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

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.

The relationship between mechanisms for curvature and Vernier detections

Tyler (Journal of Physiology 228 (1973) 637-647) reported that the sensitivity function for curvature detection has band-pass characteristics with respect to shape frequency. The shape of this function suggests that the curvature detection mechanism might consist of a set of sub-mechanisms each tuned for shape frequencies similar to mechanisms for contrast detection. In Experiment 1, we applied an adaptation for shape frequency to investigate whether shape frequency is the critical feature in curvature detection. We successfully replicated the U shape threshold function reported by Tyler (1973), but found that selective adaptation does not occur for shape frequency. These results suggest that shape frequency is not critical for curvature detection. In Experiment 2, we examined the possibility that curvature detection for the highest sensitivity range is mediated by a displacement process similar to that for Vernier acuity. The results indicate that curvature detection for this range is mediated by a mechanism that is sensitive to spatial displacement, and suggests the existence of a common mechanism for spatial displacement that mediates both curvature and Vernier detections. By comparing our results with those of several previous studies, we concluded that the apparent band-pass characteristic for curvature detection is produced by combining the characteristics of three separate limiting factors: local orientation at lower frequencies, spatial acuity at higher frequencies, and displacement in the highest sensitivity area.

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.

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.

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.