Perception of growth: a geometric analysis of how different styles of change are distinguished

Although there have been many demonstrations that human observers can accurately recognize a variety of styles of change, such as rolling, walking, or growing, there are no existing theories capable of explaining how one style of change is distinguished from another. The present article offers a hypothesis that any recognizable style of change is uniquely specified by geometric invariants- the abstract properties of a visual display that are preserved by the change. In an effort to provide an empirical test of this hypothesis, several experiments involving the perception of growth were performed. Observers were required to make perceptual judgments of consequences of facial profiles, each of which was constructed by using a different mathematical transformation. The same pattern of results was obtained on both a free response task and a growth rating task: All transformations that were consistently identified as growth preserved the same geometric invariants.