Binocular perception of slant about oblique axes relative to a visual frame of reference

From the literature it is known that the processing of disparity for slant is different in the presence and in the absence of a visual frame of reference. The experimental finding that vertical disparity is not processed for slant perception in the presence of a visual reference is elaborated. This theoretical analysis results in a reduction of the three basic first-order transformations between the retinal half images (divergence, rotation, and deformation) to only two basic orthogonal transformations. The first of these, horizontal scale, results in slant perception about the vertical axis, whereas the second, horizontal shear, results in slant perception about the horizontal axis. These transformations are based primarily on horizontal disparity. It is shown experimentally that in the presence of a frame of reference the amount of vertical transformation that is added to the two basic transformations (horizontal scale and shear) of a random-dot stimulus is indeed irrelevant for slant perception. It is suggested that, in the presence of a visual reference, slant perception about oblique axes is based solely on linear combinations of the horizontal-scale and horizontal-shear transformations. Subjects are able to reproduce slants about oblique axes experimentally merely by combining horizontal scale and shear.