Journal of mathematical psychology vol:38 issue:1 pages:59-72
Starting with Shepard and Cooper's seminal work on the perception of rotated and/or reflected 2D and 3D patterns, a series of chronometric studies have been published about the matching of visual patterns with respect to shape, regardless of differences in size or orientation. These studies are restricted to the group of Euclidean geometry. Using random polygons, we extended this research to the group of affine transformations. From the total group defined by four parameters, subgroups were made by different parameterizations of the basic matrix (e.g., holding some parameters constant or giving them 0 and 1 values). A subgroup on level l is defined as the smallest subgroup enclosing two subgroups of a lower level l - 1. In this manner, a hierarchical model with five levels is constructed with the total group at the top and the identity at the bottom. The detectability of the different transformations, as measured with reaction times in a Same/Different paradigm, was investigated to evaluate the psychological plausibility of this mathematical model. More specifically, we were interested in finding out which of all mathematically equivalent paths described best human visual perception of orthographically projected planar random polygons. Going from the top of the model to the bottom, significant differences were obtained by (1) removing the skewing in the Y-direction, (2) removing the scaling in the Y-direction, and (3) removing the skewing in the X-direction, respectively. (C) 1994 Academic Press, Inc.