This paper considers shape constancy, which is a fundamental perceptual phenomenon. Shape constancy refers to the fact that the percept of the shape of a given object remains constant despite changes in the object's retinal image. The image may change because of changes in the orientation of the object relative to the observer. In conventional approaches based on the concept of groups of transformations, formulating a theory of shape constancy requires that a group that adequately represents the viewing conditions be identified first. As a results, a given theory holds only for the assumed group, and therefore many theories are needed, one theory for each viewing condition. It is conjectured that explaining shape constancy requires a new approach, in which one theory holds across different viewing conditions. In this new approach, shape constancy is explained by using geometrical properties of image formation under perspective. Image formation is not represented by a group of transformations, but it leads to a theory that is more general than prior theories it explains shape constancy in the case of monocular and binocular viewing for both the stationary and the active observer.
Zygmunt Pizlo, Zygmunt Pizlo,
"Concept of group and the theory of shape perception", Proc. SPIE 2411, Human Vision, Visual Processing, and Digital Display VI, (20 April 1995); doi: 10.1117/12.207552; https://doi.org/10.1117/12.207552