Journal of Mathematical Psychology 43, 71101 (1999) Functional Equations in Binocular Space Perception Janos Aczel University of Waterloo Zoltan Boros L. Kossuth University Jurgen Heller Universitat Regensburg and Che Tat Ng University of Waterloo A general theory of the relationship of binocular visual space to physical space is formulated within a conjoint measurement framework. Psychophysi- cally motivated invariance relations induce various functional equations. Another class of functional equations arises if we additionally assume the validity of a different psychophysical theory that is based on a formula suggested by A. A. Blank. We solve and interpret most of these equations and point out an unsolved problem. The obtained results lead to a measurement-theoretic foundation of the psychophysical assumptions underlying the Luneburg theory of binocular vision. They also contribute to clarifying the relationship between the presented general theory and Blank's approach.  1999 Academic Press 1. BACKGROUND We perceive ourselves located in a unitary and stable perceptual space. The so-called visual space is distinguished from other perceptual spaces by its compelling phenomenological reality and its undoubted spatial character. In a highly sophisticated approach, Luneburg (1947) embodied visual space in a geometrically formulated perceptual theory. The Luneburg theory of binocular vision not only provides a geometrical characterization of the internal structure of visual space but also Article ID jmps.1998.1224, available online at http:www.idealibrary.com on 71 0022-249699 30.00 Copyright  1999 by Academic Press All rights of reproduction in any form reserved. Reprint requests should be addressed to Dr. Jurgen Heller, Institut fur Psychology, Universitat Regensburg, D-93040 Regensburg, Germany. E-mail: juergen.hellerpsychologie.uni-regensburg.de.