Curvature of visual space under vertical eye rotation: implications for spatial vision and visuomotor control

Most models of spatial vision and visuomotor control reconstruct visual space by adding a vector representing the site of retinal stimulation to another vector representing gaze angle. However, this scheme fails to account for the curvatures in retinal projection produced by rotatory displacements in eye orientation. In particular, our simulations demonstrate that even simple vertical eye rotation changes the curvature of horizontal retinal projections with respect to eye-fixed retinal landmarks. We confirmed the existence of such curvatures by measuring target direction in eye coordinates in which the retinotopic representation of horizontally displaced targets curved obliquely as a function of vertical eye orientation. We then asked subjects to point (open loop) toward briefly flashed targets at various points along these lines of curvature. The vector-addition model predicted errors in pointing trajectory as a function of eye orientation. In contrast, with only minor exceptions, actual subjects showed no such errors, showing a complete neural compensation for the eye position-dependent geometry of retinal curvatures. Rather than bolstering the traditional model with additional corrective mechanisms for these nonlinear effects, we suggest that the complete geometry of retinal projection can be decoded through a single multiplicative comparison with three-dimensional eye orientation. Moreover, because the visuomotor transformation for pointing involves specific parietal and frontal cortical processes, our experiment implicates specific regions of cortex in such nonlinear transformations.