Direct measurement of the curvature of visual space
Direct measurement of the curvature of visual space
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DOI：
10.1068/p2921
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发表时间：
2000-01-01
期刊：
影响因子：
1.7
通讯作者：
Lappin, JS
中科院分区：
文献类型：
--
作者：
Koenderink, JJ;van Doorn, AJ;Lappin, JS
我们考虑眼高处的水平面，即在地平线上看到的所有物体。虽然这个平面在视觉上退化为视野中的一条线，但“深度”维度仍然赋予它二维结构。我们解决这个平面的内禀曲率的问题。经典的几何方法是基于高斯的原始定义：三角形中的角余等于三角形面积上的积分曲率。角度直接测量的一种新的方法，偏心指向。实验在室外、自然环境中、自然观察条件下进行。观察者被指示不要从设定的位置移动并保持眼睛高度，但可以自由地进行眼睛、头部和身体运动。我们测量了等边三角形的角过剩，边长为2-20米，在重心的Vantage位置。我们发现角度的过度和赤字高达30度，从这些数据，我们构建了度量。曲率从近空间的椭圆形变为远空间的双曲线。在很大的距离上，平面变成抛物线形。
We consider the horizontal plane at eye height, that is all objects seen at the horizon. Although this plane visually degenerates into a line in the visual field, the 'depth' dimension nevertheless gives it a two-dimensional structure. We address the problem of intrinsic curvature of this plane. The classical geometric method is based on Gauss's original definition: The angular excess in a triangle equals the integral curvature over the area of the triangle. Angles were directly measured by a novel method of exocentric pointing. Experiments were performed outside, in the natural environment, under natural viewing conditions, The observers were instructed not to move from a set location and to maintain eye height, but were otherwise free to perform eye, head, and body movements. We measured the angular excess for equilateral triangles with sides of 2-20 m, the vantage position at the barycenter. We found angular excesses and deficits of up to 30 degrees, From these data we constructed the metric. The curvature changes from elliptic in near space to hyperbolic in far space. At very large distances the plane becomes parabolic.