Affine operations plus symmetry yield perception of metric shape with large perspective changes (≥ 45°): data and model.

G. P. Bingham and M. Lind (2008, Large continuous perspective transformations are necessary and sufficient for accurate perception of metric shape, Perception & Psychophysics, Vol. 70, pp. 524–540) showed that observers could perceive metric shape, given perspective changes ≥45° relative to a principal axis of elliptical cylinders. In this article, we tested (a) arbitrary perspective changes of 45°, (b) whether perception gradually improves with more perspective change, (c) speed of rotation, (d) whether this works with other shapes (asymmetric polyhedrons), (e) different slants, and (f) perspective changes >45°. Experiment 1 compared 45° perspective change away from, versus centered on, a principal axis. Observers adjusted an ellipse to match the cross-section of an elliptical cylinder viewed in a stereo-motion display. Experiment 2 tested whether performance would improve gradually with increases in perspective change, or suddenly with a 45° change. We also tested speed of rotation. Experiment 3 tested (a) asymmetric polyhedrons, (b) perspective change beyond 45°, and (c) the effect of slant. The results showed (a) a particular perspective was not required, (b) judgments only improved with ≥45° change, (c) speed was not relevant, (d) it worked with asymmetric polyhedrons, (e) slant was not relevant, and (f) judgments remained accurate beyond 45° of change. A model shows how affine operations, together with a symmetry yielded by 45° perspective change, bootstrap perception of metric shape.