1 LITHUANIAN UNIVERSITY OF HEALTH AND SCIENCES
DEPARTMENT OF PHYSICS FACULTY OF MEDICINE VI
GROUP 33 VINCENT KHOURY
“DEPENDENCE OF GEOMETRICAL LENGTH ILLUSION ON DISTRACTOR SIZE”
SUPERVISOR: PROF. ALEKSANDR BULATOV REVIEWER: PROF. A. BAGINSKAS
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TABLE OF CONTENTS
1. TITLE PAGE 1 2. TABLE OF CONTENTS 2 3. SUMMARY 3 4. ACKNOWLEDGEMENT 4 5. CONFLICTS OF INTERESTS 4 6. ABBREVIATIONS 4 7. KEY WORDS 4 8. INTRODUCTION 5-6 9. AIM AND OBJECTIVES 710. LITERATURE REVIEW 8-27 11. RESEARCH METHODOLOGY AND METHODS 28
12. RESULTS 29
13. DICUSSION OF THE RESULTS 29-30 14. CONCLUSIONS 30-32 15. PRACTICAL RECOMMENDATIONS 32 16. LITERATURE LIST 32-34
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SUMMARY
VINCENT KHOURY
“DEPENDENCE OF GEOMETRICAL LENGTH ILLUSION ON DISTRACTOR SIZE.”
AIM
Our purpose of this study is to consider the different theoretical approaches of explanation of the illusion of extent of the Muller-Lyer type in order to assess the current state of the illusion study.
OBJECTIVES
1. To describe different types of stimuli that evoke the illusion phenomenon
2. To describe the “psychological” explanations. (figures made up of lines, dots, color contrast, texture, etc.)
3. To describe “physiological” explanations (eye movements, spatial filtering, etc.) 4. To describe the “centroid” explanation.
5. To compare the features of different explanations by emphasizing the quantitative nature of the “centroid” explanation.
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METHODOLOGY
The studies were derived from various databases such ncbi, research papers (Acts Neurobiol Exp 2009, Vision Research 71, Vision Research xxx 2010, Acta Neurobiol Exp 2015 etc).
The articles were checked for bias and proper quality, then revised by the author's supervisor. Followed by studies upon graphs and results and control studies, summing up all methods and coming up with the best methods for the explanation of the Muller-Lyer type.
RESULTS
Plenty of results were written to describe the different types of stimuli that evoke an illusion and how they work. Furthermore, a comparison of the magnitudes of the two stimuli were
mentioned.
CONCLUSIONS
the outcomes of this experiments are applicable with the theories which will be mentioned.
ACKNOWLEDGEMENT
A great effort and hard work done in order to state and explain the combination of methods and techniques to explain the different types of stimuli, the psychophysical concept and the centroid concept.
CONFLICT OF INTEREST
No conflict of interest.ABBREVIATIONS
M-L (Muller-Lyer) O-K (Oppel-Kundt)KEY WORDS
Stimulus, Jolt, M-L, Contrast, Distracter, Size, Illusion, Perpendicular, Magnitude, Strength, Neural process, Visual illusion, Dots, Arrow heads.
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INTRODUCTION
Dependence of geometrical length illusion on distractor size, is one of the most recently observed topics in the optical physics field.
The Muller-Lyer type illusion, and similar illusions, demanded further explanations allowing the development of variant hypothesis to describe the topics using different methods.
Lots of studies and experiments have been performed to understand the correlation between neural cells and the distractor’s size and location; Specifically, how the first are affected by its own dimensions and placement.
The Müller-Lyer illusion is an optical illusion formulated by Franz Carl Müller-Lyer (1857– 1916), a German sociologist, in 1889. This illusion shows that when viewers are asked to mark the midpoint of a stylized arrow they tend to place it more towards the “tail” end.
A similar representation of this action today consists of a set of arrow-like figures where the line segment forming the shaft of the arrow with two tails is perceived to be longer than that forming the shaft of the arrow with two heads.
Each of the arrows is composed of middle straight-line segments of equal lengths, making up the "shafts" of the arrows, while the ends of the arrows are resembled by shorter line segment
extends known as the “fins”. There are two portrayals of the fins, one can point inwards to form an arrow "head" or outwards to form an arrow "tail".
This proposal by Müller-Lyer, just like any other visual and perceptual illusions, provides a solid base for neuroscientists to understand how human brain and visual system perceives images. Never the less, likewise conceptions have been used by different artists to convey a better effect in their works.
