Abstract
We propose a novel method to probe the depth structure of the pictorial space evoked by paintings. The method involves an exocentric pointing paradigm that allows one to find the slope of the geodesic connection between any pair of points in pictorial space. Since the locations of the points in the picture plane are known, this immediately yields the depth difference between the points. A set of depth differences between all pairs of points from an N-point (N > 2) configuration then yields the configuration in depth up to an arbitrary depth offset. Since an N-point configuration implies N(N−1) (ordered) pairs, the number of observations typically far exceeds the number of inferred depths. This yields a powerful check on the geometrical consistency of the results. We report that the remaining inconsistencies are fully accounted for by the spread encountered in repeated observations. This implies that the concept of ‘pictorial space’ indeed has an empirical significance. The method is analyzed and empirically verified in considerable detail. We report large quantitative interobserver differences, though the results of all observers agree modulo a certain affine transformation that describes the basic cue ambiguities. This is expected on the basis of a formal analysis of monocular optical structure. The method will prove useful in a variety of potential applications.
Highlights
'Pictorial space' is experienced when one looks into a picture, say a photograph or a 'realistic' drawing or painting
What is the structure of pictorial space P? two of its three dimensions are explained by the visual field
Pictorial space P is a 'fiber bundle' E2 × A—that is, the visual field augmented by the depth domain
Summary
'Pictorial space' is experienced when one looks into a picture, say a photograph or a 'realistic' drawing or painting. From a formal perspective, the structure of the Euclidean plane is induced by its group of similarities, a four-parameter group (one degree of freedom by scaling, two by translation, and one by rotation). From a technical perspective the 'proper motions' of the depth domain are arbitrary linear transformations of positive signature This has been recognized by visual artists for ages, and it was made explicit by the German sculptor Hildebrand (1901) at the end of the 19th century. Pictorial space P is a 'fiber bundle' E2 × A—that is, the visual field augmented by the depth domain. This lack of mixing vetoes periodic rotations different from those of the visual field proper It ascertains that you can never see the backsides of pictorial objects. It is very different from Euclidean three space, there are many similarities (Jaglom 1979; Sachs 1990; Strubecker 1941)
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call