Levi D M, Jiang B C, Klein S A
University of Houston, College of Optometry, TX 77004.
Vision Res. 1990;30(11):1735-50. doi: 10.1016/0042-6989(90)90156-f.
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.
我们使用相同极性和相反极性的高斯模糊线来测量模糊对三线空间间隔辨别（二等分）的影响。我们的实验结果可总结如下。空间间隔辨别（三线二等分）阈值与线的间距成正比（即韦伯定律）。在最佳间距下，相同极性线的空间间隔辨别阈值代表一种“超敏锐度”，小至2秒弧度。对于相同极性的高斯模糊线，在很宽的模糊标准差（sigma）范围内，当间距约为2 sigma时会出现最佳阈值，且最佳阈值约为0.02 sigma，或韦伯分数（δs/s）为0.01。对于相反极性的线，在相同极性刺激产生最佳阈值的条件下（间距约为2 sigma），空间间隔阈值比相同极性线的情况差一个数量级，这表明在很宽的空间尺度范围内，相反极性刺激的定位比相同极性刺激的定位差得多。在大于约5 sigma的大间距下，空间间隔辨别阈值或多或少与对比度和极性都无关。虽然超敏锐度通常是根据在小间距下由细线组成的刺激所获得的微小空间阈值来考虑的，但目前的结果以及其他研究结果表明，对于相同极性的刺激，超敏锐度阈值是视觉系统的一个普遍特性，在许多空间尺度上都会出现。目前的结果还表明，当线间距小于刺激扩散的约五倍时，相反极性线的定位不佳会在多个空间尺度上出现。我们考虑了几种可以解释我们数据特定特征的模型。
