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

Abstract

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.

Keywords

Müller-Lyer illusion geometric illusion spatial imagery imagery vividness fine arts students

Mental images are mental representations similar to perceived stimuli (Kosslyn, 1973). Both perception and mental images produce cognitive experiences that are intuitively considered akin but not identical and are often described in the same terms: intensity, distinctness, depth of nuance, vividness, etc. (Denis, 1991).

Since mental images have a similar effect to perception, a number of studies have dealt with the elicitation of optical illusions by way of mental images, bringing a portion of the figure to mind. Matters already reviewed include the horizontal-vertical illusion (Blanuša & Zdravković, 2015; Wallace, 1984a), the Ponzo, Hering, and Wundt illusions (Giusberti et al., 1998; Reisberg & Morris, 1985; Wallace, 1984b) or the Ebbinghaus illusion (Giusberti et al., 1998). All these studies corroborate that mental imagery produces optical illusions much in the same way as they are produced by figure perception.

Wallace (1984a) inquired into the horizontal-vertical illusion through mental images asking participants to complete the Vividness of Visual Imagery Questionnaire (VVIQ; Marks, 1973) in order to measure their image vividness. He found that participants high in image vividness experienced the illusion in the real situation as much as in the imagined situation. However, those low in this factor only experienced the illusion in the presence of the lines (real situation). Wallace (1984b) found the same results with the VVIQ when he studied the Ponzo illusion as well as the Hering and Wundt illusions.

Amongst the most reviewed perceptual illusions is the one obtained with the Müller-Lyer figure (see all versions used in this study, Figures 1 to 4). This figure consists of a horizontal line which looks longer or shorter according to the orientation of its arrowheads, inward (> <) or outward (< >). These fins are also known as “inward/outward-pointing arrowheads” (Dragoi & Lockhead, 1999), “wings-out/wings-in” (Porac, 1994) or “tail fins/arrowheads” (Wang et al., 1998).

Figure 1.
30° and 15 mm Müller-Lyer figure. Note. Participants must move the sliding stimulus until the horizontal length is equal to that of the standard stimulus (10 mm). This figure shows equal lengths.

Figure 2.
30° and 45 mm Müller-Lyer figure.

Figure 3.
Figure used in the imaginary situation for the 30° and 15 mm figure and for the 30° and 45 mm figure.

Figure 4.
The back side of the figures.

Berbaum and Chung (1981) aimed to compare the illusions obtained by means of the Müller-Lyer actual figures and some other Müller-Lyer imaginary lines that ended in dots instead of oblique lines. Participants were asked to imagine the lines and experience the illusion. These authors found similar optical illusions in direct perception and image-mediated perception.

Ohkuma (1986) compared the perceptive Müller-Lyer illusion to the illusion of the imagined figure. To this purpose, he carried out an investigation considering three conditions: (a) complete figure condition (perceptive situation); (b) wingless figures (imagined situation similar to that of Berbaum & Chung, 1981); and (c) condition in which the figures of the imagined situation are used but with no instructions so as to induce imagination (control condition). It was found that in all three conditions, when outward figures (> <) were presented, the horizontal line was valued as longer than in the case of inward figures (< >). As for the outward figures, the illusion was significantly larger in the perceptive condition than in the image condition. Conversely, this dissimilarity was not found between the imagined condition and the control condition. In the case of inward-oriented arrowheads, no significant differences were found between the perceptive condition and the image condition, whereas a significant difference was found between the imagined condition and the control situation.

Watters and Scott (1989) conducted a study in which three versions of the Müller-Lyer stimulus were presented with a view to attaining the illusion in its maximum effect, in an intermediate effect and in a non-existing effect. The study was comparable to the one conducted by Berbaum and Chung (1981) in the sense that they tried to induce the Müller-Lyer illusion by making participants imagine lacking portions of the standard inductive stimulus. The basic aim of the project was to compare the magnitude of the illusion in an imagined situation with that of a real situation, where the illusion stimulus was presented in full. Results revealed that the effect of the Müller-Lyer illusion appeared just as it was expected, that is, in the same way in the imagined and the real situation in all three versions of the stimulus.

