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.

Deconfounded and mixed-symmetry versions of the Ponzo illusion figure.

One of the original Ponzo illusion figures, which consists of two converging lines between which two parallel lines of similar length have been inserted orthogonal to the figure's axis of mirror symmetry, was itself mirror-reflected so that the overall shape of the figure became "< >" or "> <", and one line at a time was inserted into each half. The usual illusion - the overestimation of the length of a line that is nearer to a vertex than a farther-away comparison line - occurred. Experiments 1 and 2 used different distances of target and comparison lines to the vertices, but identical distances of these lines from the converging lines, and so, as a tandem, deconfounded the two variables. Experiments 3 and 4 changed the symmetries of the modified Ponzo figure by reducing opposing half-angles of the converging lines or by tilting target and comparison lines concordantly or discordantly. The first measure, which created unequal distances of the endpoints of the target and comparison lines from the converging lines, hardly affected the amount of illusion. The second measure often attenuated the illusion - equally so for concordant and discordant tilts - suggesting that global and local symmetries of the stimuli, and their accordance, were less important than the vertical versus oblique orientation of target and comparison lines. Descriptively, the main cause of the Ponzo illusion seems to be the size of the gap between target and converging lines. The neural substrate of the effect may be interactions between orientation-sensitive and end-inhibited neurons.

Interrelations between the Oppel-Kundt- and the T-illusion.

In order to investigate interrelations between the Oppel-Kundt- and the T-illusion, T-type figures, comprised of one dotted and one empty line (demarcated by its endpoints), separated by a gap of variable size, and rotated to oblique orientations, were judged with regard to the lengths of the two extents. The T-illusion (overestimation of the length of the undivided line) was greater for a T with a dotted undivided line and a small gap. When the divided line was dotted, the illusion vanished at a small gap and reversed at a larger one. Findings are interpreted to mirror activities of a neural T-schema as well as orientation- and density-sensitive neurons.

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.

The Oppel-Kundt Illusion and Its Relation to Horizontal-Vertical and Oblique Effects.

The Oppel-Kundt illusion consists in the overestimation of the length of filled versus empty extents. Two experiments explored its relation to the horizontal-vertical illusion, which consists in the overestimation of the length of vertical versus horizontal extents, and to the oblique effect, which consists in poorer discriminative sensitivity for obliquely as opposed to horizontally or vertically oriented stimuli. For Experiment 1, Kundt's (1863) original stimulus was rotated in steps of 45° full circle around 360°. For Experiment 2, one part of the stimulus remained at a horizontal or vertical orientation, whereas the other part was tilted 45° or 90°. The Oppel-Kundt illusion was at its maximum at a horizontal orientation of the stimulus. The illusion was strongly attenuated with L-type figures when the vertical part was empty, but not enhanced when this part was filled, suggesting that the horizontal-vertical illusion only acts on nontextured extents. There was no oblique effect.

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 ⊥ with its lines tilted-A partial replication and extension of Cormack and Cormack (1974).

Following Cormack and Cormack (Perception & Psychophysics, 16, 208-212, 1974), modified versions of Titchener's (Experimental Psychology, Vol. 1, Pt. 1, 1901) ⊥, in which the ⊥'s lines were tilted (Experiment 1), or tilted and dissected into two separate lines (Experiment 2), were used as stimuli. In Experiment 1, the overestimation of the length of the ⊥'s vertical, undivided line tended to decrease with its tilt relative to the horizontal, divided line. For ⊥s rotated 90° or 270°, the divided line was tilted, and the overestimation of the length of the now horizontal, undivided line vanished except for ⊥s with orthogonal lines. Separation of the ⊥'s lines in Experiment 2 led to an attenuation of the overestimation of the length of the undivided line for the default ⊥, and an underestimation of the length of this line for rotated ⊥s. Results only partly confirm Cormack and Cormack, probably because of the different psychophysical methods used. Findings support the notion of a T-schema as a coherent unit in midlevel visual processing, but also suggest medium- and long-range interactions between orientation-sensitive neural mechanisms.

A Note on the Horizontal-Vertical Illusion - A Reply to Wade (2014).

Like many others before him, Nicholas Wade, in a recent publication in this journal, did not provide the correct title of Adolf Fick's dissertation, approved by the University at Marburg, Germany, in 1851, and Wade also wrongly attributed now famous illusion figures, meant to illustrate the so-called horizontal-vertical illusion (the +, the L, and the inverted T), to this author. After having corrected these errors, I briefly relate Fick's work to modern work in the field and note that it has been widely neglected.

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.

Allocentric time-to-contact and the devastating effect of perspective.

With regard to impending object-object collisions, observers may use different sources of information to judge time to contact (tC). We introduced changes of the observer's vantage point to test among three sets of hypotheses: (1) Observers may use a distance-divided-by-velocity algorithm or, alternatively, elaborated τ-formulae, all of which give exact tC information; (2) observers may use simple τ-formulae (i.e., formulae of the type: visual angle divided by its own first temporal derivative); (3) observers may capitalize on non-τ variables. Hypotheses (2) and (3) imply specific patterns of errors. We presented animated, impending collisions between a moving object and a stationary pole to naïve observers. The moving object either was a square tile or a small dot of fixed size. Participants viewed these events in a prediction-motion paradigm from different vantage points, covering a full circle around the setting. As accuracy of responses varied sinusoidally with viewing angle, irrespective of the type of object used, we conclude that observers mainly responded to the perspective view of the gap between object and pole, and less to the object's changing visual angle, or τ. Results are discussed with regard to evolutionary demands and issues of generalization.

