Pursuit of metric: Operations in 3d relief space enable perception of metric slant

Abstract

Perception of three-dimensional (3D) objects has been characterized in terms of relief structure, meaning the object’s frontoparallel dimension is perceived accurately while its depth is scaled by an unknown factor. Previous research has identified a bootstrap process, in which observers identify and track a right angle on an object through large continuous perspective change to recover the object’s width-to-depth aspect ratio accurately. In this dissertation, I aimed to apply the bootstrap process to account for 3D metric slant perception. In a series of six experiments, I made four claims. First, the bootstrap process requires relief structure. This was tested in the first and second experiments by using either strictly planar surfaces that lacked a fourth non-coplanar point required to produce relief structure or instead, surfaces with the requisite non-coplanar points to yield relief structure. Second, the bootstrap process does not require trackable 2D optical points but instead, uses trackable 3D relief structure, as shown in the second experiment where dynamic random dot displays yielded similar performance as those with trackable points. Third, the original right-angle solution is not suitable to account for recovering metric slant, as tested in the third experiment where symmetric hexagonal surfaces were used to eliminate right angles in the object. Fourth, symmetry aides the recovery of slant but perspective change aids the recovery of the scaling factor, as tested in the fourth experiment where asymmetric pentagonal surfaces were used and the fifth experiment where the hexagonal object’s symmetry axis was perturbed. Finally, the last experiment replicated these findings using 3D polyhedrons. I proposed an alternative solution to the bootstrap process that only requires identifying and tracking two equidistant points. I presented simulation results based on this new solution, which further confirmed the claims that were made.