The internal representation of visually perceived three-dimensional shape: A test for metric structure on local surface patches
The internal visual representation (IR) of three-dimensional (3D) space is often assumed to share the Euclidean geometry of physical space, but this assumption has not yet been confirmed by experimental studies. Other work has lead various researchers to propose alternate (non-Euclidean) geometries or nonmetric frameworks for the IR of 3D space. The problem was considered here for the case of visually perceived 3D shape by examining the geometric properties implied by psychophysical judgements of spatial relationships on local 3D surface patches. A model was developed for the process of perceiving the distance between points on a surface. Within the model, perceived interpoint distance is derived from the combination of various intermediate spatial representations. The initial stages of processing result in separate representations of retinal separation and surface shape. The metric extent of spatial intervals corresponding to retinal separation and depth change are made commensurable by scaling according to perceived parameters of the viewing geometry. The length of the 3D separation of two points is then derived from the norm of the vector with metric components of width and depth difference. The effects of both systematic and randoms errors (bias and variability) were included. The model provided a framework for analyzing data provided by observers comparing distances between pairs of points on the surfaces of 3D objects. Stimuli were computer graphics simulations of shapes portrayed by texture, shading, and binocular disparity cues. Psychophysical performance was consistent with an IR having metric structure. Within the family of Minkowski geometric norms, the empirical metric was consistently different than Euclidean, although not significantly so. Bias indicated that percepts were generally distorted due to several sources of geometric information. Variability was consistent with a process that combines information from several intermediate representations, each with moderate sensitivity following Weber's Law.
0633: Cognitive therapy