Cases of failure of the human brain to accurately interpret certain kinds of visual scenes in the world, such as Müller-Lyer illusion’s helps further learning about the human visual system. This, have permitted several explorations attempts to explain the mechanism of the Müller-Lyer illusion.
Studies have shown culture can influence basic aspects of perception such as the length of a line. Resulting search results, it was noted by W.H.R in around the 20th century, that indigenous
6 people of the Australian Murray Island were less susceptible to the Müller-Lyer illusion. Rivers proposed that this difference may be due to Europeans living in more rectilinear environments.
Similarly, in 1960’s, John W. Berry came out with comparable outcomes during his work on Inuit, urban Scots.
Other examinations to four variant visual illusions were made on three different populations in 1963. This research conducted by Segall, Campbell and Herskovitz compared the perceptions of Caucasians, twelve Africans, and one from Philippines. The sample displayed a 1.4% to 20.3% percentage of mean fractional misperception of the length of the line segments. The three European-derived models were the three most vulnerable ones, while on the other hand, the San foragers of Kalahari Desert were the least susceptible.
In 1965, Marshal Segall, student of Donald T. Campbell and Melville J. Herskovits, was suggested to investigate the problem of whether culture could influence basic aspects of perception such as dimensions of the element after a debate between the two.
The researchers managed to conclude that different cultures differ substantially on how the experience the Müller-Lyer stimuli based on a led investigation that included seventeen cultures and was presented in their definitive paper of 1966. The paper stated that "European and
American city dwellers have a much higher percentage of rectangularity in their environments than non-Europeans and so are more susceptible to that illusion.”
"Carpentered" was a word used by the scientists to describe the environments where Europeans mostly live in- characterized by straight lines, right angles, and square corners.
What are the different theoretical approaches of explanation to the illusion extent of the Muller- Lyer type that enables us to assess the current state of the illusion study?
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AIM AND OBJECTIVES
Aim
Our purpose of this study is to consider the different theoretical approaches of explanation of the illusion of extent of the Muller-Lyer type to assess the current state of the illusion study.
Thus, by performing researches in different databases (such as Acts Neurobiol Exp 2009, Vision Research 71, Vision Research xxx 2010, Acta Neurobiol Exp 2015 etc) and collecting data on various methodologies that have been used, we can understand how the illusion of extent of the Muller-Lyer type works, along with supporting variant theories.
Objectives
1. To describe different types of stimuli that evoke the illusion phenomenon.
2. To describe the “psychological” explanations. (figures made up of lines, dots, color contrast, texture, etc.)
3. To describe “physiological” explanations (eye movements, spatial filtering, etc.) 4. To describe the “centroid” explanation.
5. To compare the features of different explanations by emphasizing the quantitative nature of the “centroid” explanation.
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LITERATURE REVIEW
- The different types of stimulus:
The Muller-Lyer illusion is not the illusion that only evokes the illusion phenomenon. Of course, there are many more illusions that produce this phenomenon.
Later on, in this discussion, we will present one of them.
One of the basic approaches of this review is to discuss the different stimulus triggers responsible for the Muller-Lyer illusion.
This discourse has been studied by various scientists throughout history trying to explain the different causes behind the illusion.
First goes back to Kundt in 1863, who discussed how a portion and a part of the line figure was re- illustrated into the example which describes vertical stripes of modifying tallness, number and dissemination.
The other goes back to 1902 where Ebbinghaus stated that the stripes that had a specific were stronger than numerous lines turns into a strong phenomenon.
Moving on to 1960 Oyama discussed how the consistency and distribution were very important for the ill to be manifested.
Then, in 1997 professor Bulatov stated that if dots formed the whole picture or figure, the illusion power would appear the same to the one made up of stripes.
One of these many studies conducted to clarify the stimuli of this illusion, has been portrayed in an article holding the following title “Temporal Dynamics of the Oppel-Kundt Illusion compared to the Muller-Lyer Illusion”. Which contrasts two different stimuli O-K and M-L which proved from here that there are different kinds of boosts.
This experiment explained in the piece argued, that the decreased length of the illusion was caused by the difference of luminosity contrast between two stimulus parts.
It also proved that the illusion magnitude was reduced by the absence of the luminance contract and that the white figured against the dark background showed that the O-K effect a bit increased with the absolute luminance contrast and was higher for the negative than for the positive
9 polarity as just as it was stated by Wackermann 2012.
It also came to the conclusion that the illusion was induced by the two filled intervals flanking the empty one which were the three-part O-K figure, the induction was 25% stronger than the one caused by conventional two-part figure with one filled interval as told by Bertulis in 2009. All of this has been obtained after leading a testing with the help of Cambridge Research
systems, VSG 2/3 and photometers and was adjusted by the Psychophysical Experiment Toolbox in Mathworks MatLab software platform.
