Graduation thesis,
Faculty of Science,
2022.

Quantitative measurement and simulation ofperceptual intensity in the vanishingillusion.

Field NameMaterials Science
Student registration no.
192052 Mr.

Name

Taiyo Kono
Supervisory teacher Michelette
1

Rudzero.

Submitted on 1 January 2023.

2

Submitted on 1 January 2023

Table of Contents
Table of Contents ........................................................................................................................ 2
1 Chapter Introduction .............................................................................................................. 3
1.1

Background. ...................................................................................................................... 3

1.2 Research objectives ........................................................................................................ 3
2 Chapter Related research ..................................................................................................... 4
2.1

Definition of optical illusions ............................................................................... 4

2.2

Illusion as a research tool ...................................................................................... 5

2.3

About the viewing angle .............................................................................................. 6

2.4

Spatial frequency characteristics of vision and contrast sensitivity
functions ......................................................................................................................... 8

2.5

Hybrid image ................................................................................................................... 9

3 Chapter 3: Experimental overview .................................................................................. 10
3.1

About PsychoPy ............................................................................................................ 10

3.2

Experimental environment and subjects................................................................ 14

3.3

On experimental equipment and vanishing illusions ........................................ 14

3.4

Experimental structure .............................................................................................. 16

3.5

Experimental methods.................................................................................................. 17

4 Chapter 18: Results and analysis of visual illusion effects ............................. 18
4.1

Verification of illusion effects with static illusions ............................... 18

4.1.1

Comparison of the illusion effect of each masked image ......................... 18

4.1.2

Relationship between observation distance and illusion effect......... 22

4.2

Verification of illusion effects by dynamic illusions. ............................... 27

4.2.1

Illusion effects associated with drift in mask images. ....................... 27

4.2.2

Illusion effect of single oscillating illusion images......................... 34

4.3 consideration ................................................................................................................. 41
5 Chapter 4: Neural circuit simulation........................................................................... 43
5.1

Hodgkin-Huxley model (HH model) .......................................................................... 43

5.2

Integral firing model (LIF model) ...................................................................... 46

5.3

ON Central retinal receptive field model ....................................................... 47

6 Chapter 4: Simulation results and analysis............................................................... 49
6.1

Simulation results.................................................................................................... 49

6.2

Considerations............................................................................................................. 50

7 Chapter Conclusions. ........................................................................................................... 51
8 Chapter References............................................................................................................... 53
9 Chapter Acknowledgements. .................................................................................................. 55
3

1 Chapter
1.1

Introduction Theory

background

Illusion research has been conducted for a long time, but with the recent
development of perceptual psychology and neuroscience, it has become a fieldthat attracts even more attention. In particular, since the beginning of the
2000s, visual illusions have been increasingly featured in TV programmes,
commercials and magazines, and we feel that visual illusions have become more familiar
to us. Thanks to the activities of the mass media, many people are now aware of theexistence of optical illusions. On the other hand, most of us do not understand thestructure and mechanism of visual illusions, the mechanism of the generation of illusions,and the benefits of research on visual illusions for our daily lives. Traditionally,
the generation of illusions has been regarded as a bug in the brain. However, recent
illusion research has quantified illusions, and some of the mechanisms that generate
illusions are now better understood. In the course of research, it has been reported thatthe illusory effects of existing illusions can be strengthened or weakened by generating
new illusions by computer or by extracting the part of the illusory effect that is causedby the illusory effect.
(Arai and Arai, 2012).
Furthermore, people obtain most of their stimuli from the outside world
through vision. In other words, a full understanding of the mechanisms of visual
illusions caused by human vision is very important for understanding the humanbrain. Thus, illusion research is closely related to human brain research, andadvances in illusion research can advance brain research. At present, amathematical model of the human brain has not yet been completed and only
partial models of the brain exist. Therefore, it is expected that illusion
research can be used as one clue to the completion of a whole-brain model of thebrain. Thus, illusion research is also meaningful from the perspective ofstudying the brain. It has also been reported that the findings obtained fromillusion research can be effectively utilised in our daily life, in addition tobrain research. In fact, the findings obtained from illusion research can beapplied to medical care, welfare, architecture, transportation, environmental
design and other engineering fields related to the mechanisms of the cranial
nervous system, thereby helping to solve problems in the real world.

