Mitchell R, Power R P
Perception. 1983;12(4):375-92. doi: 10.1068/p120375.
Three studies of apparent reversals (ARs) in rotating rectangular and trapezoid arrays are reported, together with a mathematical analysis. Study 1 explores the effect of different degrees of outline suppression on the frequency and distribution of ARs in squares and trapezia. Study 2 examines how modifications in both types of array reduce AR frequency, demonstrates a manipulation whereby ARs in rotating squares are eliminated, and suggests that ARs in squares and trapezia are of different origins. In the mathematical analysis, an invariant characteristic of the transformations of rotating rectangles is reported, and from this a numerical index is developed that expresses the extent to which a rotating trapezium may appear to pause just before each point of oscillation. In study 3 it is shown that this measure is a better predictor of AR frequencies than the heuristic proposed by Braunstein.
本文报告了三项关于旋转矩形和梯形阵列中明显反转（ARs）的研究，并进行了数学分析。研究1探讨了不同程度的轮廓抑制对正方形和梯形中ARs频率和分布的影响。研究2考察了两种阵列的修改如何降低AR频率，展示了一种消除旋转正方形中ARs的操作，并表明正方形和梯形中的ARs起源不同。在数学分析中，报告了旋转矩形变换的一个不变特征，并据此开发了一个数值指标，该指标表示旋转梯形在每次振荡点之前可能出现暂停的程度。在研究3中表明，该测量方法比布劳恩施泰因提出的启发式方法能更好地预测AR频率。
