Narrow-band radial frequency shape channels revealed by sub-threshold summation

Forgetting in visual working memory: Internal noise explains decay of feature representations

The precision of visual working memory (VWM) representations decreases as time passes. It is often assumed that VWM decay is random and caused by internal noise accumulation. However, forgetting in VWM could occur systematically, such that some features deteriorate more rapidly than others. There exist only a few studies testing these two models of forgetting, with conflicting results. Here, decay of features in VWM was thoroughly tested using signal detection theory methods: psychophysical classification images, internal noise estimation, and receiver operant characteristic (ROC). A modified same–different memory task was employed with two retention times (500 and 4000 ms). Experiment 1 investigated VWM decay using a compound grating memory task, and Experiment 2 tested shape memory using radial frequency patterns. Memory performance dropped some 15% with increasing retention time in both experiments. Interestingly, classification images showed virtually indistinguishable weighting of stimulus features at both retention times, suggesting that VWM decay is not feature specific. Instead, we found a 77% increase in stimulus-independent internal noise at the longer retention time. Finally, the slope of the ROC curve plotted as z-scores was shallower at the longer retention time, indicating that the amount of stimulus-independent internal noise increased. Together these findings provide strong support for the idea that VWM decay does not result from a systematic loss of some stimulus features but instead is caused by uniformly increasing random internal noise.

Frequency ratio determines discrimination of concentric radial frequency patterns in the peripheral visual field

Using a radial frequency discrimination task that has not been tested in many previous studies, we examined the dependence of the pattern radius (4 to 16 deg) on the radial frequency thresholds of two different types of concentric radial frequency (RF) patterns: constant circular contour frequency (CCF) RF patterns with different radii, which have the constant physical length of modulation cycle in external real-world space, and constant radial frequency magnified RF patterns with different radii, which have the constant cortical length of modulation cycles. These two types RF patterns used as the reference stimuli had an equal maximum orientation difference from circularity regardless of change in radius. The discrimination threshold expressed by the frequency ratio between RF patterns of different frequencies vs. radius functions for the constant CCF RF patterns indicated different functional forms dependent on the modulation amplitude of the RF patterns. The thresholds increased with increasing pattern radius for small modulation amplitude RF patterns but were relatively flattened for large-amplitude RF patterns. This dependence was ascribed to the eccentricity effect wherein the deformation thresholds for discriminating the RF pattern from a circle increase with increasing stimulus eccentricity (Feng et al. 2020). The discrimination thresholds vs. radius functions for the magnified RF patterns were also flattened for different modulation amplitudes and frequencies. The thresholds (frequency ratio) were similar at all eccentricities. Cortical magnification neutralized the eccentricity effect observed for the constant CCF patterns.

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.

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.

Radial frequency patterns describe a small and perceptually distinct subset of all possible planar shapes

The visual system is exposed to a vast number of shapes and objects. Yet, human object recognition is effortless, fast and largely independent of naturally occurring transformations such as position and scale. The precise mechanisms of shape encoding are still largely unknown. Radial frequency (RF) patterns are a special class of closed contours defined by modulation of a circle's radius. These patterns have been frequently and successfully used as stimuli in vision science to investigate aspects of shape processing. Given their mathematical properties, RF patterns can not represent any arbitrary shape, but the ability to generate more complex, biologically relevant, shapes depicting the outlines of objects such as fruits or human heads raises the possibility that RF patterns span a representative subset of possible shapes. However, this assumption has not been tested before. Here we show that only a small fraction of all possible shapes can be represented by RF patterns and that this small fraction is perceptually distinct from the general class of all possible shapes. Specifically, we derive a general measure for the distance of a given shape's outline from the set of RF patterns, allowing us to scan large numbers of object outlines automatically. We find that only between 1% and 6% of naturally smooth outlines can be exactly represented by RF patterns. We present results from a visual search experiment, which revealed that searching an RF pattern among non-radial frequency patterns is efficient, whereas searching an RF pattern among other RF patterns is inefficient (and vice versa). These results suggest that RF patterns represent only a restricted subset of possible planar shapes and that results obtained with this special class of stimuli can not simply be expected to generalise to any arbitrary planar shape.

