Theoretical analysis of binocular space perception

Abstract

A formalism is developed for dealing with the mapping of physical configurations onto the retinae and into the visual cortex. In this context we discuss the Luneburg-Blank theory of binocular vision, its range of validity and some of its basic difficulties. It is shown that Vieth-Müller circles and Hillebrand hyperbolae can be characterized by the invariance under shifting fixation and bihemispherical symmetry of their neural counterparts. This property justifies the use of a coordinate system based on these two families of curves and a corresponding polar coordinate system in visual space. We derive the complete set of curves in the horizontal plane which project onto the same neural units under change of fixation. Their significance lies in shewing that there exists only a restricted set of configurations which can have invariant neural representations and that the Vieth-Muller circles and Hillebrand hyperbolae are a subclass of this set. The implications for pattern recognition are treated in a separate paper.