Previous work has studied cognitive and temperamental factors that are susceptible to visual illusions (Mlyniec & Bednarek, 2016; Posner, 2012; Przedniczek & Bednarek, 2021; Witkin & Goodenough, 1981; Zawadzki & Strelau, 2018). An objectively consistent conclusion was that field-dependent subjects are more susceptible to visual illusions than field-independent subjects (Bednarek et al., 2022; Coren & Porac, 1987; Przedniczek & Bednarek, 2021; Witkin & Asch, 1948a, 1948b). Field dependence is usually treated as a global-passive dimension, while field independence is treated as an analytical-active dimension. The performance on field independence tasks primarily reflects the operations of the visuospatial and executive components of working memory (Miyake et al., 2001).

Bednarek et al. (2022) aimed to test the efficiency of cognitive training programs based on human–computer interaction and their influence on resistance to visual illusions including the Müller-Lyer illusion. They also attempted to verify whether Witkin's field dependence/independence style moderates the influence of cognitive training on resistance to visual illusions. Results showed that, in broad outline, field-dependent participants seemed to be more susceptible to visual illusions than field-independent ones. In addition, working memory training was shown to be effective in reducing the susceptibility of field-dependent participants to the Ponzo illusion. Zhang et al. (2017) found that military men showed lower magnitudes of the Müller-Lyer illusion than university students and related the former's performance in areas such as gun-shooting precision to their capacity to withstand the illusion. It should be noted that compulsory military training results in increased aiming skills (Nieuwenhuys et al., 2010). It was also found that increased attention-manipulation reduced the susceptibility to the Müller-Lyer illusion in ordinary people (Coren & Porac, 1983).

Pérez-Fabello and Campos (2022a) have recently examined the influence of the Müller-Lyer illusion on participants when asked to imagine the oblique lines of the figures. The authors also analyzed the influence of the ability of image control on participants’ performance. Results showed that the illusion was produced in the real situation as much as in the imaginary situation, but the magnitude was larger under real perception than it was when participants were asked to imagine the oblique lines. Additionally, larger illusion magnitudes were obtained in figures with longer wings, independent of the fact that these were real or imagined. However, no significant differences in the magnitude of the illusion were found between individuals high and low in image control ability, although interactions between image control and other variables were significant.

With the exception of the study by Pérez-Fabello and Campos (2022a), the few existing reports on the influence of mental images on the Müller-Lyer illusions are all focused primarily on the object, that is, on the Müller-Lyer figures themselves, overlooking people's capacities to imagine figures. Despite the fact that image control ability, as measured by the Gordon Test of Visual Imagery (Richardson, 1969) did not influence the magnitude of the illusion, we were interested in further investigating other imaging skills. We also aimed to reconfirm the influence of wings length as had been attested in previous studies (Pérez-Fabello & Campos, 2022a). For that reason, this essay is meant to find out whether the length of the oblique lines as well as the ability to form spatial mental images and vivid images have any influence on the Müller-Lyer optical illusion, be it in real or imagined situations. To this end, two hypotheses were formulated: (1) Wing length, the ability to form spatial mental images and the ability to form vivid images exert an influence on the magnitude of the optical illusion produced by real Müller-Lyer figures. (2) Wing length, the ability to form spatial mental images and the ability to form vivid images exert an influence on the magnitude of the optical illusion produced by imagined Müller-Lyer figures. The independent variables are wing length, the ability to form spatial mental imagery and the ability to form vivid mental imagery. The dependent variable is the magnitude of the Müller-Lyer illusion, which is measured as a function of individual variations in the “Point of Subjective Equality” (PSE, see Shwartz & Krantz, 2015) both in real and imagined situations.

