Contrast summation across eyes and space is revealed along the entire dipper function by a "Swiss cheese" stimulus

Abstract

Previous contrast discrimination experiments have shown that luminance contrast is summed across ocular (T. S. Meese, M. A. Georgeson, & D. H. Baker, 2006) and spatial (T. S. Meese & R. J. Summers, 2007) dimensions at threshold and above. However, is this process sufficiently general to operate across the conjunction of eyes and space? Here we used a "Swiss cheese" stimulus where the blurred "holes" in sine-wave carriers were of equal area to the blurred target ("cheese") regions. The locations of the target regions in the monocular image pairs were interdigitated across eyes such that their binocular sum was a uniform grating. When pedestal contrasts were above threshold, the monocular neural images contained strong evidence that the high-contrast regions in the two eyes did not overlap. Nevertheless, sensitivity to dual contrast increments (i.e., to contrast increments in different locations in the two eyes) was a factor of ∼1.7 greater than to single increments (i.e., increments in a single eye), comparable with conventional binocular summation. This provides evidence for a contiguous area summation process that operates at all contrasts and is influenced little, if at all, by eye of origin. A three-stage model of contrast gain control fitted the results and possessed the properties of ocularity invariance and area invariance owing to its cascade of normalization stages. The implications for a population code for pattern size are discussed.

Contrast integration over area is extensive: A three-stage model of spatial summation

“…In summation experiments with these stimuli, performance dropped to the expected factor of ¾2 (3 dB), supporting the model (Meese, 2010). Meese and Baker (2011) proposed that the process of area summation of contrast is involved in deriving a general-purpose size code for textures and patterns. They suggested that this task is achieved with the help of a contrast normalization network (Meese & Baker, 2011;Meese & Summers, 2007) that protects the suprathreshold image-contrast code (Albrecht & Geisler, 1991;Heeger, 1992).…”

“…A more successful model is one in which contrast integration (linear spatial summation of contrast) follows a nonlinear (square-law) contrast transducer (Foley, Varadharajan, Koh, & Farias, 2007;Meese & Summers, 2007, 2009) and additive noise (Meese, 2010). The cascade of the two quadratic effects produced by square-law transduction (Legge, 1984) and summation of signal and noise (Campbell & Green, 1965;Tyler & Chen, 2000) means that sensitivity improves with the fourth root of area, similar to the conventional probability summation model and several empirical reports (see Meese & Baker, 2011 for a review). However, the behavior of model and humans is very different when contrast area is manipulated in more interesting ways, as we now describe.…”

“…However, recent psychophysical evidence (Meese, 2010;Meese & Baker, 2011;Meese & Summers, 2007, 2009) is inconsistent with this. A more successful model is one in which contrast integration (linear spatial summation of contrast) follows a nonlinear (square-law) contrast transducer (Foley, Varadharajan, Koh, & Farias, 2007;Meese & Summers, 2007, 2009) and additive noise (Meese, 2010).…”

“…However, the behavior of model and humans is very different when contrast area is manipulated in more interesting ways, as we now describe. Meese and Summers (2007) designed what we have come to call a "Swiss cheese" stimulus (Meese & Baker, 2011). In this type of stimulus, diameter is constant and a sine-wave carrier is modulated by a raised plaid pattern such that it contains interdigitated patches of high-contrast regions ("cheese") and low/zero-contrast regions ("holes").…”

Binocular functional architecture for detection of contrast-modulated gratings

“…This lack of consensus probably springs, in part, from the smallness of these effects -just a few dB -coupled with the considerable difficulty of getting reliable, unbiassed threshold estimates to the required accuracy. Over the last 30 years, computer-controlled, forced-choice psychophysical methods with better display technology, and much greater numbers of trials, have improved the reliability of threshold estimation, and with these methods estimates of the binocular advantage tend to cluster around 4-5dB (Legge, 1984;Maehara & Goryo, 2005;Meese & Baker, 2011;Meese et al, 2006;Meese & Summers, 2009;Simmons & Kingdom, 1998;Simmons, 2005) -as if forming a compromise between the theoretically salient values of 3 and 6 dB (which represent an ideal observer with independent noise in the two eyes versus linear summation with fixed noise). In a retrospective analysis, however, we found that the variation between studies may not be random.…”