Monocular discs in the occlusion zones of binocular surfaces do not have quantitative depth--a comparison with Panum's limiting case

Da Vinci stereopsis is defined as apparent depth seen in a monocular object laterally adjacent to a binocular surface in a position consistent with its occlusion by the other eye. It is widely regarded as a new form of quantitative stereopsis because the depth seen is quantitatively related to the lateral separation of the monocular element and the binocular surface (Nakayama and Shimojo 1990 Vision Research 30 1811-1825). This can be predicted on the basis that the more separated the monocular element is from the surface the greater its minimum depth behind the surface would have to be to account for its monocular occlusion. Supporting evidence, however, has used narrow bars as the monocular elements, raising the possibility that quantitative depth as a function of separation could be attributable to Panum's limiting case (double fusion) rather than to a new form of stereopsis. We compared the depth performance of monocular objects fusible with the edge of the surface in the contralateral eye (lines) and non-fusible objects (disks) and found that, although the fusible objects showed highly quantitative depth, the disks did not, appearing behind the surface to the same degree at all separations from it. These findings indicate that, although there is a crude sense of depth for discrete monocular objects placed in a valid position for uniocular occlusion, depth is not quantitative. They also indicate that Panum's limiting case is not, as has sometimes been claimed, itself a case of da Vinci stereopsis since fusibility is a critical factor for seeing quantitative depth in discrete monocular objects relative to a binocular surface.