The Depth Mechanism In Wheatstone-panum's Limiting Case

Due to the fact that the human eyes are horizontally separated, the images projected onto the retinas from the three-dimensional (3D) world would, in general, be incompletely asymmetric. Except the location, these asymmetries also include asymmetry in number of features in the two images. In this situation, the originals of depths of the perceptual features is an important theme for stereoscopic vision research. However, even for the simplest case as Wheatstone-Panum's limiting case, issue of the depths of the perceived two lines was derived from double fusion (that is, both of the double lines in one eye fused with the single line in the other eye) or the single fusion (the depth of only one feature originated from binocular fusion of features, while the depth of the other derived from other non-binocular cues) has not been resolved even after over 170 years'exploration and debating.Over the years, this phenomenon was generally seen as a limiting case of normal stereopsis and if just reduced only one of the features and then stereopsis disappeared. It was generally considered that double fusion happened in the case and the relative depth contributed to the relative disparity in the two fusions. However, in recent years, with the rise of occlude theory, some researchers considered that the Wheatstone-Panum's limiting case belongs to one of occluding configurations should be seen as one version of Da Vinci stereopsis and the uniqueness constrain was still valid, that is, the single line in one just fused one of the double lines in the other eye, the other monocular line derived its depth from some non-stereopscopic factors such as occlusion, camouflage and vergence error.And in recent years, several experimental evidences based on Wheatstone-type configurations made the issue even more complicated and confusing. It's hard to understand that under the same condition of small disparities, why the Panum's limiting case based on orientation and curvature configuration (Gillam et al 1995) must be explained by double fusion, while the Panum's limiting case in that on wavy configuration (Frisby 2001) and oblique line configuration (Wang et al 2001) can only be explained by single fusion. But so far the idea of clarifying this issue is also lacking.We consider that the cause underlying this situation may be naming the depth effect derived from both Panum-type configurations composed of parallel features and Wheatstone–type configurations composed of not all parallel features Panum's limiting case without distinguishing their difference. This made the researchers ignore the difference between Wheatstone- and Panum-type stereograms, and pay little attention to other factors influencing binocular fusion, such as the disparity gradient of dichoptic features and the monocular cue about the frontal projection shape of perceptual feature besides disparity. It is the case in the recent several typical studies (Gillam et al 1995; Frisby 2001; Wang et al 2001).In the experiments, For the first time, (1) when keeping small disparity and the monocular cue about the frontal plane projection shape of perceptual feature unchanged, the rule of the change of evidence attribute was investigated by increasing or decreasing the disparity gradient of dichoptic features of Wheatstone-type configurations supporting double fusion view and that being against double-fusion view separately; and (2) when keeping disparity and the disparity gradient of dichoptic features unchanged, the rule of the change of evidence attribute about binocular fusion was investigated by increasing the monocular cues about the shape of the projection of perceptual feature.The results together demonstrated our hypotheses that the common basis underlying all kinds of Panum effects is double fusion, which is constrained by the disparity gradient of dichoptic features and affected by monocular cue about the frontal plane projection shape of perceptual feature besides disparity. Destruction of double fusion at small disparities in previous researches was just due to inappropriate usage of these factors in their Wheatstone-type stereograms. Moreover, based on these conclusions, a kind of large scale configuration was created to replace the line configurations in traditional studies, which leads to important methodological changes in researching of unpaired stereopsis :(1) The perceived features with different depths are no longer two lines but two large-scale foldline planes after fusion, consequently, for both experienced and naive subjects, the stability and significance of the observation results, and the consistency among individuals were greatly improved. (2) Being used as the fusion criterion , slant effect of large-scale foldline planes can be used directly to determine whether fusion happened between any of the double features and the single feature, the judge no more depends on comparison with the characteristics of conventional binocular fusion or other perceived features. Thereby, the simpleness and objectivity of fusion judgment were greatly improved. Therefor, these together provided new and solid evidences for human visual system to resolve the matching problem with multiple fusion in the case that the number of features in two eyes is asymmetric, and may also be great significance for understanding some related stereo phenomena such as da Vinci stereopsis and establishing a new stereopsis theory.Furthermore, it is also a useful method for investigating the processing mechanisms of some non-stereoscopic information such as luminance and color.