Perspective and perception: vision and touch

图片是我们交流信息最有效的方式之一。但它们的用途仍然是神秘的，它们的潜力仍然未知。我们如何感知和表现三维空间？值得注意的是，不仅仅是有视力的人，盲人也用透视法来解决这个问题。但如何?视觉和触觉都必须有一种方式来响应透视图像的特征。视觉在估计地面中距离物体的形状时往往是正确的。但是，自从透视的几何学被首次提出以来，人们就很明显地发现，感知所能处理的透视图像存在着惊人的局限性。远处地板上的瓷砖看起来很粗。图片侧面的瓷砖看起来很拉伸；也就是说，在完美透视图的边缘，形状显得扭曲，高度膨胀。这就是为什么日常使用的相机只包含窄角镜头，而不是广角镜头，因为广角镜头会显示边缘扭曲。这些影响可能都是由于感知对预缩的低估造成的。同样的效果也可能发生在触觉和视觉上，当蒙住双眼和真正失明的人指着一排逐渐远去的物体时。

Pictures are one of our most effective ways to communicate information. But their uses remain mysterious and their potential is still unknown. How do we perceive and represent 3D space? Remarkably, blind people use perspective to solve this problem, not just the sighted. But how? Both vision and touch must have a way of responding to the features of perspective pictures. Vision is often correct in estimating the shape of middle-distance objects sitting on the ground. But since the geometry of perspective was first devised it has been obvious that there are striking limits to the perspective pictures that perception can handle. Distant tiles on a floor can look stubby. Tiles on the sides of pictures can look very stretched; that is, on the margins of perfect perspective pictures, forms appear distorted, highly distended. This is why cameras for everyday only use contain narrow-angle lenses, not wide-angle lenses that reveal the marginal distortions. These effects may all be caused by perception's underestimation of foreshortening. The same effects may occur in touch, as well as vision, as sighted-blindfolded and truly blind people point to a row of objects receding into the distance.