Reduction and elimination of the Poggendorff misalignment effect by minor changes at intersections: implications for the perceptual-compromise explanation

Optimizing the strength of the Bourdon effect by varying the triangle arrangement

The Bourdon illusion refers to the perceived bentness of the straight collinear edges when two right-angled triangles are placed apex to apex. We studied this illusion using a cancellation method. In the first of three experiments, we manipulated the apex angle, with six different angles ranging from 4° to 45°. Results indicated that the Bourdon illusion is strongest when the angle is around 12°. In the second experiment, we compared four scalene triangles with a right-angled triangle. The angular shift was most salient when the shape corresponded to a right-angled triangle. In the third experiment, the patterns were created by varying the size of one right-angled triangle while holding the size of the second right-angled triangle constant. Results indicated that the Bourdon illusion was strongest when both right-angled triangles were of equal size. Our data suggest that the Bourdon illusion depends critically upon the specific arrangement of shapes in the display.

Geometrical features underlying the perception of collinearity

The magnitude of the Poggendorff bias in perceived collinearity was measured with a 2AFC task and roving pedestal, and was found to be in the region of 6-8deg, within the range of previous estimates. Further measurements dissected the bias into several components: (1) The small (∼1deg) repulsion of the orientation of the pointer from the parallel, probably localized in the part of the line near the intersection (2) A small (<1deg) location bias affecting the intersection of pointers and inducing lines; and (3) A larger (>1deg) bias in the orientation of virtual lines crossing the gap between two parallels, towards the orientation of the parallels, or equivalently (4) An orthogonal bias in actively constructing a virtual line across the gap. We conclude that orientation repulsion by itself is an inadequate explanation of the Poggendorff effect, and that a full explanation must take account of the way in which observers construct virtual lines in visual space in order to carry out elementary geometrical tasks such as extrapolation.