Method

Participants

The first group of participants comprised 171 students, 34 of whom were disregarded, 24 because they were already familiar with the Müller-Lyer figures and 10 because they were not able to imagine the oblique lines in the image situation. So, after the discarding process, the total participants were 137 (111 women and 26 men), all undergraduate fine art students. The mean age was 20.22 years (SD = 1.71), range 18–25 years. All students freely volunteered to participate in the study.

Materials

The figures used in this study were the same as those used by Pérez-Fabello and Campos (2022a), namely the combined or Brentano form of the Müller-Lyer illusion. On this occasion, three figures were tailored. One of them had 15 mm long wings forming an angle of 30° (see Figure 1) and the other had 45 mm long wings forming an angle of 30° (see Figure 2). The third figure consisted of a plain horizontal line (see Figure 3). The horizontal line of the standard stimulus was 10 cm long in all three figures, all consisting of a slider part plus a fixed part containing the standard stimulus. Additionally, at the back of the standard stimulus, there was a millimeter scale to rate the magnitude of the illusion in the attempt to match the 10 cm shaft of the standard stimulus and the sliding stimulus. If the PSE is different from the point of objective equality (0 in the millimeter scale) then a measure of the illusion is obtained. To this end, participants were asked to manipulate the sliding stimulus in such a way as to match the length of the horizontal line of the standard stimulus. The PSE was given in millimeters and could be either positive or negative.

Participants were also handed two image tests, one on image vividness, the Spanish version (Campos et al., 2002) of the VVIQ (Marks, 1973), and the other on spatial image, the Measure of the Ability to Form Spatial Mental Imagery (MASMI; Campos, 2009, 2013).

The VVIQ consists of 16 items referring to different situations which the subject is asked to visualize and to rate on a 5-point scale anchored by 5: “no image at all, you only know you are thinking of the skill” and 1: “perfectly clear and as vivid as normal vision”; thus, a high score indicates low imaging capacity. This questionnaire is meant to be completed twice. Firstly, participants must imagine the situations with eyes open, and secondly, they must imagine the same situation with eyes closed. An example of an item is: “Think of the front of a shop which you often go to… Consider the overall appearance of the shop from the opposite side of the road.” Although participants were provided with the original scale, scores were inverted at the time of statistical analysis in order to facilitate result understanding. The scale included the following response options: 1: “No image at all, you only “know” that you are thinking of the object”; 2: “Vague and dim”; 3: “Moderately clear and vivid”; 4: “Clear and reasonably vivid”; 5: “Perfectly clear and lively as real seeing” (see Gulyás et al., 2022; Zeman et al., 2015, 2020). At a later stage, the total score mean was calculated. Questionnaire reliability was estimated at 0.88 by Campos et al. (2002).

The MASMI consists of an unfolded cube that the participants had to mentally reassemble before replying to 23 questions related to the cube. Each question had four responses, two correct and two incorrect ones. Total scores were calculated by adding the correct responses and subtracting the wrong responses. Participants were allowed a maximum 5 min period to complete the test. The internal consistency of the MASMI, as measured by Cronbach alpha, was 0.93 (Campos, 2009).

Procedure

All fine arts students were asked to complete the VVIQ and the MASMI at their respective classrooms and in small groups of approximately 20 students per group. Then each participant was individually handed the closed figures in four situations, two real and two imagined. In one of the real situations, the real 15 mm and 30° figure was presented and its slider stimulus was to be adjusted to attain the same horizontal length as the standard stimulus (fixed stimulus). Similarly, the other real 45 mm and 30° figure was then presented (see video of the Müller-Lyer Figure of 30° and 45 mm in Supplemental Material).

In the imagined situation, the figure with no oblique lines was presented and participants had to imagine its wings (they were shown the real figure and told where the wings were located). In one of the situations, they had to imagine the 15 mm fins while in the other situation they had to imagine the 45 mm fins. In all situations, each participant's task was to manipulate the slider stimulus in order to attain the same length of the horizontal line of the standard stimulus. The PSE (positive or negative) obtained by each participant in adjusting the horizontal lines was measured in mm and could be found at the back side of the figures (see Figure 4). All participants tried the four situations. At no time were they informed of the PSE committed in each figure nor did they know the PSE was being assessed.

