parametrically varying the perceived global form (concentric, radial, translational) while ensuring that the local statistics remain similar. Our findings show a continuum of integration processes that convert selectivity for local signals (orientation, position) in early visual areas to selectivity for global form structure in higher occipitotemporal areas. Interestingly, higher occipitotemporal areas discern differences in global form structure rather than low-level stimulus properties with higher accuracy than early visual areas while relying on information from smaller but more selective neural populations (smaller voxel pattern size), consistent with global pooling mechanisms of local orientation signals. These findings suggest that the human visual system uses a code of increasing efficiency across stages of analysis that is critical for the successful detection and recognition of objects in complex environments.

Object perception and masking: contributions of sides and convexities

Object perception uses a variety of visual cues, including shape cues derived from sides and convexities. Two recent masking studies using radial frequency patterns have argued, respectively, for a predominant role of convexity [Habak, C., Wilkinson, F., Zakher, B., & Wilson, H. R. (2004). Curvature population coding for complex shapes in human vision. Vision Research, 44 (24), 2815-2823] or side information [Hess, R. F., Wang, Y. -Z., & Dakin, S. C. (1999). Are judgements of circularity local or global? Vision Research, 39, 4354-4360]. Here we resolve the controversy by separating the masks into their parts (e.g., convexities and sides), and measuring the relative masking influences of the different mask components. We found that both side and convexity information contribute to masking. However, masking due to side information was much less dependent on alignment compared to masking due to convexities. This supports a theory where convexities constitute a prime source of information for shape processing, and sides do also contribute but to a smaller extent.

Detecting low shape-frequencies in smooth and jagged contours

It is often assumed that a two-stage filter-process is involved in the coding of visual contours. In the first stage the contour is coded by localized luminance filters selective for, among other dimensions, orientation and spatial frequency. A second stage then integrates the outputs of these local luminance filters over space. In the experiments described here we address the issue of which spatial scales of early luminance filters are involved in the detection of a contour's deviation from linearity ('co-linearity failure'), especially at low contour frequencies, for both smooth contours and jagged edges. We also address the question whether it is the orientation or position of the first-stage luminance filters that is used by the second stage. We report two main conclusions. Firstly, across a wide range of shape frequencies, we find that detection thresholds are relatively independent of the spatial scale of the luminance information present in the contour, indicating that detection of co-linearity failure can be effectively mediated by luminance filters tuned to a range of spatial scales. Secondly, we find that detection of co-linearity failure in low shape-frequency contours is primarily based on the local positions, not orientations, of the first-stage luminance filters. As our results suggest that the contour's local orientation may nevertheless play a role, we hypothesize that the local orientation of the contour is not signaled by luminance filters directly but rather by second-order filters acting on the local positions of the contour.

Cortical specialization for concentric shape processing

It is current dogma that neurons in primary visual cortex extract local edges from the scene, from which later visual areas reconstruct more meaningful shapes. In intermediate areas, such as area V4, responses are driven by features more complex than local oriented edges but more basic than meaningful shapes. The present study was motivated by the proposal that concentric (circular) shape processing is an important aspect of intermediate shape processing and is proposed to occur in area V4. However, previous studies are not able to discriminate between the number of orientations within the image nor how these orientations vary across space (orientation gradient, contrast or curvature) as opposed to concentric shape processing per se. We address the question whether V4 responses are driven by curvature or circularity. We use fMRI and tightly controlled narrowband stimuli with identical local and global properties. These patterns either form random or circular patterns with tightly matched orientation gradients and therefore similar curvature. We find stronger responses to circular patterns in areas V3/VP and V4. Our results suggest that extracting circular shape is an important step in intermediate shape processing.

Detection of shape in radial frequency contours: independence of local and global form information

Radial frequency (RF) patterns have been used to study the processes involved in shape perception. The psychophysical literature suggests that there are distinct global and local shape detection processes for low and high radial frequency patterns, but this has not been tested in a combined contour pattern, such as would be needed to describe the contours of most natural objects. Here, we combined frequencies from the local and global range onto a compound RF structure. Observers' ability to detect a single RF component on the compound pattern was measured. Results show that sensitivity to high frequency local deviations in shape was not affected by the presence of a globally perceived low frequency pattern. In the reverse condition, detection of global form was not influenced by adding local deviations onto the structure. This suggests that local and global shape information can be detected independently within the human visual system.

