Solomon Joshua A, Morgan Michael, Chubb Charles
Department of Optometry and Visual Science, City University London, UK.
J Vis. 2011 Oct 19;11(12):13. doi: 10.1167/11.12.13.
Different laboratories have achieved a consensus regarding how well human observers can estimate the average orientation in a set of N objects. Such estimates are not only limited by visual noise, which perturbs the visual signal of each object's orientation, they are also inefficient: Observers effectively use only √N objects in their estimates (e.g., S. C. Dakin, 2001; J. A. Solomon, 2010). More controversial is the efficiency with which observers can estimate the average size in an array of circles (e.g., D. Ariely, 2001, 2008; S. C. Chong, S. J. Joo, T.-A. Emmanouil, & A. Treisman, 2008; K. Myczek & D. J. Simons, 2008). Of course, there are some important differences between orientation and size; nonetheless, it seemed sensible to compare the two types of estimate against the same ideal observer. Indeed, quantitative evaluation of statistical efficiency requires this sort of comparison (R. A. Fisher, 1925). Our first step was to measure the noise that limits size estimates when only two circles are compared. Our results (Weber fractions between 0.07 and 0.14 were necessary for 84% correct 2AFC performance) are consistent with the visual system adding the same amount of Gaussian noise to all logarithmically transduced circle diameters. We exaggerated this visual noise by randomly varying the diameters in (uncrowded) arrays of 1, 2, 4, and 8 circles and measured its effect on discrimination between mean sizes. Efficiencies inferred from all four observers significantly exceed 25% and, in two cases, approach 100%. More consistent are our measurements of just-noticeable differences in size variance. These latter results suggest between 62 and 75% efficiency for variance discriminations. Although our observers were no more efficient comparing size variances than they were at comparing mean sizes, they were significantly more precise. In other words, our results contain evidence for a non-negligible source of late noise that limits mean discriminations but not variance discriminations.
不同实验室已就人类观察者对N个物体集合中平均方向的估计能力达成了共识。此类估计不仅受到视觉噪声的限制，视觉噪声会干扰每个物体方向的视觉信号，而且效率低下：观察者在估计时实际上仅有效利用了√N个物体（例如，S.C.达金，2001年；J.A.所罗门，2010年）。更具争议性的是观察者估计一组圆圈中平均大小的效率（例如，D.阿利利，2001年、2008年；S.C.钟、S.J.朱、T.-A.埃马努伊尔和A.特雷斯曼，2008年；K.米采克和D.J.西蒙斯，2008年）。当然，方向和大小之间存在一些重要差异；尽管如此，将这两种类型的估计与同一个理想观察者进行比较似乎是合理的。事实上，统计效率的定量评估需要这种比较（R.A.费希尔，1925年）。我们的第一步是测量仅比较两个圆圈时限制大小估计的噪声。我们的结果（对于84%正确的二项迫选任务表现，韦伯分数在0.07至0.14之间是必要的）与视觉系统向所有对数转换的圆圈直径添加相同量的高斯噪声一致。我们通过随机改变1、2、4和8个圆圈（未拥挤）阵列中的直径来夸大这种视觉噪声，并测量其对平均大小辨别能力的影响。从所有四位观察者推断出的效率显著超过25%，在两种情况下接近100%。我们对大小方差的恰可察觉差异的测量结果更具一致性。后一组结果表明方差辨别效率在62%至75%之间
