Mathematical requirements of visual-vestibular integration.

This article addresses the intersection between perceptual estimates of head motion based on purely vestibular and purely visual sensation, by considering how nonvisual (e.g. vestibular and proprioceptive) sensory signals for head and eye motion can be combined with visual signals available from a single landmark to generate a complete perception of self-motion. In order to do this, mathematical dimensions of sensory signals and perceptual parameterizations of self-motion are evaluated, and equations for the sensory-to-perceptual transition are derived. With constant velocity translation and vision of a single point, it is shown that visual sensation allows only for the externalization, to the frame of reference given by the landmark, of an inertial self-motion estimate from nonvisual signals. However, it is also shown that, with nonzero translational acceleration, use of simple visual signals provides a biologically plausible strategy for integration of inertial acceleration sensation, to recover translational velocity. A dimension argument proves similar results for horizontal flow of any number of discrete visible points. The results provide insight into the convergence of visual and vestibular sensory signals for self-motion and indicate perceptual algorithms by which primitive visual and vestibular signals may be integrated for self-motion perception.