Ambiguity and the ‘Mental Eye’ in Pictorial Relief

Abstract

Photographs of scenes do not determine scenes in the sense that infinitely many different scenes could have given rise to any given photograph. In psychophysical experiments, observers have (at least partially) to resolve these ambiguities. The ambiguities also allow them to vary their response within the space of 'veridical' responses. Such variations may well be called 'the beholder's share' since they do not depend causally on the available depth cues. We determined the pictorial relief for four observers, four stimuli, and four different tasks. In all cases we addressed issues of reliability (scatter on repeated trials) and consistency (how well the data can be explained via a smooth surface, any surface). All data were converted to depth maps which allows us to compare the relief from the different operationalisations. As expected, pictorial relief can differ greatly either between observers (same stimulus, same task) or between operationalisations (same observer, same stimulus). However, when we factor out the essential ambiguity, these differences almost completely vanish and excellent agreement over tasks and observers pertains. Thus, observers often resolve the ambiguity in idiosyncratic ways, but mutually agree--even over tasks--in so far as their responses are causally dependent on the depth cues. A change of task often induces a change in 'mental perspective'. In such cases, the observers switch the 'beholder's share', which resolves the essential ambiguity through a change in viewpoint of their 'mental eye'.

Processing convexity and concavity along a 2-D contour: figure–ground, structural shape, and attention

“…It follows that, if neither is zero, they can both be positive (the surface is locally convex), both negative (locally concave), or one positive and one negative (saddle shaped). Koenderink (1984; see also Koenderink & van Doorn, 1982;Koenderink, van Doorn, Kappers, & Todd, Fig. 1 The C-shape on the left has a contour that changes in curvature, positive on the outside and negative on the inside.…”

A Perceptual-Statistics Shading Model

“…Summary: Koenderink and colleagues compared these three tasks [17]. Coherent results can be achieved across observers and tasks.…”

“…The works of Koenderink et al [17] and Todd [34] describe the three most frequently employed experiments for probing perceived surfaces.…”

Mirror-reflecting a picture of an object: What happens to the shape percept?

“…Previous research has shown that differences concerning depth maps between participants could be ruled out by affine transforming the depths of one participant into the depths of the other participant (Koenderink et al, 2001). We were curious whether affine regression would here, too, have more predictive power than just straight regression.…”

“…The shears between the pictorial reliefs of the original and the mirrored pictures obtained for the different participants can be compared by depicting them in a polar coordinate representation (Figure 8). In this figure, the global shear determined by the weights of the image coordinates in the regression model (see also Koenderink, van Doorn, Kappers, & Todd, 2001) is presented for each pose and for each participant. The shears for OR-LR are generally very small.…”