The order of presentation of the figures was counterbalanced both in the real and in the imagined situation. Subjects were not familiar with the figures; they reported having normal vision and gave written informed consent. The study protocol was approved by the Ethics Committee of our university and was performed in accordance with the 2013 Declaration of Helsinki.

Once all data were collected and analyzed, participants were divided according to high and low scores in the ability to form spatial imagery and according to high and low scores in image vividness. To classify participants into highs and lows in spatial image and vividness, we added and subtracted 1/10 of the SD from the mean, cancelling out participants who fell within the resulting interval (n = 18). In the MASMI (group mean = 13.29, SD = 11.10), participants were considered high in spatial image ability (n = 58) when their scores were above 14.4, and they were classified as low in the said ability (n = 77) when their scores were below 12.18. In the VVIQ (group mean = 3.80, SD = 0.56), they were considered high (n = 67) when their scores were above 3.86, whereas they were considered low (n = 54) when their scores were below 3.74.

Data Analysis

Statistical analysis was performed using the IBM SPSS Statistics, Version 25.0, statistical software (IBM Corporation, Armonk, NY, USA). The internal consistency of the tests was calculated by the Cronbach's alpha.

First, we carried out a Pearson correlation between all the variables in this study to see how they related to each other. For the purpose of determining whether wing length and the ability to form spatial images and vivid mental images had any influence on real optical illusions, we carried out a mixed three-way ANOVA. The independent variables were: 2 (15 and 45 mm wing length) × 2 (high and low spatial image ability) × 2 (high and low image vividness). In order to check whether wing length and the ability to form spatial images and image vividness had any influence on imagined optical illusions, we carried out a mixed three-way ANOVA. The independent variables were: 2 (15 and 45 mm wing length) × 2 (high and low spatial image ability) × 2 (high and low image vividness). The dependent variable in both ANOVAs corresponded to PSE values when trying to match the horizontal line in the Müller-Lyer's figure.

Results

First of all, we assessed the reliability of the MASMI (Campos, 2009, 2013) obtaining a Cronbach’s alpha of 0.90 and the reliability of the VVIQ (Campos et al., 2002) obtaining 0.93.

Table 1 shows the inter-correlations between the variables included in this study. The highest and most significant correlations correspond to the real and imaginary situation when comparing line lengths. Also noteworthy are the inter-correlations between spatial ability (MASMI) and the real 45 mm situation. Although low, this correlation is significant and has a negative sense, meaning that the higher the spatial ability, the lower the scores in the PSE. Image vividness also correlates with the real 45 mm situation. In this case, it is also weak but significant.

Table 1.
Correlations for study variables.

Variables 1 2 3 4 5

1. Real situation 15 mm _

2. Real situation 45 mm .50 _

3. Imagined situation 15 mm .41 .37 _

4. Imagined situation 45 mm .31 .34 .62 _

5. MASMI −.04 −.28* −.05 −.01 _

6. VVIQ .09 .20* −.01 −.01 .01

Note. PSE was estimated in variables 1–4.

*p < .05. **p < .01.

In the real situation (see Table 2 for mean values), the intra-subject contrast test of the mixed three-way analysis of variance revealed that wing length affected PSE, F(1, 115) = 105.91, p < .001, η_p² = 0.48, power = 1. In the case of the figure with 45 mm wings, participants obtained higher PSE values than in the case of the 15 mm set.

Table 2.
Means, standard deviations, median, and interquartile range of PSE (mm) in the real situation with 15 and 45 mm long oblique lines, as a function of the spatial ability (MASMI) and image vividness (VVIQ).

