Non-linear global pooling in the discrimination of circular and non-circular shapes

Abstract

The ability to discriminate minute deviations from circularity is dependent upon global summation mechanisms integrating information along entire contours. The aim of this study was to determine how the strength of global summation depends on various stimulus features. To determine if the strength of global summation differs between shapes, contour discrimination for various contour shapes, generated by applying a sinusoidal modulation to the radius of a circle (radial frequency - RF - patterns), was measured. Shapes differed in frequency (number of lobes RF3, RF5 and RF20) and amplitude ('sharpness' of the lobes ranged between 0 and 20× thresholds for detecting deviation from a circle). Low amplitudes test discrimination against a circle while high amplitudes measure sensitivity for highly non-circular shapes (e.g. five-pointed star-shapes). The ability to integrate information along contours was assessed by comparing the effect of applying radial deformations to the entire contour or to only fractions (various number of cycles). Results show that discrimination thresholds remain in the hyperacuity range for low amplitudes, but increase for higher amplitudes. Concerning signal integration, discrimination, expressed as a function of the amount of contour deformed, exhibits a shallow and a steep regime. Discrimination improves only slowly as more contour cycles are deformed until the point when the entire pattern is modulated, when sensitivity increases substantially. The initial shallow regime is well captured by probability summation. The increase in sensitivity when the entire pattern is modulated compared to a single cycle provides evidence for global pooling. The pattern of integration and the existence of global pooling is dependent on shape frequency. The two-part behavior is independent of shape amplitude but is only seen for low RFs (3 and 5). Data for RF20 follow the prediction of probability summation. We next investigated various stimulus characteristics and their effect on integration strength. Global pooling exceeding probability summation is evident for different pattern sizes, presentation times and for high as well as low absolute contrasts. Only if the contrasts of different fractions of a contour shape are individually scaled to match their respective visibilities is integration strength below the level of probability summation. This explains the lack of apparent global pooling in previous studies employing mixed contrasts. The marked increase in performance for discriminating completely modulated RF patterns argues in favor of highly specialized, global shape mechanisms that are seen over a wide range of stimulus configurations. The results indicate global, non-linear mechanisms, which respond most strongly when stimulated by the entire pattern and comparatively weakly when only stimulated by parts of it.

Aging and the integration of orientation and position in shape perception

“…Subjects in both age groups showed very good discrimination performance for the pairs containing the circle and somewhat poorer sensitivity for the 2.5% and 5% pentagon pair. Better discrimination performance for pairs containing the circle compared to two noncircular contours is consistent with previous studies showing a gradual increase in radial modulation thresholds with increasing amplitude of the test contour (Bell, Wilkinson, Wilson, Loffler, & Badcock, 2009;Schmidtmann et al, 2012). For example, whereas the Weber fraction for discriminating an RF5 from a circle is ,0.004 (Schmidtmann et al, 2012;Wilkinson et al, 1998), it increased to '0.005 for an RF5 with 2% amplitude (Schmidtmann et al, 2012).…”

“…Interestingly, similar to the current results, the effect of interelement spacing on contour grouping was the same in younger and older subjects (Hadad, 2012;Roudaia et al, 2013), even though overall ability to detect and discriminate contours in noise declines with aging (Del Viva & Agostini, 2007;Roudaia et al, 2011Roudaia et al, , 2013. Although Day and Loffler (2009) speculated that the shape illusion is generated by integration by a global pooling mechanism, as opposed to local contour integration mechanisms thought to underlie detection of elongated contours in noise (e.g., Field, Hayes, & Hess, 1993), there is growing evidence suggesting that global shape mechanisms do not operate directly on individual contour elements, but instead pool information from intermediate-stage mechanisms that integrate local orientation information to encode curved contour segments and inflection points (e.g., Bell et al, 2011;Bell, Hancock, Kingdom, & Peirce, 2010;Kempgens et al, 2013;Schmidtmann et al, 2012). To the extent that there may be shared, overlapping mechanisms that contribute to performance in different tasks that involve the integration of orientation information in sampled contours, the current results are consistent with previous studies (Hadad, 2012;McKendrick et al, 2010;Roudaia et al, 2013) in finding no differential effect of interelement spacing on performance with aging.…”

“…Shape perception is an intermediate-level process that appears to integrate orientation information across space using both local and global mechanisms (e.g., Achtman, Hess, & Wang, 2003;Bell, Gheorghiu, Hess, & Kingdom, 2011;Hess, Wang, & Dakin, 1999;Loffler, 2008;Loffler, Wilson, & Wilkinson, 2003;Schmidtmann, Gordon, Bennett, & Loffler, 2013;Schmidtmann, Kennedy, Orbach, & Loffler, 2012;Wilkinson, Wilson, & Habak, 1998). Studies examining whether shape perception is altered in older age have found mixed results (Habak, Wilkinson, & Wilson, 2009;Mayhew & Kourtzi, 2013;McKendrick & Battista, 2013;McKendrick et al, 2010;Rivest, Kim, Intriligator, & Sharpe, 2004;Y.…”

Global Shape Processing Deficits Are Amplified by Temporal Masking in Migraine

“…Human sensitivity for detecting subtle deformations of circular shapes is in the hyperacuity range. 25 Psychophysical, [26][27][28] monkey physiology, 29 and human fMRI 30 studies support the view that the high sensitivity may be a result of processing at intermediate, extrastriate stages. 31 According to the reduced inhibition hypothesis, if masking was a consequence of inhibition, migraineur performance should be similar to controls without a mask, but better than controls when masked.…”

“…Consistent with psychophysical and imaging studies, the output of RF templates should depend on a number of factors, including RF contour contrast, 28 amplitude, 26,30,36,55 radial frequency, 26,28,55 size, 56 and orientation. 36 We only consider contrast (c and c m ) and amplitude (A and A m ) here as the other parameters did not vary in the experiments:…”