As for the participants, they were between 19 to 70 years, and a number of 15 including males and females.
During the O-K experiments, 6 observers were present, and in the M-L studies 7 observers were present. In the two experiments, the two remaining subjects were present. In addition to the fact that there were no subjects that had any eye problem or any difficulty to see and observe.
From here, they were placed in a dark room and were asked to gaze at the monitor screen where a stimuli was induced to judge afterwards the stimulus extent after the making pattern off set. To do that they had to press a keyboard button to check if the referent part shown seemed longer than the last part.
400 cm was the distance between the screen and the participant’s visual system. Against a dak horizontally background a stimuli was showed.
Figure 1 and 2 showed the fixation point (2x3 arc min size and 52 cd/m2 luminance) for 700 ms, a stimulus itself with different duration of presentation and the mask appearing after the figure offset and lasting 2s, those were the stimulus component and how they presented.
400 ms in between the fixation point offset and the stimulus onset was the delay.
The stripes of the 1.4 arc min width, 28 arc min height and 52 cd/m2 luminance as shown in figure 1B were forming the O-K stimulus. The results showed that the O-K illusion was
relatively poor and weak at the beginning of the visual processing. Not to forget to mention that the illusion gets bigger in strength with longer time, the 700-1000 ms exposure durations were enough of the O-K illusion to complete its performance under the conditions of the experiments. The experiments used a variety of shown durations which were obtained by the psychometric
10 functions as shown in figure 3.
Establishment of the curves of the O-K illusion magnitude as functions of the stimulus duration were shown in figure 4, for all observers.
Figure 6 shows that the psychometric functions were generated in the experiment with the M-L hallucination.
The 0.5 frequency shows the seen equality of the reference and test which are illustrated more often on the curves.
As for during early steps, the M-L illusion showed to be the strongest then it decreased with time when the jolt was elongated.
Based on that the suggestion that overestimates of the filled interval in the O-K stimulus was supported by the data acquired.
In conclusion it could be said that the Muller-Lyer illusion which has been studied since the end of the 19th century is another famous example of visual length changes.
For The O-K stimulus is not the same as the M-L stimulus because the components are not uniform, there is presence of the contextual distractions composed of intersecting lines, the auditory modality has no analogous stimulus.
The temporal dynamics of the M-L illusion might be linked with the time course of subsequent neural activation at various degrees of the perceptual system, these were the results of the fMRI experiment stated by Weidner and Fink in 2007.
Somehow between a range of 85 and 130 ms after the ML stimulus onset the early perceptive zones become stimulated.
Within the range of 195-220 ms strong activation becomes stimulated it includes many parts of the brain such as the ventral perceptive stream involving the inferior occipital, inferior, temporal and fusiform gyri.
Thus, the activation locations in the brain show an influence of higher-level of perceptive processing to the M-L illusion manifestation and it shows how neural pathways are linked with the brain being responsible for objects identification, shape-size representation and detail image.
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Fig. 1. Shows the Oppel-Kundt stimulus presentation. (A) the gaze fixation point; (B) filled-unfilled figure and (C) the masking pattern.
Fig. 2. Shows the M-L stimulus presentation. (A) the gaze fixation point; (B) the M-L figure with outward-pointing wings on the left (reference); (C) the masking pattern.
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Fig. 3. Show several examples of individual psychometric functions for different duration of the O-K stimulus: 80, 200, 400 and 1000 ms. Dots, the experimental data. The horizontal line segments indicate 95% confidence intervals at the levels of the “longer-than” judgements with the 0.25, 0,50 and 0,75 frequencies. There were 7 stripes forming the filled stimulus part.
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Figure 6 illustrates examples of people psychometric functions (subject ER) in relation to non- similar duration of the M-L jolt which are sixty, eighty, one hundred and twenty, two hundred ms.
- The psychophysical concepts:
The ability of our vision plays a very important role on how to interpret the surrounding environment using light in the visible spectrum reflected by the objects in this environment. One of the major problems in our visual perception is that our eyes “lie” to us, meaning that if we look at a visual illusion our eyes can trick us. They are various components of the illusion that plays a big part in tricking our eyes, such as: the figure made up of lines, the dots, the contrast, the texture, the distance etc.
One of the basic point of view of the following experiment is to explain how different
components of the illusion (as mentioned above) and the distractor, affect the way we see the illusion in a geometrical way.
