Our formulation of the relationship between disparity threshold and image contrasts in the two eyes is based on the cross-correlation model, which has received support from many psychophysical experiments (Allenmark & Read,
2010,
2011; Banks, Gepshtein, & Landy,
2004; Cormack et al.,
1991; Filippini & Banks,
2009; Harris, McKee, & Smallman,
1997; Nienborg, Bridge, Parker, & Cumming,
2004), and has found many successful applications in computer vision (Clerc & Mallat,
2002; Donate, Liu, & Collins,
2011; Heo, Lee, & Lee,
2011; Kanade & Okutomi,
1994). The product rule in the cross-correlation model is consistent with the prevailing disparity energy models of V1 neurons (Anzai et al.,
1999a,
1999b; Chen & Qian,
2004; Filippini & Banks,
2009; Ohzawa,
1998; Ohzawa, DeAngelis, & Freeman,
1990,
1996; Qian,
1994,
1997) when the outputs of binocular complex cells with opposite preferred polarities of disparity are compared to extract the polarity of the perceived disparity. In the original cross-correlation model (Cormack et al.,
1991), stereo strength is proportional to the product of signal contrasts in the two eyes. Here, we postulate that stereo strength is proportional to the product of the signal strengths in the two eyes after contrast gain control, and disparity threshold is inversely proportional to the product:
where
k is a scaling constant, and
ρ and
γ1 are the contrast gain-control efficient and the exponent of the power-law nonlinearity in the gain-control pathway, respectively.