Bootstrapping a better slant: A stratified process for recovering 3D metric slant

Lind et al. (Journal of Experimental Psychology: Human Perception and Performance, 40 (1), 83, 2014) proposed a bootstrap process that used right angles on 3D relief structure, viewed over sufficiently large continuous perspective change, to recover the scaling factor for metric shape. Wang, Lind, and Bingham (Journal of Experimental Psychology: Human Perception and Performance, 44(10), 1508-1522, 2018) replicated these results in the case of 3D slant perception. However, subsequent work by the same authors (Wang et al., 2019) suggested that the original solution could be ineffective for 3D slant and presented an alternative that used two equidistant points (a portion of the original right angle). We now describe a three-step stratified process to recover 3D slant using this new solution. Starting with 2D inputs, we (1) used an existing structure-from-motion (SFM) algorithm to derive the object's 3D relief structure and (2) applied the bootstrap process to it to recover the unknown scaling factor, which (3) was then used to produce a slant estimate. We presented simulations of results from four previous experiments (Wang et al., 2018, 2019) to compare model and human performance. We showed that the stratified process has great predictive power, reproducing a surprising number of phenomena found in human experiments. The modeling results also confirmed arguments made in Wang et al. (2019) that an axis of mirror symmetry in an object allows observers to use the recovered scaling factor to produce an accurate slant estimate. Thus, poor estimates in the context of a lack of symmetry do not mean that the scaling factor has not been recovered, but merely that the direction of slant was ambiguous.