Discriminability in length of lines in the Müller-Lyer figure

The BTPI: An online battery for measuring susceptibility to visual illusions

Visual illusions provide a powerful tool for probing the mechanisms that underlie perception. While most previous studies of visual illusions focused on average group-level performance, less attention has been devoted to individual differences in susceptibility to illusions. Unlike in other perceptual domains, in which there are established, validated tools to measure individual differences, such tools are not yet available in the domain of visual illusions. Here, we describe the development and validation of the BTPI (Ben-Gurion University Test for Perceptual Illusions), a new online battery designed to measure susceptibility to the influence of three prominent size illusions: the Ebbinghaus, the Ponzo, and the height-width illusions. The BTPI also measures perceptual resolution, reflected by the just noticeable difference (JND), to detect size differences in the context of each illusion. In Experiment 1 (N = 143), we examined performance in typical self-paced tasks, whereas in Experiment 2 (N = 69), we employed a fixed presentation duration paradigm. High test-retest reliability scores were found for all illusions, with little evidence for intercorrelations between different illusions. In addition, lower perceptual resolution (larger JND) was associated with a larger susceptibility to the illusory effect. The computerized task battery and analysis codes are freely available online.

Effectiveness of the ability to form mental images in Müller-Lyer optical illusions

The purpose of this study was to establish whether wing length and the ability to form spatial mental images and vivid images affected optical illusions obtained in the Müller-Lyer figures, both real and imagined. The study involved a group of 137 fine arts college students who were shown two forms of the Müller-Lyer figures with different wing length (15 and 45 mm). In the imagined situation, a plain horizontal line was presented, and participants were expected to imagine the arrowheads aligned in the same way as in the real situation. Discrepancies in the perception of the horizontal lines in the Müller-Lyer illusion ("Point of Subjective Equality") were measured both in the real and imagined situation. Participants were then asked to complete the Vividness of Visual Imagery Questionnaire and the Measure of the Ability to Form Spatial Mental Imagery. It emerged that, in the condition of 45 mm wing length, participants were significantly more susceptible to the illusion than those in the condition of 15 mm wing length. Additionally, in the real situation, participants scoring high in spatial image were significantly more resistant to the illusion than those scoring low.

The Müller-Lyer illusion through mental imagery

Previous studies have pointed to a link between visual perception and mental imagery. The present experiment focuses on one of the best-known illusions, the Müller-Lyer illusion, now reproduced under conditions of real perception and by means of imagery. To that purpose, a tailored ad-hoc set of combined figures was presented to a total of 161 fine art students (M age = 20,34, SD = 1,75) who individually worked with two different variations of the Müller-Lyer figures which consisted of a 10 mm long shaft and two fins set at an angle of 30º, being 15 mm long in one instance and 45 mm long in the other. In small groups, participants also completed an image control questionnaire. Results yielded that the longer the oblique lines, the larger the magnitude of the illusion both in the situation of real perception and in the imaginary situation. Also, the magnitude of the illusion augmented in the situation of perception in contrast to the imaginary situation, both with 15 mm long fins and with those of 45 mm. However, no significant differences were found in the magnitude of the illusion between high and low individuals in image control, although interactions between image control and other variables were indeed significant. The consistency of the outcome is a step forward in the study of illusions through mental images and opens the door to new lines of research that could involve innovative methods of analysis, different versions of the illusion and wider groups of participants.

The Müller-Lyer line-length task interpreted as a conflict paradigm: A chronometric study and a diffusion account

We propose to interpret tasks evoking the classical Müller-Lyer illusion as one form of a conflict paradigm involving relevant (line length) and irrelevant (arrow orientation) stimulus attributes. Eight practiced observers compared the lengths of two line-arrow combinations; the length of the lines and the orientation of their arrows was varied unpredictably across trials so as to obtain psychometric and chronometric functions for congruent and incongruent line-arrow combinations. To account for decision speed and accuracy in this parametric data set, we present a diffusion model based on two assumptions: inward (outward)-pointing arrows added to a line (i) add (subtract) a separate, task-irrelevant drift component, and (ii) they reduce (increase) the distance to the barrier associated with the response identifying this line as being longer. The model was fitted to the data of each observer separately, and accounted in considerable quantitative detail for many aspects of the data obtained, including the fact that arrow-congruent responses were most prominent in the earliest RT quartile-bin. Our model gives a specific, process-related meaning to traditional static interpretations of the Müller-Lyer illusion, and combines within a single coherent framework structural and strategic mechanisms contributing to the illusion. Its central assumptions correspond to the general interpretation of geometrical-optical illusions as a manifestation of the resolution of a perceptual conflict (Day & Smith, 1989; Westheimer, 2008).

Detection-theoretic analysis of same-different judgments for the amplitude discrimination of acoustic sinusoids

Three methods were applied to determine which decision model best accounted for same-different judgments about the amplitude of acoustic sinusoids. The methods were (1) analysis of the shape of the receiver operating characteristic; (2) analysis of an observer's decision space; and (3) a correlation method based on the conditional-on-single-stimulus procedure. In one experiment, observers rated their confidence that a pair of 1-kHz sinusoids was drawn from the same or from different sets. The two sets had identical Gaussian distributions of decibel amplitudes, but their mean amplitudes differed by 3 dB. The differencing model, in which observers base their decision on the absolute difference between the two observations, accounted for the data better than the independent-observation model, in which observers compute independent likelihood ratios for each observation. A second experiment added to every trial an interval that contained a 1-kHz sinusoid whose amplitude equaled the grand mean of both stimulus sets. Despite this additional information, which is needed to adopt the independent-observation model, the differencing model again better accounted for the data.