Biases and sensitivities in the Poggendorff effect when driven by subjective contours.

The Poggendorff effect (1860) is a well-documented geometric illusion in which there is a perceptual misalignment of two collinear oblique lines when separated by a pair of parallel contours (henceforth referred to as the transversals and parallels respectively; see Fig. 1A). Several explanations have been put forward to account for the effect, including a misestimation of the orientation of the transversals through lateral inhibition, obtuse angle contraction, or angular induction,1-5 a bowing of the transversals at points of intersection with the parallels,6 a misestimation of the orientation of a projected line connecting the transversals as a result of neural blurring,7,8 a perceptual contraction or expansion of the space between the parallels,9-11 a misinterpretation of the transversals as receding in depth,12-14 or an inherent calibration bias in the visual system reflecting the statistics of natural scene geometry.15 Deconstruction of the Poggendorff figure into its component parts, however, suggests that the illusion is a combination of several composite effects,9,16-19 the influence of which may be either additive or subtractive on the perceived degree of misalignment, depending on the precise configuration used. Figure 1 The range of Poggendorff and control figures used throughout the study. The classical Poggendorff figure (A) is shown in its less common horizontal orientation. Dimensions of the figure are indicated in degrees of visual angle when viewed from a distance ... If the parallel lines in a Poggendorff figure are replaced with subjective contours, the effect would seem to persist.20 This may be true of subjective contours defined by Kanizsa-like Pac-Man tokens,20 luminance steps, texture borders,21 and complex composite images that define the parallels through “good continuation” or “closure.”22 However, in many of these studies, interpretation of the results is complicated by the absence of quantitative measures of effect size, a lack of statistical tests of significance, or a failure to include the appropriate controls and measures of baseline biases.20,21,23-25 To demonstrate that subjective contours are truly driving the Poggendorff effect, the baseline bias (the degree of misalignment perceived between two transversal lines in the absence of further context) must first be subtracted from the overall bias. This is because reports of colinearity between spatially separated lines (even in the absence of parallel contours) may be distorted26,27 as a result of tilt assimilation toward the nearest cardinal axis,16,28 a perceptual expansion of the vertical axis,9 the Zehender effect,29 or personal response biases. In addition, the magnitude of the bias must be significantly larger than the effect induced by a suitable control image in which the perception of subjective contours is abolished without changing the overall image structure. Meyer and Garges30 and Day et al.31 addressed the issue of control figures and baseline biases in their examination of subjective contours and the Poggendorff effect. Taken together, these papers demonstrate that significant differences from baseline were not significant when the basic Kanizsa-like Pac-Man tokens were used to generate the parallels. Significant effects were only observed when high contrast hemisegments were added along the length of the subjective contours to increase their saliency (Figs. ​(Figs.1B1B​,​30 ​1D1D​,​31). This introduces a genuine luminance step across sections of the subjective contours, raising the question whether they are true subjective contours or simply luminance-defined contours with periodic discontinuities. This is of particular relevance to the study by Day et al.31 in which sections of luminance-defined contour separated by <1° of visual angle constituted over half of the subjective contours length. Finally, it is unclear whether the presence of subjective contours in the Poggendorff figure causes a reduction in judgment precision (i.e., increased positional uncertainty) and a systematic bias. In the study of geometric illusions this issue is rarely addressed, despite the fact that differences in bias and sensitivity may be informative as to the underlying mechanisms of a visual phenomenon.32 Thus, in a study by Morgan et al.,7 a misestimation of length associated with the Muller-Lyer illusion did not entail a parallel decrease in sensitivity to length differences, a finding which the authors took as evidence for an early site of action, i.e., when length is first encoded. The purpose of this study was thus to consolidate previous reports of the Poggendorff effect using true subjective contours and appropriate control conditions, addressing the issues of judgment sensitivity and judgment bias.