Large continuous perspective transformations are necessary and sufficient for accurate perception of metric shape

Abstract

524Object shape entails both qualitative and quantitative properties. On the one hand, shape entails relief structure or relative variations in the surface conformation (e.g., ellipsoidal vs. cylindrical). As has been described by Perotti, Todd, Lappin, and Phillips (1998), this characteristic of shape can be measured locally for smoothly curved surfaces by the shape characteristic, a ratio of the principal curvatures. On the other hand, metric shape can be measured by curvedness (Koenderink, 1990) or, alternatively, the ratio of an object's width to its depth. As has been reviewed by Todd, Tittle, and Norman (1995) and shown by Perotti et al. (1998), among many others (e.g., Brenner & van Damme, 1999;Lappin & Ahlström, 1994;Scarfe & Hibbard, 2006;Tittle, Todd, Perotti, & Norman, 1995;Todd & Norman, 1991), observers do not appear to be able to perceive metric shape, or the relative depth of objects, very accurately. Perotti et al. (1998), in particular, found that observers were well able to judge the shape characteristic but that judgments of curvedness were biased and highly variable. These studies involved structure from motion or stereo computer graphic displays of objects. Lind, Bingham, and Forsell (2003) asked observers to judge the shape of textured wooden cylinders-that is, actual objects that were about 7 cm in size. Aspect ratios (depth/width [D/W ]) between 0.46 and 1.81 were tested. Observers used binocular vision with free head movement in normal lighting, and the objects sat on a tabletop within reach distance, so that the tops of the objects could be seen. The participants adjusted the shape of an elliptical outline on a computer screen to match the perceived cross-sectional shape of each object. The results were much like those in Perotti et al. (1998). Judgments were highly variable and inaccurate. Lind et al. (2003) replicated the result with variations in viewing height and distance. The participants did not reliably begin to get it right until they were essentially looking straight down at the tops of the objects, so they could match their outline to the top edge of the cylinders appearing in a frontoparallel plane. It is clear that observers cannot judge metric shape under viewing conditions that allow only relatively small perspective variations ( 10º).There We investigated the ability to perceive the metric shape of elliptical cylinders. A large number of previous studies have shown that small perspective variations ( 10º) afforded by stereovision and by head movements fail to allow accurate perception of metric shape. If space perception is affine (Koenderink & van Doorn, 1991), observers are unable to compare or relate lengths in depth to frontoparallel lengths (i.e., widths). Frontoparallel lengths can be perceived correctly, whereas lengths in depth generally are not. We measured reaches to evaluate shape perception and investigated whether larger perspective variations would allow accurate perception of shape. In Experiment 1, we replicated previous results showing poor perception wi...

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