Monocentric Optical Space

摘要

The objective content of the visual world of a monocular, immobile observer is entirely due to "monocular cues". These cues only partially constrain the geometry, the remaining ambiguities define a freedom of the observer to commit "mental changes of viewpoint". Though fully idiosyncratic, such changes cannot possibly violate the optical data. We use this group of "visual congruences" (for that they must be) to deduce the geometry of monocentric visual space. Visual space is a homogeneous, flat non-Euclidean space. Homogeneity implies that the space admits of a group of isometries (the aforementioned cue ambiguities) or "free mobility of rigid configurations". Thus visual space is the same near any one of its points. The theory has many applications, among more in the rendering of scenes at inappropriate sizes as is typical in printing.