Abstract
Stereopsis is 3-D vision that results from small differences (disparities) between the image patterns formed on the retinas of our eyes. In spite of having two physical vantage points, the two eyes, the general belief is that we judge direction from a hypothetical eye, called the cyclopean eye. In this concept, depth and direction are treated as independent dimensions that can be studied in separation. Visual directions have mainly been investigated in alignment tasks. These tasks are not suited for studying metric properties. Here we measured the metric of binocular visual direction using a 3-D bisection task. The bisection stimulus consisted of three lines of which two were lying in one depth plane and the third line was placed in another. We find bisection errors for vertical lines that increase with disparity if the results are expressed in cyclopean directions. Bisection is almost veridical if the results are expressed in directions from the left or right eye. Which eye is used depends on the 3-D layout of the bisection stimulus. Two mutually exclusive models describe the results: 1) a cyclopean-eye model, in which visual direction depends on depth, and 2) a two-eye model, in which direction and depth are independent. We support the latter model because it is consistent with shape perception whereas the former is not.