A stratified process for the perception of objects: From optical transformations to 3D relief structure to 3D similarity structure to slant or aspect ratio

Previously, we developed a stratified process for slant perception. First, optical transformations in structure-from-motion (SFM) and stereo were used to derive 3D relief structure (where depth scaling remains arbitrary). Second, with sufficient continuous perspective change (>= 45 degrees), a bootstrap process derived 3D similarity structure. Third, the perceived slant was derived. As predicted by theoretical work on SFM, small visual angle (< 5 degrees) viewing requires non-coplanar points. Slanted surfaces with small 3D cuboids or tetrahedrons yielded accurate judgment while planar surfaces did not. Normally, object perception entails non-coplanar points. Now, we apply the stratified process to object perception where, after deriving similarity structure, alternative metric properties of the object can be derived (e.g. slant of the top surface or width-to-depth aspect ratio). First, we tested slant judgments of the smooth planar tops of three different polyhedral objects. We tested rectangular, hexagonal, and asymmetric pentagonal surfaces, finding that symmetry was required to determine the direction of slant (AP&P, 2019, https://doi.org/10.3758/s13414-019-01859-5). Our current results replicated the previous findings. Second, we tested judgments of aspect ratios, finding accurate performance only for symmetric objects. Results from this study suggest that, first, trackable non-coplanar points can be attained in the form of 3D objects. Second, symmetry is necessary to constrain slant and aspect ratio perception. Finally, deriving 3D similarity structure precedes estimating object properties, such as slant or aspect ratio. Together, evidence presented here supports the stratified bootstrap process for 3D object perception. Statement of significance: Planning interactions with objects in the surrounding environment entails the perception of 3D shape and slant. Studying ways through which 3D metric shape and slant can be perceived accurately by moving observers not only sheds light on how the visual system works, but also provides understanding that can be applied to other fields, like machine vision or remote sensing. The current study is a logical extension of previous studies by the same authors and explores the roles of large continuous perspective changes, relief structure, and symmetry in a stratified process for object perception.