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

We investigated the ability to perceive the metric shape of elliptical cylinders. A large number of previous studies have shown that small perspective variations (#10°) 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 with small perspective variations. In Experiment 2, we found that a 90° continuous change in perspective, which swapped depth and width, allowed accurate perception of the depth/width aspect ratio. In Experiment 3, we found that discrete views differing by 90° were insufficient to allow accurate perception of metric shape and that perception of a continuous perspective change was required. In Experiment 4, we investigated continuous perspective changes of 30°, 45°, 60°, and 90° and discovered that a 45° change or greater allowed accurate perception of the aspect ratio and that less than this did not. In conclusion, we found that perception of metric shape is possible with continuous perspective transformations somewhat larger than those investigated in the substantial number of previous studies.