Length of oblique lines

15 mm 45 mm

Imagery M SD Mdn IQR M SD Mdn IQR

Low MASMI 23.06 7.60 24.00 9.00 32.97 8.69 33 12.00

High MASMI 22.56 6.40 23.00 7.00 27.88 9.04 29 15.25

Low VVIQ 21.59 6.60 23.00 8.25 28.93 9.41 29 11.25

High VVIQ 23.30 7.35 24.00 9.00 31.97 8.38 32 12.00

Total 22.78 7.09 23.00 8.00 30.63 9.25 31 12.50

Note. All PSE values indicated refer to positive illusion effect.

The interaction between wing length and spatial ability was also significant (MASMI) F(1, 115) = 10.09, p < .01, η_p² = 0.08, power = 0.88 (see Figure 5). However, no significant interaction was found between wing length and image vividness (VVIQ), F(1, 115) = 1.26, p = .26, η_p² = 0.01, power = 0.20, nor between the three variables (wing length, spatial ability, and image vividness), F(1, 115) = 0.60, p = .44, η_p² = 0.01, power = 0.12.

Figure 5.
Interaction between the length of the oblique lines and MASMI in PSE in the real situation.

The inter-subject effect tests showed that the participants’ spatial ability (MASMI) affected the magnitude of the Müller-Lyer illusion, F(1, 115) = 5.55, p < .05, η_p² = 0.05, power = 0.65. The PSE obtained by students high in spatial ability was significantly lower than students low in the said ability. However, participants’ image vividness (VVIQ) did not exert any influence on the magnitude of the illusion, F(1, 115) = 3.75, p = .06, η_p² = 0.03, power = 0.48, nor was the interaction of spatial ability and image vividness significant, F(1, 115) = 0.26, p = .61, η_p² = 0.01, power = 0.08.

In the imagined situation (see Table 3 for mean values), the intra-subject contrast test of the mixed three-way analysis of variance showed that wing length had an influence on the PSE, F(1, 115) = 33.39, p < .001, η_p² = 0.23, power = 1. In the case of the figure with 45 mm wings, just as in the real situation, participants obtained significantly higher PSE values than in the case of the 15 mm set. However, the magnitude of the illusion was not affected and nor were spatial ability (MASMI), F(1, 115) = 0.01, p = .91, η_p² = 0.01, power = 0.05, image vividness (VVIQ), F(1, 115) = 0.05, p = .83, η_p² = 0.01, power = 0.06, or the interaction between the three variables (wing length, spatial ability, and image vividness), F(1, 115) = 0.51, p = .48, η_p² = 0.01, power = 0.11.

Table 3.
Means, standard deviations, median, and interquartile range of PSE (mm) in the imagined situation with 15 and 45 mm long oblique lines, as a function of the spatial ability (MASMI) and image vividness (VVIQ).

Length of oblique lines

15 mm 45 mm

Imagery M SD Mdn IQR M SD Mdn IQR

Low MASMI 8.70 8.09 7.00 8.50 12.60 10.57 10.00 15.50

High MASMI 7.95 7.07 6.00 7.50 12.38 8.35 10.00 9.25

Low VVIQ 8.44 8.32 7.50 9.00 12.72 10.16 10.00 14.50

High VVIQ 7.87 6.56 6.00 7.00 12.45 8.64 10.00 11.00

Total 8.28 7.64 7.00 8.50 12.48 9.58 10.00 12.00

Note. All PSE values indicated refer to positive illusion effect.

The inter-subject effect tests revealed that the participants’ spatial ability did not significantly influence the magnitude of the illusion, F(1, 115) = 0.12, p = .73, η_p² = 0.01, power = 0.06. Image vividness was not affected either, F(1, 115) = 0.20, p = .66, η_p² = 0.01, power = 0.07, nor was the interaction between the three variables, F(1, 115) = 0.15, p = .70, η_p² = 0.01, power = 0.08.

Discussion

We first examined the reliability of the MASMI (Campos, 2009, 2013) finding that, according to the criteria proposed by George and Mallery (2003), it was excellent and similar to that of previous works (Campos, 2009, 2013). The reliability found for the VVIQ was also excellent according to the mentioned criteria, which confirms previous reports (Campos et al., 2002).