First goes back to Morgan and Casco in 1990, who discussed the centroid biases concept as being an idea explaining that, our visual system uses indirect zones that corresponding through centroids of the response of “electric” entities with big receptive fields.
This psychophysical study examines positional coding via the concept of centroids, the article is titled “Influence of Distracter on Perceived Stimulus Length and Angle Size”.
14 The experiment was performed in a dark chamber.
27 participants were used for this experiment, such as university teachers and students.
The keyboard buttons were pressed by the participants to change the dots position to the told and required directions one pixel at a time. The object’s shape, size and distance did not change while the dots position was being changed by the participants. No instruction about eye fixation was handled to the participants in experiments 1 and 2 unlike experiment 3 where the participant were obliged to keep their eyes fixed at the position 25 min of arc above the central spot of the jolt.
3 kinds of stimuli were used in this experiment as shown in figure 1, and, 2 kinds of experiments were performed.
3 dots positioned vertically or horizontally composed the first jolt.
The participant had to observe how the dots were aligned and then judge them with the presence of the flanking line distracter jolt seen in figure 1A.
3 dots were positioned in a manner of right angled geometrical triangle as seen in jolt 2, the ones who were observing were told to judge when they saw the figure and should tell whether the right angle of the triangle was big or shorter than 90 degrees while not forgetting the distracter who were positioned vertically, horizontally and at 45 degrees as seen in figure 1B.
Figure 1. A showing the flanking line distracter jolt, B showing
a 45 degrees angle, C showing a Bretano type jolt.
Later in this experiment, the participants who were observing were told to link the seen linear extent of an interpolated Bretano type jolt as seen in figure 1C.
Experiment 1 was described in the following.
15 jolt spots and the distracting stripes of stimulus type 1 is main goal of experiment 1.
The middle spot were corrected in a way which made all three dots to form an imaginary line, this action was done by the participants.
The results of experiments 1 described a misalignment of the three dot stimulus was the positions of the dots from a straight line were reported by the observers.
Figure 2 showed this information and this information pointed that the illusion is absent when the place of the stripes intersect with those of the dots.
This experiment presented the following results:
The results were symmetrical and they were given for the horizontal and vertical jolts
orientations and those information showed the borders of the distance of the seen action of the distracting stripes.
In experiment 2, 3 dots seen in type 2 formed a right angle jolt which showed in a form of an imaginary triangle with the orthogonal orientations of two sides equal in length (30, 69, 90 min of arc).
Figure 1B depicts and shows two flanking striped at the end sports that were pointed parallelly with the imaginary sides, the third stripe angle was 45 degree to the vertical.
The measurement of the stripes were 2.5, 5.0 or 7.5 min of arc long.
The fluctuation of the stripes were 25 min of arc limits in the 0.5 min of arc steps with a random distribution in this experiment.
The angle sides appeared orthogonally due to the fact that the participants told that interpolated angle size and modified it by changing the two end spots at the same time.
The participants modified the angle in a row of 0.2 degrees steps.
The results were showed in Figure 3 which exposes the flanking stripes that cause the distortions of the right angle which are increased in amplitude (10-15 min of arc) in contrast to those which were takes in the seen alignment tast.
Figure 3 also describes a regularity in growth of the illusion strength up to maximum when the stripe-to-spot distance got bigger on either side of the dots, and a decrease of the illusion was noted while the distance increased.
16 Figure 4 shows the maximum value of the illusion and its place on the curves which increases linearly with the increasing size of the sides of the interpolated angle.
These data also support the explanation of the origin of distortions by the local integration processes within the proximal surroundings of the stimulus parts and by a perceptual shift of the positions of the stimulus basic spots toward the flanking spot pairs.
- The centroid concept:
The centroid concept plays an enormous role on the illusion and how it affects our visual pathways because the centroid is one of the main components of how the illusion work. In 2006, Searleman, mentioned that the concept of the centroid extraction is the core and the basis of how the M-L illusion works. Searlman theory was validated when he performed various psychophysical studies and experiments with additional points as non-target jolts when they were positioned in different areas near the wings at the intersections.
It goes back to Poggendorff in 1994 and the Ponzo in 2004 who applied the theory of the
centroid extraction, they reported by performing various studies, that this theory was successful. The upcoming article titled “Centroid extraction and illusions of extent with different
contextual flanks” has an objective to fabricate a computation model which relies on the centroid theory, then to compare the outcome.
This experiment used, three types of object which had non similar 3D structure and they were producing the same visual distortions.
