Ambiguity in pictorial depth

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.