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.

Poorer Search Efficiency in Healthy Young Adults With High Schizotypal Personality Traits

Perceptual organization (PO) difficulties have repeatedly been reported in people with schizophrenia, and in healthy individuals with high levels of schizotypy traits, who are at increased risk for schizophrenia. In particular, poor performance on the Embedded Figures Test (EFT) has been interpreted as an atypically strong preference for global over local processing, even though these processes cannot be clearly disambiguated on this test. Here we use two separate versions of the Radial Frequency Search Task (RFST), a new index of PO abilities, to selectively investigate global and local processing of shape information in trait schizotypy. Schizotypy traits were assessed using the Wisconsin Schizotypy Scales-Brief. Individuals selected for high and low levels of positive schizotypy [assessed with the Wisconsin Schizotypy Scales-Brief Perceptual Aberration (PAb) scale] completed the EFT, along with the Global RFST and the Local RFST, all of which require participants to find a target shape amongst distractor elements. The High PAb group (n = 83) were less efficient (i.e., reactions times slowed more as the set size increased) than the Low PAb group (n = 146) on the Global RFST (significant group differences for Target Absent conditions only), but not the Local RFST. High and Low PAb groups also differed on other schizotypy traits, so the specificity of the results to positive schizotypy cannot be assured. Unexpectedly, no group differences were observed on the EFT; however, there was a small, but significant, positive correlation between RFST search efficiency and EFT performance, indicating that they shared some common processes. Overall, the pattern of results suggests that global (but not local) processing difficulties may be contributing to the poorer perceptual organization observed in groups with high levels of schizotypy traits. In addition, the confinement of this result to the Target Absent condition suggests that the underlying mechanism involves differences in decisional processes on the RFST between high and low schizotypy groups. The RFST shows promise as a useful tool for measuring specific perceptual organization abilities in non-clinical, and potentially clinical, samples.

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.

Visual search targeting either local or global perceptual processes differs as a function of autistic-like traits in the typically developing population

Relative to low scorers, high scorers on the autism-spectrum quotient (AQ) show enhanced performance on the embedded figures test and the radial frequency search task (RFST), which has been attributed to both enhanced local processing and differences in combining global percepts. We investigate the role of local and global processing further using the RFST in four experiments. High AQ adults maintained a consistent advantage in search speed across diverse target-distracter stimulus conditions. This advantage may reflect enhanced local processing of curvature in early stages of the form vision pathway and superior global detection of shape primitives. However, more probable is the presence of a superior search process that enables a consistent search advantage at both levels of processing.

Near their thresholds for detection, shapes are discriminated by the angular separation of their corners

Observers make sense of scenes by parsing images on the retina into meaningful objects. This ability is retained for line drawings, demonstrating that critical information is concentrated at object boundaries. Information theoretic studies argue for further concentration at points of maximum curvature, or corners, on such boundaries [1]–[3] suggesting that the relative positions of such corners might be important in defining shape. In this study we use patterns subtly deformed from circular, by a sinusoidal modulation of radius, in order to measure threshold sensitivity to shape change. By examining the ability of observers to discriminate between patterns of different frequency and/or number of cycles of modulation in a 2x2 forced choice task we were able to show, psychophysically, that difference in a single cue, the periodicity of the corners (specifically the polar angle between two points of maximum curvature) was sufficient to allow discrimination of two patterns near their thresholds for detection. We conclude that patterns could be considered as labelled for this measure. These results suggest that a small number of such labels might be sufficient to identify an object.

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.

