Panum's Limiting Case: Double Fusion, Convergence Error, or ‘Da Vinci Stereopsis’

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Abstract
Panum's limiting case—a perceived depth difference between two lines in one eye combined with only one in the other eye—has long been considered weak or reversible. In the last few years this has led to strong promotion of the view that Panum's case is not based on a stereoscopic process involving double fusion, that only one line is fused, with the depth of the other one attributable either to fixation disparity or to occlusion cues. This view is refuted in two ways. First it is shown that when the separation of the two lines, considered as a disparity, is within the range of ‘patent stereopsis’, depth is perceived with a precision and accuracy indistinguishable from regular stereopsis. The predictions of nonstereoscopic theories concerning the effects of fixation are not borne out at small disparities. Second, very compelling Panum versions of orientation and curvature disparity are introduced, which are difficult to account for except by a process of double fusion. Finally it is shown that at large disparities the depth in Panum's case deviates from prediction more frequently than does regular stereoscopic depth.