Local shape of pictorial relief

How is pictorial relief represented in visual awareness? Certainly not as a "depth map," but perhaps as a map of local surface attitudes (Koenderink & van Doorn, 1995). Here we consider the possibility that observers might instead, or concurrently, represent local surface shape, a geometrical invariant with respect to motions. Observers judge local surface shape, in a picture of a piece of sculpture, on a five-point categorical scale. Categories are cap-ridge-saddle-rut-cup-flat, where "flat" denotes the absence of shape. We find that observers readily perform such a task, with full resolution of a shape index scale (cap-ridge-saddle-rut-cup), and with excellent self-consistency over days. There exist remarkable inter-observer differences. Over a group of 10 naive observers we find that the dispersion of judgments peaks at the saddle category. There may be a relation of this finding to the history of the topic-Alberti's (1827) omission of the saddle category in his purportedly exhaustive catalog of local surface shapes.