The Emergence of Tuning to Global Shape Properties of Radial Frequency Patterns in the Ventral Visual Pathway.

Radial frequency (RF) patterns, created by sinusoidal modulations of a circle's radius, are processed globally when RF is low. These closed shapes therefore offer a useful way to interrogate the human visual system for global processing of curvature. RF patterns elicit greater responses than those to radial gratings in V4 and more anterior face-selective regions of the ventral visual pathway. This is largely consistent with work on nonhuman primates showing curvature processing emerges in V4, but is evident also higher up the ventral visual stream. Rather than contrasting RF patterns with other stimuli, we presented them at varied frequencies in a regimen that allowed tunings to RF to be derived from 8 human participants (3 female). We found tuning to low RF in lateral occipital areas and to some extent in V4. In a control experiment, we added a high-frequency ripple to the stimuli disrupting the local contour. Low-frequency tuning to these stimuli remained in the ventral visual stream, underscoring its role in global processing of shape curvature. We then used representational similarity analysis to show that, in lateral occipital areas, the neural representation was related to stimulus similarity, when it was computed with a model that captured how stimuli are perceived. We therefore show that global processing of shape curvature emerges in the ventral visual stream as early as V4, but is found more strongly in lateral occipital regions, which exhibit responses and representations that relate well to perception.SIGNIFICANCE STATEMENT We show that tuning to low radial frequencies, known to engage global shape processing mechanisms, was localized to lateral occipital regions. When low-level stimulus properties were accounted for such tuning emerged in V4 and LO2 in addition to the object-selective region LO. We also documented representations of global shape properties in lateral occipital regions, and these representations were predicted well by a proxy of the perceptual difference between the stimuli.

Shape discrimination in peripheral vision: Addressing pragmatic limitations of M-scaling radial frequency patterns.

Peripheral worsening in shape discrimination (SD) can be compensated by size-scaling of peripheral stimuli. However, such scaling results in production of large stimuli that occupy a vast range of eccentricities. We used six proportionally decreasing spatial scales to address this pragmatic limitation and to explore how shape discrimination varies with radius in the nasal visual field. Five participants with normal vision discriminated circles and radial frequency (RF) patterns presented nasally to the fixation point at 5°, 10°, 15° and 20°. Stimuli were scaled with the nasal cortical magnification factor (nCMF) from a central stimulus in six spatial scales, which varied from 0.125 to 1, where 1 corresponded to 1.2° radius. Thresholds expressed in Weber fractions remained constant at eccentricities up to 20° regardless of the spatial scale. Weber fractions for the smaller spatial scales (0.125-0.5) were higher and more variable than for the larger spatial scales (0.75-1), yet still constant across periphery. The results provide evidence that peripheral shape discrimination is constrained by low-level properties, such as eccentricity, and can be predicted by the cortical magnification theory. However, above the peripheral modulation resolution limits, RF shape discrimination is based on the proportion between the modulation amplitude and the radius for larger scales (0.75-1), and demonstrates peripheral scale invariance for these stimuli. For eccentric shape discrimination tests, stimuli with low spatial frequency, high contrast, and radii corresponding to SS 0.75-0.875 should be used to ensure constant Weber fractions, small variability, and peripheral stimuli that are not excessively magnified.

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.

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.

Shape partitioning interacts with global shape integration.

Objects are often identified by the shape of their profiles but complex objects are often comprised of multiple articulated components. It has been proposed that complex objects are decomposed and recognized by their component parts. This study exploits the proposition that the visual system decomposes objects at matched deep concavities on their boundaries. Rapid decreases in thresholds for detection of sinusoidal deformation of a circle's radius with number of cycles of modulation shows that shape information is integrated around radial frequency (RF) patterns. Here we merge RF patterns to form composite patterns with concavities and show that integration around the RF patterns is disrupted if the concavities are shallow but preserved if they are deep, consistent with their decomposition at matched deep concavities. Geon theory identifies complex patterns through a structural description of viewpoint invariant primitives known as geons. Geons are defined by properties on their boundaries that co-occur in a non-accidental manner across viewpoint changes rather than by reconciling metric properties such as curvature with viewpoint specific templates. Similarly, shapes of RF patterns are defined by the positions of curvature features on their boundaries. We argue that RF patterns provide flexible stimuli that might be used to study geons.

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.

I know that "Kiki" is angular: The metacognition underlying sound-shape correspondences.

