On the relative detectability of configural properties.

A match-to-sample shape-discrimination task was employed to measure the detectability of different types of transformations. To create the foils for this task, the standard object could be altered by adding a small hole (a topological property), adding small bumps to straight edges (a projective property), changing the relative orientations of parallel contours (an affine property), or stretching the standard object to alter its aspect ratio (a Euclidean property). The results revealed that the relative perceptual salience of different types of shape change is consistent with the Klein hierarchy of geometries. That is to say observers were most sensitive to changes in topological structure, followed by changes in projective, affine, and Euclidean structure, respectively. The predicted patterns of performance among the different conditions were computed using a wide variety of commonly used shape-difference metrics, but none of them had a significant positive correlation with the observers' thresholds.