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Andrew Isaac Meso, Robert F. Hess; Visual detection of orientation modulators suggests limitations to scale invariance of second order mechanisms. Journal of Vision 2010;10(15):71. doi: 10.1167/10.15.71.
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Using a second-order visual stimulus in which the orientation of a noise carrier was spatially modulated, we probed the relationship between the frequency of the band-pass filtered carrier and that of the envelope periodic spatial modulator. In a 2-AFC psychophysical detection task, we obtained the threshold tuning functions for both the carrier luminance contrast and the modulation depth for a range of ratios of the two frequency parameters using a foveally presented stimulus in a circular aperture. With a scale invariant neural mechanism, suggested for second-order stimuli, functions of the ratio of carrier and modulator frequencies should show consistent tuning, largely independent of the specific pair of frequency parameters. We found that was not the case. For the carrier contrast threshold, the functions showed a low-pass tuning when the carrier frequency was varied and band-pass tuning when the modulator frequency was varied. For both parametric manipulations, the ratio had a similar range of tested values. When we measured modulation depth thresholds with the stimuli controlled for luminance contrast detectability, the functions showed more modest differences in tuning. To exclude an explanation based on averaging of any optimal tuning spatially across the visual field, we repeated the measurements for a stimulus confined in eccentricity (Annulus, radius 14.6 deg of visual angle). That configuration was more difficult to detect and returned broadly similar tuning functions. These results do not support the idea of a constant coupling between the scales of mechanisms detecting the carrier and modulator that would be required for scale invariance.
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