The trials were completed in a dim room (the encompassing brightening <0.2 disc/m2). A Sony SDM-HS95P 19-inch LCD screen (spatial determination 1280×1024 pixels, outline revive rate 60 Hz) was utilized for the jolts introductions. A Cambridge Exploration Frameworks OptiCAL photometer was connected to the screen luminance go alignment and gamma remedy. A button and temple rest was utilized to keep up a consistent survey separation of 300 cm (at this separation every pixel subtended around 0.33 min of circular segment); a simulated understudy (an opening with a 3 mm breadth of a stomach put before the eye) was connected to diminish optical abnormalities.
17 disc/m2 in luminance (the screen was secured with a dark cover with a roundabout gap to keep onlookers from having the capacity to utilize the edges of the screen as a vertical/even
reference). For every one of the boosts illustrations, the Microsoft GDI+ antialiasing system was connected to keep away from spiked edge impact.
Figure 1A showed the object of the M-L wings. Figure 1B showed an object made of vertical striped included into a three-spot figure. Figure 1C showed a pattern that was illusory.
At the start of the experiment, the centroid extraction was presented as a physical and physiological background of the centroid extraction. The equation of the modelling was:
where the normalized mass, m = Ma/M. In the present approach, mass is considered as the amplitude of the neural excitation which is proportional to the object luminance, e.g., M and Ma are taken as luminance of the target (stimulus terminator) and distractor (contextual flank), respectively.
Experiment 1 has the objective to quantitatively show the power of the three illusion as functions of the length of the wings (w) or the sides that are diagonal of the triangle that is imaginary. Only four participants in this experiment. The results of this experiment, exposed the same and one tone of growth of the visual illusion’s magnitude. The magnitude got taller in length of the wings. The increasing wings grew from to 0 to about 7 min of arc as shown in Figure 4A. But there was an absence of difference of the wings less than 9 min of arc.
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Figure 1, (A) shows arrows made from segments that are diagonal, (B) shows stripes that are vertical. (C) shows pairs of spots that are vertical
The internal angle of the contextual wings (α) were changed in random way from 10 degrees to 350 degrees in steps of 8.5 degrees as shown in Experiment 2.
64 min of arc was the length of the referential part of the stimuli, 8 min of arc were the fixed length of the wings. The same four participants who took part in Experiment 2 also were present in Experiment 1.
The result were the following: symmetrical curves were shown by the visual illusions of the functions of the internal angle of the wings in which figure 5A shows the two parts comprising positive and negative values. The power of the illusions went back to zero when the internal angle was near 180 degrees.
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Figure A shows the increasing wings expressed as the curve.
The results of experiment 2 correspond the explanations of the result of Experiment 1. Meaning that there was a good link between the computational and experimental information that validate the concept about the same neurophysiological mechanism of automatic centroid extraction of the visual illusion due the three different appendages as shown in Table II in the coefficient of determination R2 where is it is bigger than 0.9 in all the cases.
Later, Experiment III was done to analyze the jolt size influence on the illusion magnitude. Figure 1C shows the further details. In this experiment, only three subjects were present. One of them participated in Experiments 1 and 2.
The size of the stimulus changed, its size of the referential was 32, 64 and 96 min of arc. The experimenters measured the power of the visual illusion as a function of the wing size, w varied in a random way from 0 to 20 min of arc in 0.5 min of arc steps.
The results were exposed in Figure 6A and 6B that show a shift in the positions of the maxima on the curves toward the longer wings, which provides a good support for the assumption that
20 averaged area of the centroid extraction, Ωaveraged increases with the size of the referential part of the stimulus.
Figure 6, A, B show a shift in the positions of the maxima on the curves toward the longer wings and C.
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Table 2 showing the data of Experiment 2.
Like we mentioned earlier, the centroid concept, plays a big and important on the illusion and how our visual perception perceives it.
Things goes back in 1990 and 1991, where Morgan and Glennerster talk about the hypothesis in relation to the non direct coding position with the help of centroids.
Also, another theory states that, spatial assimilation of neural excitations stimulated by the neighboring parts of the stimulus explain and discusses the M-L illusion.
Furthermore, this hypothesis states the figure terminators or in other words the wings apexes are failed to be located by the visual system independently from the wings themselves.
Therefore, according to the “centroid” hypothesis the illusions comes the terminators positional errors.
The following article titled “A quantitative analysis of illusion magnitude changes induced by rotation of contextual distractor”, article discusses the centroid hypothesis which stats that the illusion is the main reason for the perception of the eliminators restriction errors.
The experimental and theoretical information of this experiment validate the idea that local positional biases caused by the neural processes of centroid extraction is one of the causes of birth of the illusion of the M-L type.
