PII: S0042-6989(97)00002-3

When we view objects at various depths, the 3-D rotations of our two eyes are neurally yoked in accordance with a recently discovered geometric rule, here called the binocular extension of Listing's law; or L2. This paper examines the visual and motor consequences of this rule. Although L2 is a generalization of Listing's original, monocular law, it does not follow from current theories of the latter's function, which involve minimizing muscle work or optimizing certain aspects of retinal image flow. This study shows that a new optimization strategy that combines stereo vision with motor efficiency does explain L2, and describes the predictions of this new theory. Contrary to recent suggestions in the literature, L2 does not ensure vision of lines orthogonal to the visual plane, but rather reduces cyclodisparity of the visual plane itself; and L2 does not arise because a single, conjugate angular velocity command is sent to both eyes, but actually requires that the two eyes rotate with different speeds and axes when scanning an isovergence surface. This study shows that L2 is compatible with a 1-D control system for vergence alone (because horizontal and torsional vergence are yoked) and a 3-D system for combined, head-fixed saccades and vergence.

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