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

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.

Mutual Information and Categorical Perception

Categorical perception refers to the enhancement of perceptual sensitivity near category boundaries, generally along dimensions that are informative about category membership. However, it remains unclear exactly which dimensions are treated as informative and why. This article reports a series of experiments in which subjects were asked to learn statistically defined categories in a novel, unfamiliar 2D perceptual space of shapes. Perceptual discrimination was tested before and after category learning of various features in the space, each defined by its position and orientation relative to the maximally informative dimension. The results support a remarkably simple generalization: The magnitude of improvement in perceptual discrimination of each feature is proportional to the mutual information between the feature and the category variable. This finding suggests a rational basis for categorical perception in which the precision of perceptual discrimination is tuned to the statistical structure of the environment.

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.

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 Integration of Local Orientation Information Occurs in Students With High Schizotypal Personality Traits

Contour integration is impaired in schizophrenia patients, even at the first episode, but little is known about visual integration abilities prior to illness onset. To examine this issue, we compared undergraduate students high and low in schizotypal personality traits, reflecting putative liability to psychosis, on two psychophysical tasks assessing local and global stages of the integration process. The Radial Frequency Jittered Orientation Tolerance (RFJOT) task measures tolerance to orientation noise at the local signal level, when judging global stimulus orientation, whilst the Radial Frequency Integration Task (RFIT) measures the ability to globally integrate the local signals that have been extracted during shape discrimination. Positive schizotypy was assessed with the Perceptual Aberration (PAb) scale from the Wisconsin Schizotypy Scales-Brief. On the RFJOT task, the High PAb group (n = 55) tolerated statistically significantly less noise (d = -0.494) and had a lower proportion of correct responses (d = -0.461) than the Low PAb group (n = 77). For the RFIT there was no statistically significant difference in integration abilities between the High and Low PAb groups. High and Low PAb groups also differed on other positive and disorganized (but not negative) schizotypy traits, hence poorer performance on the RFJOT may not be solely related to unusual perceptual experiences. These findings suggest that difficulties with local noise tolerance but not global integration occur in healthy young adults with high levels of schizotypal personality traits, and may be worth investigating as a marker of risk for schizophrenia.

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.