Intrinsic uncertainty and integration efficiency in bisection acuity

A spatial perturbation paradigm was used to determine equivalent intrinsic uncertainty and spatial integration efficiency in bisection. Specifically, three-line bisection thresholds were measured in the fovea of four normal observers with stimulus lines comprised of discrete dark dots distributed randomly around the mean line position according to a Gaussian function. The standard deviation of the Gaussian distribution (sigma e), the number (N), and the strength (C) of the dots as well as line separation were varied. Bisection thresholds were modeled by an ideal integrator, from which the magnitude of equivalent internal uncertainty (sigma i), the equivalent effective number of dots (k), and equivalent integration efficiency (k/N) were quantified. At the 2 min arc separation, sigma i decreases (down to a few sec arc) as N and/or C increases. The effects of both N and C can be accounted for by the stimulus visibility (V, in multiples of detection threshold). At the 16 min arc separation, sigma i is independent of N, C, or V, and is about 1 min arc. The two different forms of sigma i indicate that bisection judgments are limited by at least two separate sources of limiting noise, consistent with the hypothesis of two separate mechanisms (i.e. spatial filters and local signs). A visibility dependent sigma i at the 2 min arc separation can be explained on the basis of contrast sensitive spatial filter mechanisms. A fixed sigma i at the 16 min arc separation indicates a genuine positional uncertainty, consistent with local-sign mechanisms. Interestingly, equivalent integration efficiency (k/N) is very similar at the two line separations. k/N is critically dependent on, and proportional to C, indicating a common limitation in a detection mechanism.