22 The trials were completed in a dim room (the encompassing brightening <0.2 disc/m2).
A Sony SDM-HS95P 19-inch LCD screen (spatial determination 1280×1024 pixels, outline revive rate 60 Hz) was utilized for the jolts introductions. A Cambridge Exploration Frameworks OptiCAL photometer was connected to the screen luminance go alignment and gamma remedy. A button and temple rest was utilized to keep up a consistent survey separation of 300 cm (at this separation every pixel subtended around 0.33 min of circular segment); a simulated understudy (an opening with a 3 mm breadth of a stomach put before the eye) was connected to diminish optical abnormalities.
Jolts were displayed in the focal point of a round shaped foundation of 5º in width and 0.4 disc/m2 in luminance (the screen was secured with a dark cover with a roundabout gap to keep onlookers from having the capacity to utilize the edges of the screen as a vertical/even
reference). For every one of the boosts illustrations, the Microsoft GDI+ antialiasing system was connected to keep away from spiked edge impact.
The subjects were requested to control the console catches "←"and "→" to move the Müller- Lyer wings into a position that makes both jolt interims perceptually parallel long; the deviation of the situation of the focal eliminator from the physical midpoint between the sidelong
eliminators was considered as the estimation of the illusion size. A solitary catch push changed the situation of the eliminator by one pixel comparing around to 0.33 min of circular segment. The underlying length contrasts between the left and right boost interims were randomized and conveyed uniformly inside a scope of ±10 min of circular segment.
The subjects were urged to keep up their look on the focal jolts.
The result showed, that while the distractor declined from the horizon the illusion magnitude decreases and went to zero when the tilt angle got closer to 90 degrees or 270 as can be seen in Figure 4.
23
Figure 3 displays the illusion magnitude as a function of the tilt angle
From this experiment, we can conclude and assume that it describes the procedure of the centroid extraction because lots of following neural processes has not been mentioned.
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Figure 4 shows the illusion magnitude as a function of the tilt angle of the long symmetric M- L wings. The left column shows the circles for tilting of the acuteαangle which is equal to 30 degrees, and right the obtuse angleαequals 120 degrees.
The way the illusion presented as an image, or as a right angled triangle or as circle plays enormous role on how the visual system perceives it.
Let’s take for example the M-L illusion, the stimulus terminators or the wings vertices and the adjacent contextual flanks or the wings themselves are failed to be extracted or perceived by the visual system. The length of the spatial intervals flanked by outward-going or inward-going wings are overestimated or underestimated by the observer.
25 components.
In the article titled “Perpendicularity misjudgments caused by contextual stimulus elements” the influence of the rotation of contextual distracters of the magnitude of the illusion of
perpendicularity are going to be explained by the “centroid” approach. Four participants were present in this experiment.
In a obscure room, the experiment took place. A Sony LCD monitor was used. In the center round-shaped background the stimuli were presented.
In the following quotation the stimuli used in this experiment were described as follow: “Stimuli used in experiments consisted of three terminators (three dots, or one dot and two vertices of the Müller-Lyer wings, or two dots and one vertex of the wings) placed at the apexes of an imaginary isosceles rectangular triangle; the distracters, either the Müller-Lyer wings themselves or short bars, were rotated around the corresponding terminators (Fig.1). Two
different modes of stimulus presentation were employed in two series of experiments. In the first series, two distracters were rotated around the lateral stimulus terminators (i.e., those at the crossings of the triangle legs and hypotenuse); the central terminator was represented by a single dot (Fig.1, upper row). The tilt angle, of the bisector of the lower distracter (i.e., that is adjacent to the dot forming the horizontal leg an imaginary triangle) was randomly changed from 0 to 360 degrees, whereas the tilt angle of the upper distracter was varied as 90 degrees. In the second series of experiments, a single distracter was rotated around the central terminator (i.e., that at the apex of the right angle), and the lateral stimulus terminators were represented by dots (Fig 1, lower row).”
Into the position that made the two triangle legs perceptually orthogonal to each other, the participants were told to change the keyboard buttons “left arrow” and “right arrow” to move the lateral stimulus terminators symmetrically along the arc of a circle.
In these experiments, they used two types of stimulus.
Bars were the stimulus in the first stimulus condition, in the second one the stimulus was the M- L wings.
26 In this case the neural processes of centroid extraction which increases visual illusionary
positional shifts of jolts terminators toward the adjacent contextual distracters are the cause of the misjudgments of the perpendicularity.
Figure 2A shows the rotation of two lateral distracter, by this law:
It evokes perceptual modifications changes of the size of the “right” angle.
