The psychophysical function of binocular space perception

Abstract

A psychophysical study of binocular space perception is conducted because our understanding about this psychological phenomenon is inadequate for several reasons. The traditional psychophysical function induces a dependency of apparent distance on apparent direction. However, it fails to capture the uniqueness of the visual origin, as opposed to the location of two eyes in physical space, and is highly irregular at the boundaries of visual space. All of these deficiencies may be attributed to the fact that the traditional psychophysical function was developed with the sole objective of fitting the data. A general postulate concerning the generic psychophysical function is presented first in order to introduce a psychologically meaningful invariance property. Invariance is defined as perceptability of rigid motion. The postulate amounts to the application of R. D. Luce's ((1959). On the possible psychophysical laws. Psychological Review, 66, 81–95) principle for “possible psychophysical laws,” weakened for non-Euclidean perceptual spaces. Second, the paper presents different possible psychophyscaal laws for binocular space perception. This presentation leads to ζ = √ z 2+ c 2, with z as the (complex-valued) stimulus localization, c as the (real-valued) interpupiliary distance of the subject, and ζ as the (complex-valued) localization in the visual plane. This function captures most of the empirical horopters in a qualitatively valid manner. Moreover, the function is shown to be a conformal map and thus satisfies the general principle of independence of apparent distance and apparent direction. Finally, the relationship among the laboratory plane, the visual plane, and Euclidean maps of the visual plane is discussed.