The effects of peripheral and central fixation on a Poggendorff-like vernier alignment task

Saccades to Explicit and Virtual Features in the Poggendorff Figure Show Perceptual Biases

Human participants made saccadic eye movements to various features in a modified vertical Poggendorff figure, to measure errors in the location of key geometrical features. In one task, subjects (n = 8) made saccades to the vertex of the oblique T-intersection between a diagonal pointer and a vertical line. Results showed both a small tendency to shift the saccade toward the interior of the angle, and a larger bias in the direction of a shorter saccade path to the landing line. In a different kind of task (visual extrapolation), the same subjects fixated the tip of a 45° pointer and made a saccade to the implicit point of intersection between pointer and a distant vertical line. Results showed large errors in the saccade landing positions and the saccade polar angle, in the direction predicted from the perceptual Poggendorff bias. Further experiments manipulated the position of the fixation point relative to the implicit target, such that the Poggendorff bias would be in the opposite direction from a bias toward taking the shortest path to the landing line. The bias was still significant. We conclude that the Poggendorff bias in eye movements is in part due to the mislocation of visible target features but also to biases in planning a saccade to a virtual target across a gap. The latter kind of error comprises both a tendency to take the shortest path to the landing line, and a perceptual error that overestimates the vector component orthogonal to the gap.

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.

Poggendorff and Müller-Lyer illusions: common effects

Previous investigations have shown that the magnitude of the Müller-Lyer illusion is a function of the linear and angular dimensions of the figure. If the Müller-Lyer and Poggendorff illusions share a common basis, then the magnitude of the Poggendorff illusion should similarly be a function of the analogous configural dimensions. A study is reported in which changes were made in the dimensions of the Poggendorff figure that are analogous to the dimensions of the Müller-Lyer figure: the length of the parallel components (analogous to the wings of the Müller-Lyer figure); the length of the intertransversal extent (analogous to Müller-Lyer shaft length); and the angle formed between the parallel components and the intertransversal extent (analogous to the angle of wing attachment in the Müller-Lyer figure). The relationship between the magnitude of the illusion and the dimensions of the Poggendorff figure was found to be generally in line with previous findings relating to the Müller-Lyer illusion. Adaptation-level theory and the positive-context model accommodate the major findings of the present study.

The role of the second oblique in the Poggendorff illusion

It has been observed previously in the classic Poggendorff illusion figure that the end of the oblique line which abuts onto the vertical parallel appears more misaligned than its free end. Various theories suggest that angular distortions are largest at the point of abutment. Two experiments are reported which, however, suggest that, compared to displays in which a single dot is aligned with an oblique line, the introduction of a second, parallel oblique segment does not increase errors more at the abutting tip than at the free end, but, rather, reduces them more at the free end. These results not only cast doubt on the relative importance of angular effects alone in the classic Poggendorff display, but also emphasise the complexity of that figure as a tool in the investigation of visual processing.

A comparison of visual tilt illusions measured by the techniques of verticle setting, parallel matching, and dot alignment

The tilt illusion (TI) was investigated by using both short (19 min) and long (2 deg 6 min) test lines, at three angles of test line-inducing line separation (15 degrees, 45 degrees, and 75 degrees). Three groups of ten observers each provided data under one of three task conditions: vertical judgment, parallel matching, and dot alignment on a common visual display. The main result was that both the vertical judgment and the parallel matching task provided similar, classic TI angular functions with the means ordered 15 degrees greater than 45 degrees greater than 75 degrees and with small attraction effects at 75 degrees in three of the four relevant functions. The third task, dot alignment, yielded results different from the average of the other two: no attraction effects occurred and, with the short test line, the obtained mean illusion at 45 degrees exceeded those at the other intersect angles. These results are consistent with alignment data reported by others. One explanation is that the inducing line produces an apparent bowing of the test line which would be reflected in dot alignments but not in vertical setting or in parallel matching. However, direct evidence does not support this hypothesis. An alternate hypothesis, for which independent evidence exists, is that alignment errors reflect perceptual mistracking but that the origin of these errors is not the tip of the test line but within it. Although this does not explain dot alignment errors, it highlights their complexity and the need to interpret them with caution.