The determination of the magnitude of the right-angle adjustment errors caused by the perceptual displacements of the lateral stimulus terminators is the objective of the first series of
experiments.
Figure 3 shows the magnitude of the illusion is plotted as a function of the tilt angle of bisector of the lower distracter as expected according to formula (3):
Formula (3) the experimental results shows a sinusoidal pattern of modification in illusion magnitude for both types of distracters.
Graph 3, shows that the illusion magnitude decreases with distracters bisectors deviation from perpendicularity and diminishes with distracters bisectors deviation from perpendicularity and went back to zero when the tilt angle “θ” went toward 0 degrees or 180 degrees for instance: along the triangle, the bisectors were oriented.
The second series of the experiment had an aim to see the effect of a single distracter rotation. Θ, the tilt angle, of the distracter bisector was modified from 0 degrees to 360 degrees. The results for the two types of distracters show the curves similar to the inverted sinusoid shifted along the abscissa axis to the left approximately by 40-50 degrees as shown in Figure 4.
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Figure 4 shows the magnitude of right-angle adjustment errors as a function of the tilt angle of two types of distracters: bars (circles) and the M-L (squares). The mode of stimulus
presentation is the rotation of a single central distracter. Solid and dash-dot curves show the least squares fits of Eq. (2) with the corresponding substitution by formulas (7) or (9) for the stimuli comprising the bars or the M-L wings, respectively. Error bars.
All in all, we can conclude that there is a demonstration that the function (1) and (2) agree with the modification and changes of the illusion for the two distracters as shown in Figure (3) and Figure (4), the “solid and “dash-dot” curves.
In summary, the outcomes of this experiments are applicable with the concept that local positional shifts of stimulus terminators can be one of the main reasons of emergence of the illusion of the perpendicularity studied.
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METHODOLOGY AND METHODS
In all of the experiments described in the “Literature review” section. The experiments started with introduction that introduced the experiments and mentioning the objective, followed by the number of participants that were present and a description on how the experiment was taking place; describing the room and the stimulus for instance. Moving to the results and discussion then finally a conclusion that aims at answering the objective of the experiment. Different kinds of tables, curves and equations were used.
Different hypothesis and objectives were used according to each experiment.
For instance in the article entitled “Temporal dynamics of Oppel-Kundt illusion compared to the Müller-Lyer illusion”, they were different aims such as demonstrating that the decreased length of the illusion was caused by the difference of luminosity contrast between two stimulus parts and another objective was to prove that the illusion magnitude was reduced by the absence of the luminance contract and that the white figured against the dark background showed that the O-K effect a bit increased with the absolute luminance contrast and was higher for the negative than for the positive polarity as just as it was stated by Wackermann 2012.
As for the participants, they were between 19 to 70 years, and a number of 15 including males and females.
In summary the most reliable method used to determine the illusion strength with time were the graphs which were including curves.
This means that the longer the person looks at the illusion the lesser the effect of the illusion on the person.
The opposite happened for the O-K stimulus.
Figure 1 and figure 2, were not enough to describe the power and the duration of both stimulus. They were good at only presenting: the arrows pointed outward or inward, the reference interval, the gaze fixation dot and the masking pattern. But, they could not provide any further
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RESULTS
The results showed that the O-K illusion was relatively poor and weak at the beginning of the visual processing. Not to forget to mention that the illusion gets bigger in strength with longer time, the 700-1000 ms exposure durations were enough of the O-K illusion to complete its performance under the conditions of the experiments.
The experiments used a variety of shown durations which were obtained by the psychometric functions as shown in figure 3.
Establishment of the curves of the O-K illusion magnitude as functions of the stimulus duration were shown in figure 4, for all observers.
Figure 6 shows that the psychometric functions were generated in the experiment with the M-L hallucination.
The 0.5 frequency shows the seen equality of the reference and test which are illustrated more often on the curves.
As for during early steps, the M-L illusion showed to be the strongest then it decreased with time when the jolt was elongated.
Based on that the suggestion that overestimates of the filled interval in the O-K stimulus was supported by the data acquired.
DISCUSSION OF THE RESULTS
As we mentioned earlier in the results section, both stimulus begin at the same duration interval which is between 80 to 100 ms. But, at a longer period of time, the show opposite results. We can notice an increase of the O-K visual illusion power while the opposite effect is seen in the M-L illusion.
These result are consistent when it comes to the outcomes which goes back to Bailes in 1995 and to van Zoest and Hunt 2011.
