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

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.

Analysis of shape uses local apparent position rather than physical position

Objects are often identified by the shapes of their boundaries. Here, by measuring threshold amplitudes for detection of sinusoidal modulation of local position, orientation and centrifugal speed in a closed path of Gabor patches, we show that the positions of such boundaries are misperceived to accommodate local illusions of orientation context and motion induced positional bias. These two types of illusion are shown to occur independently, but the misperception of position is additive. We conclude that, in the analysis of shape, the visual system uses the apparent rather than the veridical boundary conformation.

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

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

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.

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.