Visual search performance in the autism spectrum II: the radial frequency search task with additional segmentation cues

The Embedded Figures Test (EFT) requires detecting a shape within a complex background and individuals with autism or high Autism-spectrum Quotient (AQ) scores are faster and more accurate on this task than controls. This research aimed to uncover the visual processes producing this difference. Previously we developed a search task using radial frequency (RF) patterns with controllable amounts of target/distracter overlap on which high AQ participants showed more efficient search than low AQ observers. The current study extended the design of this search task by adding two lines which traverse the display on random paths sometimes intersecting target/distracters, other times passing between them. As with the EFT, these lines segment and group the display in ways that are task irrelevant. We tested two new groups of observers and found that while RF search was slowed by the addition of segmenting lines for both groups, the high AQ group retained a consistent search advantage (reflected in a shallower gradient for reaction time as a function of set size) over the low AQ group. Further, the high AQ group were significantly faster and more accurate on the EFT compared to the low AQ group. That is, the results from the present RF search task demonstrate that segmentation and grouping created by intersecting lines does not further differentiate the groups and is therefore unlikely to be a critical factor underlying the EFT performance difference. However, once again, we found that superior EFT performance was associated with shallower gradients on the RF search task.

Perception of shapes targeting local and global processes in autism spectrum disorders

BACKGROUND

Several researchers have found evidence for impaired global processing in the dorsal visual stream in individuals with autism spectrum disorders (ASDs). However, support for a similar pattern of visual processing in the ventral visual stream is less consistent. Critical to resolving the inconsistency is the assessment of local and global form processing ability.

METHODS

Within the visual domain, radial frequency (RF) patterns - shapes formed by sinusoidally varying the radius of a circle to add 'bumps' of a certain number to a circle - can be used to examine local and global form perception. Typically developing children and children with an ASD discriminated between circles and RF patterns that are processed either locally (RF24) or globally (RF3).

RESULTS

Children with an ASD required greater shape deformation to identify RF3 shapes compared to typically developing children, consistent with difficulty in global processing in the ventral stream. No group difference was observed for RF24 shapes, suggesting intact local ventral-stream processing.

CONCLUSIONS

These outcomes support the position that a deficit in global visual processing is present in ASDs, consistent with the notion of Weak Central Coherence.

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.

(In) sensitivity to spatial distortion in natural scenes

The perception of object structure in the natural environment is remarkably stable under large variation in image size and projection, especially given our insensitivity to spatial position outside the fovea. Sensitivity to periodic spatial distortions that were introduced into one quadrant of gray-scale natural images was measured in a 4AFC task. Observers were able to detect the presence of distortions in unfamiliar images even though they did not significantly affect the amplitude spectrum. Sensitivity depended on the spatial period of the distortion and on the image structure at the location of the distortion. The results suggest that the detection of distortion involves decisions made in the late stages of image perception and is based on an expectation of the typical structure of natural scenes.

A new step towards understanding Embedded Figures Test performance in the autism spectrum: the radial frequency search task

The Embedded Figure Test (EFT) requires locating a simple shape embedded within a background of overlapping target-irrelevant scene elements. Observers with autism, or those with high levels of autistic-like traits, typically outperform matched comparison groups on the EFT. This research investigated the critical visual properties which give rise to this improved performance. The EFT is a search task and so here a radial frequency (RF) search task was created to directly explore efficacy of visual search and also the influence of element overlap on performance. In all conditions, the task was to detect whether the target RF3 (a triangular shape chosen for its visual properties) was present among a number of distracter RF4 (a square shape) patterns. The conditions employed were: 'singles', where all the patterns were spatially discrete, 'pairs', where two overlapping elements formed each cluster, and 'quads', comprising four overlapping elements per cluster. Compared to students scoring low on the Autism Spectrum Quotient (AQ; n=27), those scoring high on the AQ (n=23) were faster on the EFT and also significantly less influenced by increasing set size of the stimulus array in all RF search task conditions. However, the group difference in RF search performance was unaffected by the amount of stimulus overlap. Thus a simple search task is sufficient to detect a performance advantage associated with higher levels of autistic traits and has the advantages of a solid footing in visual theory and being readily repeatable for the purpose of assessing performance variability and change with interventions.