Spatial interval discrimination with blurred lines: black and white are separate but not equal at multiple spatial scales

We used Gaussian blurred lines of same- and opposite-polarity to measure the effects of blur on 3-line spatial interval discrimination (bisection). The results of our experiments can be summarized as follows. Spatial interval discrimination (3-line bisection) thresholds are proportional to the separation of the lines (i.e. Weber's law). At the optimal separation, spatial interval discrimination thresholds for same-polarity lines represent a "hyperacuity" as small as 2 sec arc. For same-polarity Gaussian blurred lines, over a wide range of the blur standard deviations (sigma), the optimal threshold occurs when the separation is approx. 2 sigma, and the optimal threshold is about 0.02 sigma, or a Weber fraction (delta s/s) of 0.01. For opposite-polarity lines, under conditions where same-polarity stimuli yield the best thresholds (at a separation approximately 2 sigma), spatial interval thresholds are an order of magnitude worse than that for same-polarity lines, suggesting that the localization of stimili of opposite-polarity is much worse than that of same-polarity stimuli over a wide range of spatial scales. At large separations, greater than about 5 sigma, spatial interval discrimination thresholds are more or less independent of both contrast and polarity. While hyperacuity is generally thought of in terms of the tiny spatial thresholds which are obtained at small separations with stimuli comprised of thin lines, the present results, and those of others, suggest that for same-polarity stimuli, hyperacuity thresholds are a general property of the visual system, occurring at many spatial scales. The present results also suggest that the poor localization of opposite-polarity lines occurs at multiple spatial scales, when the line separation is less than about five times the stimulus spread. We consider several models which can account for particular features of our data.