On the Psychophysics of Binocular Visual Space

Binocular vision gives rise to a perceptual space that is endowed with a rich geometrical structure, which according to Luneburg [1947 Mathematical Analysis of Binocular Vision (Princeton, NJ: Princeton University Press)] is a non-Euclidean Riemannian geometry of constant curvature. This hypothesis, together with certain psychophysical assumptions, provides a qualitative explanation of classical empirical phenomena. The Luneburg theory has been less successful in quantitatively predicting individual data, a fact that has sometimes been taken as evidence against the presumed geometrical structure. Some of these shortcomings, however, may also be attributed to psychophysical assumptions that do not depend on the geometry of visual space. The locus of perceived egocentric equidistance, for example, has been found to deviate systematically from the Vieth-Müller circle postulated by Luneburg (eg Foley, 1966 Journal of the Optical Society of America 56 822 – 827).

To account for these findings a generalisation of Luneburg's psychophysical mapping is proposed that actually realises his original intentions. Because of the theoretical basis of its measurement, the adequacy of this general psychophysical frame of reference may be empirically tested. The results of an experimental test of one of the key conditions, which strongly support the presented theory, are reported. It is also shown that psychophysical invariances lead to restrictions on the possible form of the psychophysical mapping, and the approach is discussed from the viewpoint of retinal correspondence.