The Poggendorff illusion: a bias in the estimation of the orientation of virtual lines by second-stage filters.

The veridical perception of collinearity between two separated lines is distorted by two parallel lines in the space between them (the Poggendorff illusion). This paper tests the conjecture that the perception of collinearity of separated lines is based on a two-stage mechanism. The first stage encodes the orientation of the virtual line between the proximal terminators of the target lines. The second stage compares this virtual orientation with the orientation of the target lines themselves. Errors can and do arise from either process. Two parallel lines, abutting against the target lines, cause the classical Poggendorff misalignment bias. The magnitude of the bias is increased by Gaussian blur, as is a version of the Poggendorff figure containing only acute angles. In the obtuse-angle figure, on the other hand, blur decreases the misalignment bias. We argue that the acute- and obtuse-angle biases depend upon different mechanisms, and that the obtuse-angle effect is more related to the obtuse-angle version of the Muller-Lyer illusion, which is also decreased by blur. If observers attempt to match the orientation of the virtual line between the two line intersections in the Poggendorff figure they make an error in the same direction as the Poggendorff bias. The orientation of the target lines in the figure, however, is veridically matched to a Gabor-patch probe, unless the target lines are very short, in which case the error is in the same direction as the Poggendorff bias. A small bend in the target lines where they abut the parallels increases the Poggendorff bias if it makes the line more orthogonal to the parallel, but has little effect in the opposite direction. The Poggendorff bias is unlikely to depend upon biases in first-stage linear filters because (a) it still exists in figures composed of short, luminance-balanced lines which are defined by contrast only; and (b) it also exists if the parallels are replaced by grating patches with the same mean luminance as the background. The orientation of the grating in the latter case affects the magnitude of the bias, but even an orientation which should reverse the Poggendorff bias by the mechanism of cross-orientation inhibition fails to do so. The Poggendorff bias is a complex effect arising from several sources. Blurring in second-stage filters with large receptive fields can explain many aspects of the phenomenon.