The correlation between the image tests, that is, visual image vividness (VVIQ) and spatial mental imagery (MASMI), was weak and nonsignificant, confirming previous results, namely −0.15 (Campos, 2009) and −0.02 (Campos & Campos-Juanatey, 2020). This is also in line with findings made in the field of neuroscience and cognition, which exposed the existence of ventral (object) and dorsal (space) visual processing streams (Goodale & Milner, 1992) and showed that the two image sub-systems codify and process visual images differently. Furthermore, in a recent study on aphantasia, that is, the inability to generate visual images, Zhao et al. (2022) demonstrated that spatial transformation is not affected in individuals who suffer from this condition. These findings suggest that, at least under specific experimental conditions, the inability to create a depictive representation of the stimuli does not prevent the engagement of spatial transformation in aphantasia.

The correlations between image measures and the real and imagined situations were low and the only significant correlation was that of spatial ability (MASMI) and the real situation of the 45 mm wings. The Müller-Lyer illusion is more intense in the real situation—perceptive—than in the imagined situation and it is also bigger in the case of figures with 45 mm fins than with 15 mm fins (Pérez-Fabello & Campos, 2022a). On the other hand, the negative correlation of the MASMI indicates that the higher the spatial ability, the lower the scores in the PSE when adjusting the shaft, which is interpreted as a higher resistance to the illusion (ver Zhang et al., 2017). Image vividness and spatial ability measure different aspects of mental imagery. When assessing possible associations between visual illusions of Ponzo and Müller/Lyer and personality traits, Grzeczkowski et al. (2017) found significant correlations between the personality trait cognitive disorganization, mental images (VVIQ) and 3 out of 4 Ponzo illusions. Hence, there are links between illusion strength and personality but only in the case of certain illusions. In another work, Mlyniec and Bednarek (2016) attempted to identify cognitive predictors of susceptibility/resistance to visual illusions of orientation in architects, that is, individuals with visuospatial skills who, during their studies, go through systematic training on spatial thought, which should be conductive to greater resistance to visual illusions. The authors were able to confirm their model, albeit weakly, since it explains 6% to 14% of the variance of the dependent variable working memory.

The aim of this study was to determine whether wing length, the ability to form spatial mental imagery, and the ability to form vivid images exerted any influence on optical illusions obtained in the Müller-Lyer figures, both real and imagined. We observed that, both in the real and in the imagined situation, wing length affected the magnitude of the illusion, with 45 mm wings generating more illusion than 15 mm wings. This result confirms a previous one obtained by Perez-Fabello and Campos (2022a). Longer oblique lines appear to generate more depth, creating richer contexts that increase the illusion (Cretenoud et al., 2020). In any case, this outcome needs to be confirmed by further studies.

The spatial ability influenced the magnitude of the illusion. Participants high in spatial ability obtained lower PSE scores when trying to adjust the length of the horizontal line of the standard stimulus, and therefore, experienced a significantly smaller illusion effect than low-skilled students. Results of the interrelation between wing length and spatial ability are somewhat similar with students in the condition of 45 mm wings being more affected by the illusion. Also, the difference between those high and low in spatial ability is stronger in this condition than in the case of 15 mm wings. There are no similar previous studies to which results can be compared, however, there are works on cognitive and temperamental factors that are susceptible to visual illusions (Mlyniec & Bednarek, 2016; Posner, 2012; Przedniczek & Bednarek, 2021; Witkin & Goodenough, 1981, Zawadzki & Strelau, 2018). Also, as already stated, Mlyniec and Bednarek (2016) studied cognitive predictors of susceptibility/resistance to visual illusions regarding orientation in architects, whose visuospatial skills should be associated with a stronger resistance to visual illusions. Furthermore, it has been consistently confirmed that field-dependent subjects are more susceptible to visual illusions than field-independent subjects (Bednarek et al., 2022, Coren & Porac, 1987, Przedniczek & Bednarek, 2021; Witkin & Asch, 1948a, 1948b). Przedniczek and Bednarek (2021) showed that individual differences in experiencing the Müller-Lyer illusion could be related to the field-dependence/independence cognitive style (Witkin & Goodenough, 1981), the low efficacy of the alerting attentional network (Posner, 2012) and temperament trait rhythmicity (Zawadzki & Strelau, 2018).

