On the relative salience of Euclidean, affine, and topological structure for 3-D form discrimination

A match-to-sample task was performed, in which observers compared configurations of line segments presented stereoscopically in different three-dimensional orientations. Several different structural properties of these configurations were manipulated, including the relative orientations of line segments (a Euclidean property), their coplanarity (an affine property), and their patterns of cointersection (a topological property). Although the differences in these properties to be detected were all metrically equivalent, they varied dramatically in their relative perceptual salience, such that the error rates and reaction times in the three conditions varied by as much as 400%. Performance was highest in the topological condition, intermediate in the affine condition, and lowest in the Euclidean condition. These findings suggest that the relative perceptual salience of object properties may be systematically related to their structural stability under change, in a manner that is similar to the Klein hierarchy of geometries.