We examined the ability of people to evaluate their confidence when making perceptual judgments concerning a classic crossmodal correspondence, the Bouba/Kiki effect: People typically match the "Bouba" sound to more rounded patterns and match the "Kiki" sound to more angular patterns instead. For each visual pattern, individual participants were more confident about their own matching judgments when they happened to fall in line with the consensual response regarding whether the pattern was rated as "Bouba" or "Kiki". Logit regression analyses demonstrated that participants' confidence ratings and matching judgments were predictable by similar regression functions. This implies that the consensus and confidence underlying the Bouba/Kiki effect are underpinned by a common process, whereby perceptual features in the patterns are extracted and then used to match the sound according to rules of crossmodal correspondences. Combining both matching and confidence measures potentially allows one to explore and quantify the strength of associations in human knowledge.

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.

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.

Nothing more than a pair of curvatures: A common mechanism for the detection of both radial and non-radial frequency patterns.

Radial frequency (RF) patterns, which are sinusoidal modulations of a radius in polar coordinates, are commonly used to study shape perception. Previous studies have argued that the detection of RF patterns is either achieved globally by a specialized global shape mechanism, or locally using as cue the maximum tangent orientation difference between the RF pattern and the circle. Here we challenge both ideas and suggest instead a model that accounts not only for the detection of RF patterns but also for line frequency patterns (LF), i.e. contours sinusoidally modulated around a straight line. The model has two features. The first is that the detection of both RF and LF patterns is based on curvature differences along the contour. The second is that this curvature metric is subject to what we term the Curve Frequency Sensitivity Function, or CFSF, which is characterized by a flat followed by declining response to curvature as a function of modulation frequency, analogous to the modulation transfer function of the eye. The evidence that curvature forms the basis for detection is that at very low modulation frequencies (1-3 cycles for the RF pattern) there is a dramatic difference in thresholds between the RF and LF patterns, a difference however that disappears at medium and high modulation frequencies. The CFSF feature on the other hand explains why thresholds, rather than continuously declining with modulation frequency, asymptote at medium and high modulation frequencies. In summary, our analysis suggests that the detection of shape modulations is processed by a common curvature-sensitive mechanism that is subject to a shape-frequency-dependent transfer function. This mechanism is independent of whether the modulation is applied to a circle or a straight line.

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.

Modulated textures with shape structures implied by a closed flow are processed globally.

Radial frequency (RF) patterns, shapes deformed from circular by a sinusoidal modulation of radius, have been used to demonstrate global integration of shape information around a closed path by showing that the modulation depth required to detect shape deformation decreases rapidly as larger segments of the contour are modulated. In this psychophysical study we use a field of Gabor patches to examine integration of shape information in sampled RF patterns either alone or placed within an orientation-noise background and show that orientation-noise can be disregarded during the integration of modulation information. We also examine integration in modulated textures with local orientations that flow parallel or perpendicular to an underlying RF shape-structure. In using modulated textures comprising of elements with a random radial position but with orientation modulated such that it conforms to the local orientation of an RF pattern (RF texture) we demonstrate integration around texture patterns that imply shape. Texture patterns with element orientations locally orthogonal (RFO textures) to those of RF textures, however, exhibit a rate of decrease in modulation threshold, which is substantially reduced. When the textures are scrambled by permuting the polar positions of the patches the rate of decrease in threshold with increasing number of patches modulated in orientation is reduced for RF textures but not RFO textures. Detection of modulation in both scrambled textures is shown to be consistent with the detection of local cues. We conclude that implied closure in a modulated flow appears to be critical for global integration of textures.

Detection and recognition of angular frequency patterns.

Previous research has extensively explored visual encoding of smoothly curved, closed contours described by sinusoidal variation of pattern radius as a function of polar angle (RF patterns). Although the contours of many biologically significant objects are curved, we also confront shapes with a more jagged and angular appearance. To study these, we introduce here a novel class of visual stimuli that deform smoothly from a circle to an equilateral polygon with N sides (AF patterns). Threshold measurements reveal that both AF and RF patterns can be discriminated from circles at the same deformation amplitude, approximately 18.0arcsec, which is in the hyperacuity range. Thresholds were slightly higher for patterns with 3.0 cycles than for those with 5.0 cycles. Discrimination between AF and RF patterns was 75% correct at an amplitude that was approximately 3.0 times the threshold amplitude, which implies that AF and RF patterns activate different neural populations. Experiments with jittered patterns in which the contour was broken into several pieces and shifted inward or outward had much less effect on AF patterns than on RF patterns. Similarly, thresholds for single angles of AF patterns showed no significant difference from thresholds for the entire AF pattern. Taken together, these results imply that the visual system incorporates angles explicitly in the representation of closed object contours, but it suggests that angular contours are represented more locally than are curved contours.

Tolerance for local and global differences in the integration of shape information.