Image vividness did not exert any influence on the magnitude of the illusion. The image control ability rendered similar results according to Pérez-Fabello and Campos (2022a). In any case, new studies are needed not only to confirm conclusions but also to learn about new abilities and conditions that counteract geometric illusions, especially the Müller-Lyer illusion.

In the imagined situation, both spatial ability and image vividness exerted no influence on the Müller-Lyer illusion. This may be due to the fact that the illusion effect is not as powerful through images as via perception (Denis, 1991; Kosslyn, 1973; Ohkuma, 1986). Equally, Ohkuma (1986) also found no significant differences as for the size of the illusion between those high and low in image capacity using the VVIQ (Marks, 1973). Wallace (1984a, 1984b) found that participants high in image vividness, measured through the VVIQ, were able to form illusions in real as well as in imagined figures. Instead, those low in image vividness only reported the illusion effect in real figures but not in imagined ones.

The study of visual illusions enables us to understand more about our perceptual system by revealing its limitations. In fact, according to Morgan (2018), the perceptual biases seen in the Müller-Lyer figures are biases in basic perceptual geometry. This is to say, they involve perceptually based judgments of angle and distance. Gory et al. (2016) argue for the legitimacy of using visual illusions to investigate brain processing and group perceptual differences in behavioral studies of perception. They also believe that measures of visual illusions convey more information about neural mechanisms than ordinary stimuli because of their ability to bring out the limitations of the visual system. Over the history of the science of vision, several illusions successfully provided the first insights into how the brain processes a stimulus and the tools to investigate the neurologic characteristics of the visual system (see Eagleman, 2001, for a review). Besides, illusions are crucial from a practical perspective, especially for people handling advanced technology, for example, military pilots, drone operators, racing drivers, and surgeons using laparoscopic equipment (Ansari, 2018; Previc & Ercoline, 2004). In those cases, perceptual errors could have serious professional consequences.

The centroid hypothesis explains visual Müller-Lyer-type illusions in which subjects mistakenly perceive lines or spaces to be longer or shorter depending on surrounding distracters and states that these illusions result from a combination of neural positioning signals that cause the perceived object to be displaced towards the distracters (Morgan et al., 1990; Surkys, 2021). Length misperceptions in Müller-Lyer illusions can be accounted for by the spatial combination of positional cues that are elicited by the visual landmarks of target objects and distracting neighboring objects (Morgan et al., 1990) in such a way that the perceptual position of the target is encoded through a centroid and attracted to nearby distracters. This perceptual bias seems to increase as a function of wing length. The greater the wings length, the greater the magnitude of the illusion, both in the real (Restle & Deckler, 1977; Pérez-Fabello & Campos, 2022a) and in the imagined conditions (Pérez-Fabello & Campos, 2022a). Indeed, in their early studies, Restle and Deckler (1977) estimated that the V-shaped function of wing length was attributable to a combination of confluence (when wings are short) and contrast (which has a stronger effect when wings are longer). Essentially, the argument put forward by Restle (1977) suggests that short wings have very small weights and wing weight, that is, its relative influence on shaft length, increases as the wing gets longer.

This essay has been conducted entirely with fine art students, who have certain special features related to imagery: they are highly skilled in image abilities related to visual details (Pérez-Fabello et al., 2014, 2016, 2018), they present dissociative experiences related to absorption, fantasy proneness, and imagination (Pérez-Fabello & Campos, 2011a) and they demonstrate a remarkable creativity (Pérez-Fabello & Campos, 2011b, 2011c) which increases as they progress through their program of study (Pérez-Fabello & Campos, 2022b). All subjects were alike in age, which explains a lack of data on the influence of age on the illusion effect.

