Characterisation of the misalignment and misangulation components in the Poggendorff and corner-Poggendorff illusions

In the Poggendorff illusion, two colinear segments abutting obliquely on an intervening configuration (often consisting of two long parallel lines) appear misaligned. We report here the results of a component analysis of the illusion and several of its variants, including in particular the 'corner-Poggendorff' illusion, and variants with a single arm. Using a nulling method, we determined an 'orientation profile' of each configuration, that is, how the illusions varied as the configuration was rotated in the plane of the display. We were able to characterise a pure-misalignment component (having peaks and dips around the +/- 22.5 degrees and +/- 67.5 degrees orientations of the arms) and a pure misangulation component of constant sign, having peaks at the +/- 45 degrees orientations of the arms. Both these components were present in both the classic and the corner-Poggendorff configurations. Thus, the misangulation component appears clearly in the classic Poggendorff illusion, once the misalignment component is partitioned out. Similarly, the corner-Poggendorff configuration, which essentially estimates a misangulation component, contains a misalignment component which becomes apparent once the misangulation is nulled. While our analysis accounts for much of the variability in the shapes of the profiles, additional assumptions must be made to explain the relatively small misangulation measured in the corner-Poggendorff configuration (1.5 degrees, on average, at peak value), and the relatively large illusion measured in the configurations with a single arm (above 6 degrees, on average, at peak values). We invoke the notion that parallelism and colinearity detectors provide counteracting cues, the first class reducing misangulation in the corner-Poggendorff configuration, and the second class reducing the illusion in the Poggendorff configurations with two arms.