Battu Balaraju, Kappers Astrid M L, Koenderink Jan J
Physics of Man, Helmholtz Institute, Utrecht University, The Netherlands.
Perception. 2007;36(9):1290-304. doi: 10.1068/p5591.
Pictorial space is the 3-D impression that one obtains when looking 'into' a 2-D picture. One is aware of 3-D 'opaque' objects. 'Pictorial reliefs' are the surfaces of such pictorial objects in 'pictorial space'. Photographs (or any pictures) do in no way fully specify physical scenes. Rather, any photograph is compatible with an infinite number of possible scenes that may be called 'metameric scenes'. If pictorial relief is one of these metameric scenes, the response may be considered 'veridical'. The conventional usage is more restrictive and is indeed inconsistent. Thus the observer has much freedom in arriving at such a 'veridical' response. To address this ambiguity, we determined the pictorial reliefs for eight observers, six pictures, and two psychophysical methods. We used 'methods of cross-sections' to operationalise pictorial reliefs. We find that linear regression of the depths of relief at corresponding locations in the picture for different observers often lead to very low (even insignificant) R2s. Thus the responses are idiosyncratic to a large degree. Perhaps surprisingly, we also observed that multiple regression of depth and picture coordinates at corresponding locations often lead to very high R2s. Often R2s increased from insignificant up to almost 1. Apparently, to a large extent 'depth' is irrelevant as a psychophysical variable, in the sense that it does not uniquely account for the relation of the response to the pictorial structure. This clearly runs counter to the bulk of the literature on pictorial 'depth perception'. The invariant core of interindividual perception proves to be of an 'affine' rather than a Euclidean nature; that is to say, 'pictorial space' is not simply the picture plane augmented with a depth dimension.
图像空间是人们在“审视”二维图片时所获得的三维印象。人们能感知到三维的“不透明”物体。“图像浮雕”是指在“图像空间”中此类图像物体的表面。照片（或任何图片）都无法完整地呈现物理场景。相反，任何一张照片都与无数可能的场景相匹配，这些场景可被称为“同色异谱场景”。如果图像浮雕是这些同色异谱场景之一，那么相应的反应可被视为“真实的”。传统用法更为严格，实际上也并不一致。因此，观察者在得出这种“真实的”反应时具有很大的自由度。为了解决这种模糊性，我们针对八名观察者、六张图片以及两种心理物理学方法确定了图像浮雕。我们采用“横截面法”来实现图像浮雕的操作化。我们发现，对于不同观察者，图片中相应位置的浮雕深度进行线性回归时，所得的决定系数（R2）往往非常低（甚至不显著）。因此，这些反应在很大程度上是因人而异的。也许令人惊讶的是，我们还观察到，在相应位置对深度和图片坐标进行多重回归时，往往会得到非常高的R2值。通常，R2值会从不显著增加到几乎为1。显然，从心理物理学变量的角度来看，在很大程度上“深度”是无关紧要的，因为它并不能唯一地解释反应与图像结构之间的关系。这显然与关于图像“深度感知”的大量文献相悖。个体间感知的不变核心被证明具有“仿射”而非“欧几里得”性质；也就是说，“图像空间”并非简单地在图像平面上增加一个深度维度。
