Symmetry mediates the bootstrapping of 3-D relief slant to metric slant

Empirical studies have always shown 3-D slant and shape perception to be inaccurate as a result of relief scaling (an unknown scaling along the depth direction). Wang, Lind, and Bingham ( Journal of Experimental Psychology: Human Perception and Performance, 44 (10), 1508–1522, 2018 ) discovered that sufficient relative motion between the observer and 3-D objects in the form of continuous perspective change (≥45°) could enable accurate 3-D slant perception. They attributed this to a bootstrap process (Lind, Lee, Mazanowski, Kountouriotis, & Bingham in Journal of Experimental Psychology: Human Perception and Performance , 40 (1), 83, 2014 ) where the perceiver identifies right angles formed by texture elements and tracks them in the 3-D relief structure through rotation to extrapolate the unknown scaling factor, then used to convert 3-D relief structure to 3-D Euclidean structure. This study examined the nature of the bootstrap process in slant perception. In a series of four experiments, we demonstrated that (1) features of 3-D relief structure, instead of 2-D texture elements, were tracked (Experiment 1 ); (2) identifying right angles was not necessary, and a different implementation of the bootstrap process is more suitable for 3-D slant perception (Experiment 2 ); and (3) mirror symmetry is necessary to produce accurate slant estimation using the bootstrapped scaling factor (Experiments 3 and 4 ). Together, the results support the hypothesis that a symmetry axis is used to determine the direction of slant and that 3-D relief structure is tracked over sufficiently large perspective change to produce metric depth. Altogether, the results supported the bootstrap process.