The visuomotor transformation for arm movement accounts for 3-D eye orientation and retinal geometry.

Abstract

To point or reach to a visual target, you need to know its direction relative to your shoulder. That direction can be computed from the retinal image, if the brain also knows the orientation of the eyeball, head, and clavicle. To be geometrically exact, the neural computation would have to involve rotary operations.1 When the eye was turned 30° up, for instance, the brain would take the locations of all objects relative to the eye and rotate them 30° down to find the locations relative to the head. Some theories2,3,5–7 suggest that the brain might approximate that rotation by a simpler vector addition, merely shifting all retinal locations by the same vector. But that strategy would lead to marked errors in some situations. FIGURE 1A shows five earthfixed, horizontal arcs wrapped around a cylinder centered on an eyeball. In front of the eye are two spheres and 90° to the right are two cubes, one sphere-cube pair at eye level and the other 30° up. When the eye fixates the eye-level sphere, the retinal image of the eye-level cube falls on the eye’s horizontal meridian (FIG. 1B). But when the eye fixates the sphere at 30° up, the retinal image of the corresponding cube falls well below the horizontal meridian (FIG. 1C). That is, both pairs of spheres and cubes are horizontally separated, but in one case their retinal images are not, owing to the rotation of the eye. If the brain tried to compute these objects’ locations relative to the head or the shoulder simply by shifting all their retinal locations by a fixed vector, it would misestimate the elevations of at least some objects, and would misaim its eye and arm movements. Here we study whether the visuomotor transformation for arm movements uses a vector-additive strategy or correctly accounts for the rotary geometry of retinal projection.