In accordance with the foregoing methodology, further research may well be directed to the way other image measures, both of spatial image, mental image rotation and image vividness, affect the Müller-Lyer illusion. It would also be engaging to investigate contrasting individuals, different academic disciplines and wider age ranges.

Major goals for future research should include two particular variables: the gender of participants and the size of the figures, especially considering the fact that previous studies (Blanuša & Zdravković, 2015) indicate that these two variables affect the horizontal-vertical illusion and they may have some influence on the Müller-Lyer illusion as well.

Normally, whenever we talk about perceptual illusions, we almost always refer to visual illusions such as those we have pointed out in this essay. However, perceptual illusions can also be created by way of the sense of touch, once again using the Müller-Lyer figures (Brown et al., 2021; Heller et al., 2002; Karpinskaia et al., 2020; Millar et al., 2002; Surkys, 2021). It would certainly be compelling to create this kind of illusions via the sense of touch using mental images.

Conclusion

Based on the result of this study, it can be concluded that the length of the oblique lines exerted an influence on the magnitude of the Müller-Lyer illusion. In the condition of 45 mm wings, participants were more susceptible to the illusion than in the condition of 15 mm wings, both in the real and in the imagined situation. In the real situation, participants high in spatial ability were more resistant to the illusion. However, image vividness did not exert any influence on the illusion magnitude. In the situation in which the figures were presented in an imagined way, no significant differences were found between the magnitude of the illusion obtained by those high and low in spatial ability, nor between those high and low in image vividness.

Variables	1	2	3	4	5
1. Real situation 15 mm	_
2. Real situation 45 mm	.50**	_
3. Imagined situation 15 mm	.41**	.37**	_
4. Imagined situation 45 mm	.31**	.34**	.62**	_
5. MASMI	−.04	−.28*	−.05	−.01	_
6. VVIQ	.09	.20*	−.01	−.01	.01

	Length of oblique lines
Low MASMI	23.06	7.60	24.00	9.00	32.97	8.69	33	12.00
High MASMI	22.56	6.40	23.00	7.00	27.88	9.04	29	15.25
Low VVIQ	21.59	6.60	23.00	8.25	28.93	9.41	29	11.25
High VVIQ	23.30	7.35	24.00	9.00	31.97	8.38	32	12.00
Total	22.78	7.09	23.00	8.00	30.63	9.25	31	12.50

	Length of oblique lines
Low MASMI	8.70	8.09	7.00	8.50	12.60	10.57	10.00	15.50
High MASMI	7.95	7.07	6.00	7.50	12.38	8.35	10.00	9.25
Low VVIQ	8.44	8.32	7.50	9.00	12.72	10.16	10.00	14.50
High VVIQ	7.87	6.56	6.00	7.00	12.45	8.64	10.00	11.00
Total	8.28	7.64	7.00	8.50	12.48	9.58	10.00	12.00

Footnotes

Author Contribution(s)

María José Pérez-Fabello: Conceptualization; Data curation; Formal analysis; Formal analysis; Investigation; Methodology; Project administration; Resources; Software; Supervision; Validation; Visualization; Writing – original draft; Writing – review & editing.

Alfredo Campos: Conceptualization; Formal analysis; Investigation; Methodology; Project administration; Supervision; Validation; Visualization; Writing – original draft; Writing – review & editing.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

María José Pérez-Fabello

Supplemental Material

Supplemental material for this article is available online.

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0.00 MB

	Length of oblique lines
	15 mm				45 mm
Imagery	M	SD	Mdn	IQR	M	SD	Mdn	IQR
Low MASMI	23.06	7.60	24.00	9.00	32.97	8.69	33	12.00
High MASMI	22.56	6.40	23.00	7.00	27.88	9.04	29	15.25
Low VVIQ	21.59	6.60	23.00	8.25	28.93	9.41	29	11.25
High VVIQ	23.30	7.35	24.00	9.00	31.97	8.38	32	12.00
Total	22.78	7.09	23.00	8.00	30.63	9.25	31	12.50