van de Grind W A, Erkelens C J, Laan A C
Helmholtz Institute, Utrecht, The Netherlands.
Perception. 1995;24(2):215-35. doi: 10.1068/p240215.
Two classic theories of direction vision, one by Hering, the other by Wells, are expressed in mathematical form and compared. The Hering disparity field differs considerably from the Wells disparity field, but if both are scaled for the change of acuity with eccentricity their differences are much more subtle. This explains why it is hard to determine which theory predicts direction perception best, although the tests favour Hering's theory. It is proved that Wells's construction (his rule 3) follows directly from his first two rules and Aguillonius's assumption that the horopter in the fixation plane is a frontoparallel line. Wells's theory is clearly outdated and does not mesh well with modern three-dimensional geometry of binocular vision, which Hering's theory does. Moreover, Wells inextricably mixes distance and direction vision right from the start, whereas Hering properly treats the two-dimensional manifold of directions and the depth-gauging principles separately. The use of terms such as 'Wells-Hering' rules should be discouraged and both Wells and Hering should be remembered separately for their clearly distinct and independent contributions. The work of Hering is still relevant to modern theory and praxis of binocular vision. The extension of Hering's approach to vertical disparities is treated for stimuli in frontoparallel planes. It is shown that acuity-scaled vertical-disparity information sampled at a single glance is below resolution beyond about arm's length. It can only be used if eye movements are allowed. Throughout, the simplest derivations of the geometrical relations that it was possible to find are given, so that the review of binocular geometry might also be of some didactical use. Finally it is indicated in which direction it might be necessary to modernise the concept of binocular correspondence.
方向视觉的两种经典理论，一种由赫林提出，另一种由韦尔斯提出，以数学形式表述并进行了比较。赫林视差场与韦尔斯视差场有很大不同，但如果两者都针对视敏度随偏心率的变化进行缩放，它们的差异就会更加细微。这就解释了为什么尽管测试倾向于赫林的理论，但很难确定哪种理论能最好地预测方向感知。证明了韦尔斯的构造（他的规则3）直接源于他的前两条规则以及阿吉洛尼乌斯关于注视平面中的双眼单视界是一条额状平行线的假设。韦尔斯的理论显然已经过时，与现代双眼视觉的三维几何不相符，而赫林的理论则相符。此外，韦尔斯从一开始就将距离视觉和方向视觉紧密地混在一起，而赫林则正确地分别处理二维方向流形和深度测量原理。应避免使用诸如“韦尔斯 - 赫林”规则之类的术语，应分别记住韦尔斯和赫林各自清晰独特且独立的贡献。赫林的工作在现代双眼视觉理论和实践中仍然具有相关性。针对额状平行平面中的刺激，探讨了赫林方法在垂直视差方面的扩展。结果表明，在大约一臂距离之外，一眼采样的经视敏度缩放的垂直视差信息低于分辨率。只有在允许眼球运动的情况下才能使用。自始至终，都给出了可能找到的几何关系的最简单推导，以便对双眼几何的综述也可能具有一定的教学用途。最后指出了在哪些方向上可能需要使双眼对应概念现代化。