The spatial feature underlying the shape-frequency and shape-amplitude after-effects

The shape-frequency and shape-amplitude after-effects, or SFAE and SAAE, refer respectively to the shifts observed in the perceived shape-frequency and shape-amplitude of a sinusoidal test contour following adaptation to a similar-shaped contour. As with other shape after-effects the shifts are in a direction away from that of the adapting stimulus. Using a variety of procedures we tested whether the spatial feature that was adapted in the SFAE and SAAE was (a) local orientation, (b) average unsigned curvature, (c) periodicity/density, (d) shape-amplitude and (e) local curvature. Our results suggest that the last of these, local curvature, underlies both the SFAE and SAAE. The evidence in favour of local curvature was that the after-effect reached its maximum value when just half-a-cycle of the test contour, in +/-cosine phase, was present. We suggest that the SFAE and SAAE are mediated by intermediate-level mechanisms that encode the shapes of contour fragments with constant sign of curvature. Given the neurophysiological evidence that neurons in area V4 encode parts of shapes with constant sign of curvature, we suggest V4 is the likely neural substrate for both the SFAE and SAAE.

A biologically plausible model of human radial frequency perception

Several recent studies have used radial frequency patterns to investigate intermediate-level shape perception, a critical precursor to object recognition. Here, we developed the first neural model of RF perception based on known V4 properties that exhibits many of the characteristics of human RF perception. The model is composed of two main parts: (1) recovery of object position using large-scale non-Fourier V4-like concentric units that respond at the center of concentric contour segments across orientations, and (2) curvature detectors that encode local shape information. Each curvature mechanism combines multiplicatively the responses of three oriented filters, the positions and orientation preferences of which determine the curvature mechanism's tuning properties for position, orientation, and degree of curvature. When responding to RF patterns, peak responses occur at points of maximum curvature. Shape is represented as curvature responses as a function of orientation around the object center, and the cross-correlation of that function with a sine wave peaks when the frequency of the sine wave matches the number of peaks in the stimulus. Cross-correlation strength can be used to model human performance. Model and human performance are comparable for detection, identification, and lateral masking tasks. Moreover, the model also shows size invariance of detection performance due to scaling of the curvature mechanisms. The model is then used to make novel predictions.

Luminance-contrast properties of contour-shape processing revealed through the shape-frequency after-effect

We investigated the first-order inputs to contour-shape mechanisms using the shape-frequency after-effect (SFAE), in which adaptation to a sinusoidally modulated contour causes a shift in the apparent shape-frequency of a test contour in a direction away from that of the adapting stimulus [Kingdom F. A. A., & Prins N. (2005a). Different mechanisms encode the shapes of contours and contour-textures. Journal of Vision 5(8), 463, (Abstract)]. We measured SFAEs for adapting and test contours (and edges) that differed in the contrast-polarity, scale (or blur) and magnitude of luminance contrast. The rationale was that if the SFAE was found to be reduced when adaptor and test differed along a particular dimension of luminance contrast, contour-shape mechanisms must be tuned to that dimension. Our results reveal that SFAEs manifest (i) a degree of selectivity to luminance contrast polarity for both even-symmetric (contours only) and odd-symmetric (both contours and edges) luminance profiles; (ii) a degree of selectivity to luminance scale (or blur); (iii) higher selectivity to fine compared to coarse scale for broadband edges (iv) a small preference for equal-in-contrast adaptors and tests. These results suggest that contour shapes are not encoded in the form of a sparse, cartoon-like sketch, as might be presumed by local energy (i.e. non-phase-selective) or form-cue invariant models, but instead in a form that is relatively 'feature-rich.'

Effects of global shape on angle discrimination

Previous studies have been inconclusive as to whether angle discrimination performance can be predicted by the sensitivity of orientation discrimination mechanisms or by that of mechanisms specialised for angle coding. However, these studies have assumed that angle discrimination is independent of the shape of the object of which the angle is a part. This assumption was tested by measuring angle discrimination using angles that were parts of different triangular shapes. Angle discrimination thresholds were lowest when angles were presented in isosceles triangles (sides forming the angle were of identical length). Performance was significantly poorer when angles were presented in scalene triangles (sides of different lengths) and as much as three times worse when the sides forming the angle varied randomly in length between presentations. Comparing orientation discrimination for single lines with angle discrimination for different stimulus conditions (isosceles, scalene and random triangles) leads to conflicting conclusions as to the mechanisms underlying angle perception: line orientation sensitivity correctly predicts angle discrimination for random triangles, but underestimates angle acuity for isosceles triangles. The fact that performance in angle discrimination tasks is strongly dependant on the overall stimulus geometry implies that geometric angles are computed by mechanisms that are sensitive to global aspects of the stimulus.