Does monocular visual space contain planes?

The issue of the existence of planes-understood as the carriers of a nexus of straight lines-in the monocular visual space of a stationary human observer has never been addressed. The most recent empirical data apply to binocular visual space and date from the 1960s (Foley, 1964). This appears to be both the first and the last time this basic issue was addressed empirically. Yet the question is of considerable conceptual interest. Here we report on a direct empirical test of the existence of planes in monocular visual space for a group of sixteen experienced observers. For the majority of these observers monocular visual space lacks a projective structure, albeit in qualitatively different ways. This greatly reduces the set of viable geometrical models. For example, it rules out all the classical homogeneous spaces (the Cayley-Klein geometries) such as the familiar Luneburg model. The qualitatively different behavior of experienced observers implies that the generic population might well be inhomogeneous with respect to the structure of visual space.