Spatial integration in position acuity

To determine whether and how spatial integration takes place in position acuity, bisection and Vernier thresholds were measured in the fovea of four normal observers with spatially "undersampled" dark lines (i.e. lines comprised of discrete samples). The size, contrast, and density of samples, and the separation of the lines were varied. For a given sampling density, sample size (0.17-2.72 min) has negligible effect on position threshold. For all sample sizes, position threshold decreases as sampling density increases, indicating that spatial integration takes place. The form of spatial integration depends on line separation. At the optimal line separation (2 min for bisection and 0 min for Vernier), position threshold decreases as sampling density increases with a slope of about -0.8 on log axes, steeper than a slope of -0.5 as would be expected from statistical position averaging. This effect of sampling density can be completely explained by spatial contrast summation for visibility. At the 16 min line separation, position threshold also decreases as sampling density increases but with a slope shallower than -0.5. However, this effect of sampling density can not be explained by contrast summation. Position thresholds decrease even after discounting the effect of contrast summation on visibility, suggesting a genuine position averaging. These findings are independent of line orientation (horizontal or vertical), and hold for both random and uniform dot distributions, and for both bisection and Vernier. Thus, two separate mechanisms of position acuity are suggested. A spatial filter mechanism operates at the optimal (or narrow) line separation where position threshold is critically dependent on stimulus visibility. A local sign mechanism operates at the relatively wider line separation where position acuity benefits from local sign position averaging. For both mechanisms, spatial integration is not perfect.