Shape is a critical cue to object identity. In psychophysical studies, radial frequency (RF) patterns, paths deformed from circular by a sinusoidal modulation of radius, have proved valuable stimuli for the demonstration of global integration of local shape information. Models of the mechanism of integration have focused on the periodicity in measures of curvature on the pattern, despite the fact that other properties covary. We show that patterns defined by rectified sinusoidal modulation also exhibit global integration and are indistinguishable from conventional RF patterns at their thresholds for detection, demonstrating some indifference to the modulating function. Further, irregular patterns incorporating four different frequencies of modulation are globally integrated, indicating that uniform periodicity is not critical. Irregular patterns can be handed in the sense that mirror images cannot be superimposed. We show that mirror images of the same irregular pattern could not be discriminated near their thresholds for detection. The same irregular pattern and a pattern with four cycles of a constant frequency of modulation completing 2π radians were, however, perfectly discriminated, demonstrating the existence of discrete representations of these patterns by which they are discriminated. It has previously been shown that RF patterns of different frequencies are perfectly discriminated but that patterns with the same frequency but different numbers of cycles of modulation were not. We conclude that such patterns are identified, near threshold, by the set of angles subtended at the center of the pattern by adjacent points of maximum convex curvature.

Investigating shape perception by classification images.

Radial frequency (RF) patterns are circular contours where the radius is modulated sinusoidally. These stimuli can represent a wide range of common shapes and have been popular for investigating human shape perception. Theories postulate a multistage model where a global contour integration mechanism integrates the outputs of local curvature-sensitive mechanisms. However, studies on how the local contour features are processed have been mostly based on indirect experimental manipulations. Here, we use a novel way to explore the contour integration, using the classification image (a psychophysical reverse-correlation) method. RF contours were composed of local elements, and random "radial position noise" offsets were added to element radial positions. We analyzed the relationship between trial-to-trial variations in radial noise and corresponding behavioral responses, resulting in a "shape template": an estimate of the contour parts and features that the visual system uses in the shape discrimination task. Integration of contour features in a global template-like model explains our data well, and we show that observer performance for different shapes can be predicted from the classification images. Classification images show that observers used most of the contour parts. Further analysis suggests linear rather than probability summation of contour parts. Convex forms were detected better than concave forms and the corresponding templates had better sampling efficiency. With sufficient presentation time, we found no systematic preferences for a certain class of contour features (such as corners or sides). However, when the presentation time was very short, the visual system might prefer corner features over side features.

Discriminating facial expressions of emotion and its link with perceiving visual form in Parkinson's disease.

We investigated the link between the ability to perceive facial expressions of emotion and the ability to perceive visual form in Parkinson's disease (PD). We assessed in individuals with PD and healthy controls the ability to discriminate graded intensities of facial expressions of anger from neutral expressions and the ability to discriminate radial frequency (RF) patterns with modulations in amplitude from a perfect circle. Those with PD were, as a group, impaired relative to controls in discriminating graded intensities of angry from neutral expressions and discriminating modulated amplitudes of RF patterns from perfect circles; these two abilities correlated positively and moderately to highly, even after removing the variance that was shared with disease progression and general cognitive functioning. The results indicate that the impaired ability to perceive visual form is likely to contribute to the impaired ability to perceive facial expressions of emotion in PD, and that both are related to the progression of the disease.

Enhanced global integration of closed contours in individuals with high levels of autistic-like traits.

Individuals with autistic traits (measured with Autism-spectrum Quotient, AQ) often excel in detecting shapes hidden within complex structures (e.g. on the Embedded Figures Test, EFT). This facility has been attributed to either weaker global integration of scene elements or enhanced local processing, but 'local' and 'global' have various meanings in the literature. The function of specific global visual mechanisms involved in integrating contours, similar to EFT targets was examined. High AQ scorers produced enhanced performance on the EFT and an alternative Radial Frequency Search Task. Contrary to 'generic' interpretations of weaker global pooling, this group displayed stronger pooling of contour components that was correlated with search ability. This study therefore shows a global contour integration advantage in high AQ observers.

Neural correlates of radial frequency trajectory perception in the human brain.

Radial frequency (RF) motion trajectories are visual stimuli that consist of a difference of Gaussians moving along a closed trajectory defined by a sinusoidal variation of the radius relative to a circular path. In the current study, multivoxel fMRI analyses demonstrated that spatial patterns of activity in visual regions V2, V3, and MT can predict RF motion trajectory shape regardless of whether an observer can behaviorally identify the shape or not. This result suggests that processing in these regions is concerned with local properties of the trajectories and not directly linked with a conscious percept of global trajectory shape. Whole-brain analyses show that RF motion trajectories also evoke premotor and posterior parietal cortical activity that may be a neural correlate of shape recognizability. Further, comparisons with activity evoked by static versions of the RF shapes reveal cue-invariant processing in regions of the posterior parietal and occipitotemporal cortices. Interestingly, the RF motion trajectories evoke patterns of dorsal visual stream cortical activity typical of visually guided movement preparation or action observation, suggesting that these stimuli may be processed as potential motor actions rather than as purely visual experiences.

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.