Titchener's ⊥ in context 1--delimited, discrete monomotif patterns, line arrangements, and branching patterns

Sanford’s L dissected: A partial replication and extension of Cai et al. (2017)

Partial replications of experiments reported by Cai et al. (Attention, Perception, & Psychophysics, 79(4), 1217-1226, 2017) on the so-called Horizontal-vertical illusion confirmed that dissecting L-figures into two separate lines yields greater overestimation of (near-)verticals than do intact Ls. However, contrary to Cai et al.'s findings, which had been obtained with a staircase procedure, with the method of constant stimuli, the amount of illusion was much smaller. This divergence is explained by the self-reinforcing nature of adjustment procedures. Another finding, already reported by Cormack and Cormack (Perception & Psychophysics, 16(2), 208-212, 1974), that obtuse angles between an L's lines yield greater bias than acute angles, was also replicated in one experiment but tended to be reversed in another. Mixing dissected, upright and top-down inverted Ls and laterally oriented Ts, both with tilted lines, within one experiment confirmed that the bias for Ts is opposite to the one for Ls: For Ts, the effect of (virtual) bisection dominates, yielding an overestimation of the length of the undivided line, whereas for Ls, the horizontal-vertical anisotropy dominates, yielding an overestimation of the length of the vertical line. The differential gap effects can possibly be explained by interactions within the neural substrate between orientation-sensitive and end-inhibited neurons, and the method effects by perceptual learning.

The long and short of it? A novel geometric illusion

Here we present what we believe to be a novel geometric illusion where identical lines are perceived as being of differing lengths. Participants were asked to report which of the two parallel rows of horizontal lines contained the longer individual lines (two lines on one row and 15 on the other). Using an adaptive staircase we adjusted the length of the lines on the row containing two to estimate the point of subjective equality (PSE). At the PSE, the two lines were consistently shorter than the row containing the fixed length of 15 lines demonstrating a disparity in perceived length such that lines of identical length are perceived as longer in a row of two than in a row of 15. The illusion magnitude was unaffected by which row was presented above the other. Additionally, the effect persisted when using one as opposed to two test lines, and when the line stimuli on both rows were presented with alternating luminance polarity the illusion magnitude decreased, but was not abolished. The data indicate a robust geometric illusion that may be modulated by perceptual grouping processes.

The Prospects of Utilizing Geometrical Visual Illusions as Tools for Neuroscience

Geometrical visual illusions have long been used as tools in neuroscience. Most commonly, researchers have taken illusions as a given and attempted to explain phenomenal impressions in terms of known neural mechanisms. In a psychophysical approach to this topic, it is customary to modify stimuli until conditions for which illusions are enhanced, attenuated, or annihilated have been found. Additionally, the focus is not exclusively on response bias but equally on sensitivity, because observers may fall prey to an illusion but at the same time be able to discriminate between stimuli perfectly. For the T-figure, the length of the undivided line is usually overestimated relative to the length of the divided line, and evidence has accrued that suggests that the illusion may be due to the processing of the figure as a coherent unit (a “T-schema”). Dissecting the T or tilting its lines influenced the amount of illusion, suggesting that interactions between orientation-sensitive and end-inhibited neurons are at work. Examples of cognate research with the Ponzo, Ebbinghaus, and Müller-Lyer illusions are also discussed.

Bimanual thumb-index finger indications of noncorresponding extents

Two experiments tested a prediction derived from the recent finding that the Oppel-Kundt illusion - the overestimation of a filled extent relative to an empty one - was much attenuated when the empty part of a bipartite row of dots was vertical and the filled part horizontal, suggesting that the Horizontal-vertical illusion - the overestimation of vertical extents relative to horizontal ones - only acted on the empty part of an Oppel-Kundt figure. Observers had to bimanually indicate the sizes of the two parts of an Oppel-Kundt figure, which were arranged one above the other with one part vertical and the other part tilted -45°, 0°, or 45°. Results conformed to the prediction but response bias was greater when observers had been instructed to point to the extents' endpoints than when instructed to estimate the extents' lengths, suggesting that different concepts and motor programs had been activated.

Titchener's T in context 2 - Symmetric patterns of two Ts

Patterns of two Ts, materializing different symmetry groups, were used to explore conditions that would lead to a modulation of the typically observed overestimation of the length of a T's undivided line relative to its divided line. Observers either had to compare the lengths of the lines of one or the other of the Ts in a pattern, or noncorresponding lines between the two Ts. For both tasks alike, the T-illusion was found to be markedly greater with twofold mirror-symmetric 2-T patterns than it usually is with individual Ts. A control experiment suggested that the effect was probably due to the collinearity of the two Ts' undivided lines in these patterns rather than the additional axis of mirror symmetry. Findings are interpreted in terms of interactions between orientation-sensitive neurons that respond to the Ts' individual lines.

Titchener's T with flanks

Flanks were added to Titchener's (1901) T-illusion figure to test its susceptibility to context stimuli. The addition of a second divided line yielded H-type figures, and the addition of a second undivided line, +-type figures. The lengths of the Ts' undivided lines was expected to be overestimated relative to the lengths of the divided lines, when all lines were about equally long, and the illusion was expected to become smaller when one or two gaps had been introduced between the lines. Results conformed to the predictions. The amount of illusion was larger for the no-gap H than the T, and was almost annihilated with the two-gaps H, with 3 out of 14 observers showing an inverse response bias. The +-type stimuli produced analogous results. Findings are interpreted in terms of the nonequivalence of the endpoints of the stimuli's lines, which are thought to elicit different responses in end-inhibited cortical neurons, thereby affecting length estimates.

Titchener's ⊥ dissected

In three experiments, two independent samples of 12 observers each visually inspected modified versions of Titchener's ⊥ from which the T-junctions had been deleted. For Experiment 1, the ⊥'s two lines had been replaced by dashed lines not meeting in a common point; for Experiment 2, the ⊥ had been reduced to five dots, representing the original lines' end- and midpoints; and for Experiment 3 (in which the second sample of observers served), the ⊥ had been dissected into two separate lines, differently spaced from each other. Observers haptically indicated the lengths of the two orthogonal lines of the modified ⊥s and verbally judged their relative lengths or the distances between the corresponding dots. The common perceptual illusions persisted in Experiments 1 and 2, but were markedly weakened in Experiment 3. Implications for a neurophysiological account of the illusions in terms of bottom-up, long-range interactions between orientation-sensitive mechanisms versus top-down activation of a figural schema are spelled out.