Stimulus configuration and the perceived rigidity of eight-vertex polyhedra

Abstract

In a series of four experiments, subjects examined the perceived rigidity of rotating eight-vertex polyhedra. Four different categories of polyhedra were observed under parallel projection: (1) line drawings where the initial orientation appeared to be a cube (LN), though the depth components of the eight vertices were randomly positioned (upon rotation, it could be seen that the stimuli were not cubes); (2) line drawings where the vertices were randomly placed (LR); (3) vertex-only drawings where the initial orientation appeared to be a cube (VN), though the depth components of the eight vertices were randomly positioned; and (4) vertex-only drawings with randomly positioned vertices (VR). Preliminary observations indicated that some of the mathematically rigid configurations were perceived as deforming in a nonrigid manner. Given the different stimulus categories, the following questions were addressed: (1) Could subjects identify stimuli that appeared to deform based on a large set of mathematically rigid objects?; and (2) Was it possible to identify gross qualities about the stimulus that control whether or not the human visual system adopts a rigid versus a nonrigid interpretation? Through several deformation-rating tasks, the results indicated that although most of the configurations maintained a rigid appearance throughout their rotations, the LN stimuli appeared to deform more than the LR, VN, and VR categories of stimuli. In addition, based on a signal detection paradigm, when subjects were asked to detect a physical nonrigidity embedded within mathematically rigid rotations, they had a more difficult time doing so when viewing the LN stimuli, compared to the other three stimulus categories. To account for these findings, a theory was formulated based on the behavior of line segments as they are projected onto the two-dimensional image plane. It seems that when the visual system is forced to interpret such images, two conflicting sources of information may exist: local shape cues formed by the intersecting line segments and motion-induced depth information. In order for the visual system to make sense of these images, the conflicting cues need to be driven into agreement with one another, via the adoption of a nonrigid interpretation