Visual and visually mediated haptic illusions with Titchener's ⊥.

For a replication and expansion of a previous experiment of mine, 14 newly recruited participants provided haptic and verbal estimates of the lengths of the two lines that make up Titchener's ⊥. The stimulus was presented at two different orientations (frontoparallel vs. horizontal) and rotated in steps of 45 deg around 2π. Haptically, the divided line of the ⊥ was generally underestimated, especially at a horizontal orientation. Verbal judgments also differed according to presentation condition and to which line was the target, with the overestimation of the undivided line ranging between 6.2 % and 15.3 %. The results are discussed with reference to the two-visual-systems theory of perception and action, neuroscientific accounts, and also recent historical developments (the use of handheld touchscreens, in particular), because the previously reported "haptic induction effect" (the scaling of haptic responses to the divided line of the ⊥, depending on the length of the undivided one) did not replicate.

Luminance and contrast in visual perception of time to collision.

Many animals avoid dark, approaching objects seen against a lighter background but show no or weaker reactions to stimuli with inverted contrast. We investigated whether human observers would respond differently to such stimuli in terms of estimated time-to-arrival. We varied luminances of an approaching, light or dark disk and a plain, grey background, and for several conditions, continuously adjusted calibrations so as to keep contrast and/or overall lightness constant. Since no effects were found, we conclude that humans are able to discard luminance and contrast for the task at hand. Generally, however, performance was affected by different, consecutive regimes of feedback: Initially, without feedback, observers responded inconsistently and much too late; they improved after correct feedback, and in a third block of trials with pseudo-random feedback, they responded increasingly early without reverting to the initial level of uncertainty. We discuss our findings with regard to implications for neural mechanisms, put them in the context of evolutionary considerations, and propose continuative animal behavioral studies.

Visual discrimination thresholds for time to arrival.

In a seminal article, Todd (Journal of Experimental Psychology: Human Perception and Performance 7:795-810, 1981) reported a difference threshold of about 50 ms to discriminate the times of arrival of two differently sized objects that simultaneously approached head-on at constant but different velocities. Subsequent investigators, however, have often found much higher thresholds. We did one complete replication of Todd's experiment, and then modified his stimuli and experimental regime, which we hypothesized may have been responsible for some of the discrepancies reported in the literature. Unlike Todd and most other researchers, we exclusively used untrained observers. Several of our participants performed almost as well as the trained observers used by Todd and others, but the performance of most of our participants fell short of this standard. Furthermore, thresholds were affected by the experimental regimes, with large differences between objects' sizes and speeds compromising performance. Analyses of the response patterns revealed that the responses were driven mainly by the objects' relative apparent sizes.

Effects of task-irrelevant texture motion on time-to-contact judgments.

We investigated the effect of local texture motion on time-to-contact (TTC) estimation. In Experiment 1, observers estimated the TTC of a looming disk with a spiral texture pattern in a prediction-motion task. Rotation of the spiral texture in a direction causing illusory contraction resulted in a significant TTC overestimation, relative to a condition without texture rotation. This would be consistent with an intrusion of task-irrelevant local upon task-relevant global information. However, illusory expansion did not cause a relative TTC underestimation but rather also a tendency towards overestimation. In Experiment 2, a vertical cylinder moved on the frontoparallel plane. Observers judged its TTC with a finish line. The cylinder was textured with stripes oriented in parallel to its longitudinal axis. It was either not rotating, rotating such that the stripes moved towards the finish line (i.e., in the same direction as the contour), or rotating such that the stripes moved away from the finish line. Both types of texture motion caused TTC overestimation compared to the static condition. Experiment 3 showed that the different effects of task-relevant and task-irrelevant texture motion are not a mere procedural effect of the prediction-motion task. In conclusion, task-irrelevant local motion and global motion are neither averaged in a simple manner nor are they processed independently.

Opposite haptic and visual induction effects observed with Titchener's [perp].

Nineteen psychology undergraduates were requested to "grasp" the lines of a computer image of Titchener's perpendicular with a thumb and index finger pincer grip immediately after the line to be grasped had been indicated and the whole figure extinguished. The hand remained visible. Lines were of three different lengths (6.5, 7, and 7.5 cm), and perpendiculars were presented at eight different orientations (rotated in steps of 45 degrees ). Lines also had to be judged longer, shorter, or equal, relative to one another. Haptically, subjects responded correctly to the perpendiculars' undivided lines, but scaled their responses to the divided ones according to the undivided ones. Categorical judgments yielded comparable psychometric functions for both kinds of lines, with a significant shift of points of subjective equality from a difference in length between lines of 9.8% to 13.5% when the divided or the undivided line was target. Haptic sensitivity, therefore, appears to be constrained by context, whereas the classical "visual illusion," associated with Titchener's perpendicular, may be regarded a mere decisional criterion shift.

Camouflaged symmetry.

The notions of symmetry group and camouflage are explained, and a technique is introduced to visually camouflage symmetry groups in natural textures. Two experiments were carried out to test discriminability of symmetry groups p1, p2, pm, and pg in 4-oddity and 5AFC designs with different or same texture per set of stimulus pictures, respectively. In 4-oddity, detection of p1 was enhanced by pm distractors and impaired by those of pg. In 5AFC, p2 proved discriminable against p1; pg did not. Findings are interpreted as qualifying broad claims about symmetry as an organisational principle for vision. Further investigations of visual discrimination of symmetry operations and groups are suggested.