Both illusion are accomplished in about an interval of 700 to 1000 ms. At the shortest duration of time the strongest stimulus and illusion appears.
The hypothesis of low- or band- pass spatial frequencies mentioned by Ginsburg in 1984 and Bulatov in 1997 is reliable to the idea that the most powerful M-L effect matches with the
30 shortest stimulus duration.
The hypotrophy of the receptive fields shows a that the M-L illusion magnitude decreases at short which is less than 150 ms.
Due to the fact that higher-level neural processing provides corrected interpretation of spatial relationships of stimulus elements, longer duration of observing the illusion allows the collection of data that shows inaccurate initial perception.
Extra time consuming integration processes are accountable for the evolution of the O-K illusion as shown by the illusion magnitude growth with increasing stimulus duration (Fig. 5).
A neural activation located in the limits of spatiotemporal window, are caused by the parts of the O-K figure such as when perceiving as one entity during comparison.
Reynolds in 1981 and Mather in 1988 showed outcomes from different studies, they point that vision in a continuous way when observing contours that illusory, these contours arise after an interval of 80 to 100 ms of duration.
There is no contradiction between the outcomes of the experiments evoked earlier, and, the fact the visual perception of continuity plays a role in the presentation of the illusion.
Last but not least, further investigations should be taken into consideration to check the theory on the vision of the filled area of the O-K stimulus as one body.
CONCLUSIONS
We described and introduced two different types of stimuli that evoke the illusion phenomenon: the O-K and the M-L. Also, we explained how their strength magnitude varies with the duration. At first, between the interval of 80 to 100 ms (duration) the O-K is not strong. But, with time and for about a duration of 700-1000 ms the O-K becomes stronger.
Conversely, at early phases, the M-L is shown to be stronger but with the duration they become weak.
Also, we have been introduced to psychophysical accept of the illusion. How the lines, the dots, the arrowheads, contrast, somehow the eye movements, the spatial filtering, the magnitude. The psychophysical study examined the psychophysical idea in the article titled “Influence of Distracter on Perceived Stimulus Length and Angle Size”, that investigates and studies the
31 illusion of alignment, orthogonal orientation and length matching. The outcomes where the quantitative criteria of different perceptual illusions.
Subsequently, we mentioned the centroid concept and we explained how it worked.
The result showed, that while the distractor declined from the horizon the illusion magnitude decreases and went to zero when the tilt angle got closer to 90 degrees or 270. The experiment showed curves that were symmetrical with parts including positive and negative values. From this experiment, we can conclude and assume that it describes the procedure of the centroid extraction because lots of following neural processes has not been mentioned.
The upcoming article titled “Centroid extraction and illusions of extent with different
contextual flanks” has an objective to fabricate a computation model which relies on the centroid theory, then to compare the outcome. The experiment shows a shift in the positions of the maxima on the curves toward the longer wings, which provides a good support for the
assumption that averaged area of the centroid extraction, Ω averaged increases with the size of the referential part of the stimulus.
The way the illusion presented as an image, or as a right-angled triangle or as circle plays
enormous role on how the visual system perceives it. Let’s take for example the M-L illusion, the stimulus terminators or the wings vertices and the adjacent contextual flanks or the wings
themselves are failed to be extracted or perceived by the visual system. The length of the spatial intervals flanked by outward-going or inward-going wings are overestimated or underestimated by the observer. The visual system has an ability and a skill to evaluate the mutual
perpendicularity of image components. The result showed, that while the distractor declined from the horizon the illusion magnitude decreases and went to zero when the tilt angle got closer to 90 degrees or 270. The experiment showed curves that were symmetrical with parts including positive and negative values.
From this experiment, we can conclude and assume that it describes the procedure of the centroid extraction because lots of following neural processes has not been mentioned.
The way the illusion presented as an image, or as a right-angled triangle or as circle plays enormous role on how the visual system perceives it.
32 Let’s take for example the M-L illusion, the stimulus terminators or the wings vertices and the adjacent contextual flanks or the wings themselves are failed to be extracted or perceived by the visual system. The length of the spatial intervals flanked by outward-going or inward-going wings are overestimated or underestimated by the observer.
The visual system has an ability and a skill to evaluate the mutual perpendicularity of image components.
In the article titled “Perpendicularity misjudgments caused by contextual stimulus elements” we can conclude that the outcomes of this experiments are applicable with the concept that local positional shifts of stimulus terminators can be one of the main reasons of emergence of the illusion of the perpendicularity studied.
PRACTICAL RECOMMENDATIONS
The experimenters should have mentioned a more detailed explanation about neural processes.
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