Measuring 3D point configurations in pictorial space

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. © 2011 J Wagemans, A J van Doorn, J J Koenderink.