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Arash Yazdanbakhsh, Takeo Watanabe; Horizontal and vertical illusory lines are different in determining the depth of their embedded surface. Journal of Vision 2004;4(8):476. doi: 10.1167/4.8.476.
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A novel phenomenon of subjective surface formation in an Ehrenstein-style configuration within a stereogram is reported. The inducing elements of the subjective surface are at different depths, therefore it is surprising that this depth difference leads to the emergence of a subjective surface. Notably, the resultant surface is not interpolating between different depths of the inducers to form a concave, convex or slanted surface, rather it is on the frontoparallel plane. However, the formation of the surface is more likely under certain relative depth conditions: Different sets of experiments by separate groups of subjects suggest that when the subjective square forms, it is at the depth of vertical illusory sides, rather than horizontal ones. When the vertical side inducers are behind the horizontal ones, subjective surface formation is less likely or unstable, but even in this case, given the surface forms, the depth of the square is at the depth of the vertical illusory sides. In our stereograms there are no explicit monocular occlusion zones or half visible parts, as opposed to the stereopairs with Kanizsa triangles or squares that have half visible parts on their inducers equivalent to occluded zones (Watanabe and Cavanagh, 1991). We interpret the dominance of vertical sides over horizontal ones in depth assignment geometrically: Vertical orientation can convey the horizontal disparity —a critical factor for Wheatstone (classic) stereopsis- but horizontal orientation per se lacks horizontal disparity information, the fact that is used in some 3D vision theories (Grossberg, 1994). However, this still cannot explain why the subjective surface formation is less likely when the vertical illusory sides are behind the horizontal ones; perhaps it is then difficult to make any perceptual sense out of the configuration: The subjective square as a perceptually occluding surface (Gillam and Nakayama, 2002) can not be behind the perceptually occluded inducers.
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