Anticipating the three-dimensional consequences of eye movements

doi:10.1073/pnas.0409241102

Anticipating the three-dimensional consequences of eye movements

Mark Wexler*

Laboratoire de Physiologie de la Perception et de l'Action, Centre National de la Recherche Scientifique, Collège de France, 11 Place Marcelin Berthelot, 75005 Paris, France

Communicated by Richard M. Held, Massachusetts Institute of Technology, Cambridge, MA, December 13, 2004 (received for review February 16, 2004)

Abstract

Rapid eye movements called saccades give rise to sudden, enormous changes in optic information arriving at the eye; how the world nonetheless appears stable is known as the problem of spatial constancy. One consequence of saccades is that the directions of all visible points shift uniformly; directional or 2D constancy, the fact that we do not perceive this change, has received extensive study for over a century. The problems raised by 3D consequences of saccades, on the other hand, have been neglected. When the eye rotates in space, the 3D orientation of all stationary surfaces undergoes an equal-and-opposite rotation with respect to the eye. When presented with a an optic simulation of a saccade but with the eyes still, observers readily perceive this depth rotation of surfaces; when simultaneously performing the corresponding saccade, the 3D orientations of surfaces are perceived as stable, a phenomenon I propose calling 3D spatial constancy. In experiments presented here, observers viewed ambiguous 3D rotations immediately before, during, or after a saccade. The results show that before the eyes begin to move the brain anticipates the 3D consequences of saccades, preferring to perceive the rotation opposite to the impending eye movement. Further, the anticipation is absent when observers fixate while experiencing optically simulated saccades, and therefore must be evoked by extraretinal signals. Such anticipation could provide a mechanism for 3D spatial constancy and transsaccadic integration of depth information.

Footnotes

↵ * E-mail: wexler{at}ccr.jussieu.fr.
Author contributions: M.W. designed research, performed research, analyzed data, and wrote the paper.
Abbreviations: FP, fixation point; SfM, structure from motion; SO, stimulus onset; PSML, perisaccadic mislocalization.
↵ † The term depth rotation refers to a rotation about an axis in the image plane, perpendicular to the direction of gaze. Because according to Listing's law, which is approximately true, the eye also rotates about an axis this plane, relative rotations between stationary surfaces and the eye will be (mostly) depth rotations.
↵ ‡ This demonstration can be refined in several ways. First, instead of showing just two frames, the camera can be made to follow a typical saccadic trajectory. Second, the observer should be placed so that the angular displacement of the images equals the camera rotation. Third, the images should cover as large a part of the visual field as possible. Finally, one should eliminate static borders and any other stationary objects in the visual field that might lead to a perception of relative rotation. With or without these refinements, observers report strong perceptions of surface rotations in simulated saccades.
↵ § Slant and tilt are a common way of parametrizing the orientation of a plane. Slant is the magnitude of the plane`s inclination from the frontoparallel; tilt is the projected direction of that inclination. For example, the surface in Fig. 2c has tilt 0°, whereas the one in Fig. 2d has tilt 180°, and the two have equal slant.
↵ ¶ There are two solutions in the space of possible tilts. If the solution space is extended to the full surface normal (tilt and slant), there is an infinite number of solutions in parallel projection or in the limit of small stimuli, because optic flow depends only on the product ω tan σ, with ω the angular speed and σ the surface slant. See ref. 35 for further details.
↵ ∥ Although a more complicated error pattern also has been reported (18), it only seems to hold in the case of a visible background (19), unlike the experiments reported here.