4

1.2 research objectives
The aim of this study is to elucidate the mechanism of new illusory figures whose
generation mechanism has not yet been elucidated. For this purpose, quantitative
measurement of the illusion effect, its analysis and simulation of the firing of neurons
during the observation of illusion images are conducted. To quantitatively measure theillusion effect, we conduct perceptual experiments with subjects, collect and analyse thedata. There are no previous studies that have quantitatively measured and analysed thisillusion image, and it can be said to be novel. In the simulation, the ON-centred
receptive field model is used to simulate the firing of neurons in the retinal
receptive field when the illusion is observed. The aim of this simulation is toqualitatively observe the effect of the illusion. As mentioned above, the illusion

5

The findings from visual research can be applied to brain research and various
other fields to help solve real-world problems. The ultimate goal of thisresearch is also to understand brain algorithms through visual illusions.

2 Chapter-related research research
2.1

Definition of optical illusions

In the present study, a perceptual experiment was conducted using illusion
figures. Therefore, we first check the definition of the phenomenon called
illusion. When considering the definition of an illusion, it is good to consider
several illusions. For example, one of the most famous illusions is the Müller-Lyer ilusion(Nicola
Bruno, et al. 2009) (Figure 2-1A). In this illusion, one segment appears to belonger than the other due to the different orientations of the arrow feathers
drawn above and below, even though the lengths of the two segments are the same.
There is another illusion called the Necker cube (Fig. 2-1B). When a projection ofa cube is drawn on a plane, the two-dimensional projection appears as if it were
there in three dimensions. Furthermore, it is known that this illusion can beseen in two different ways, depending on how you look at it (J.mason, et al.
(J.mason,et al. 1973)
Thus, an optical illusion states that when some figure is given as an input toa certain visual information processing system, such as the brain, a perception
deviating from the prediction from that system is produced. This is called anillusion, and the figure that produces it is called an illusory figure.(Murakami,2010) A rough classification of illusion figures has been submitted by Gregory etal. (Gregory, et al. 1998). (Gregory, et al. 1998) However, it has been reported that
illusions are merely the final output results of multi-stage information
processing in the brain and cannot be clearly classified. (Murakami, 2010)6

Figure 2-1(A) Müller-Lyer illusion. In reality, the lengths of the left

and right central line segments are equal, but they appear to bedifferent when the directions of the arrow feathers in the upper andlower parts are opposite. (b) Necker cube.Thefigure is a two-dimensional
projection of a cube, butitappears to be three-dimensional. It can be seenin two ways depending on which side is regarded as the front.

7

2.2

Illusion as a research tool

Section 2.1 provided a definition of illusions. In this section, we discuss
why illusions are used in brain research.
In general, most of us humans perceive the relationship between stimuli fromthe outside world and our brain's perception as if it were a constant map. In
fact, if you saw a red strawberry in a supermarket, you would not doubt that it
was a red strawberry. However, our perceptions, including this one, are merely
the output of our brain as perceptions based on all the stimuli from the realworld. Therefore, red strawberries are in fact "strawberries that look red".
When we see red strawberries, it does not mean that red strawberries exist in
the real world. The colour of strawberries is based on visible light reflectedfrom the surface of the strawberry and detected by the retina, which is thenused by the brain to create a "red" strawberry in the brain. There is also an
optical illusion that utilises the brain's colour perception, which is called
colour constancy. Colour constancy is the effect that the surface colour
perceived by the brain remains constant, regardless of the spectral changes inthe surrounding illumination (G. Monge, 1789). Figure 2-2 below shows an illusion
using colour constancy created by Akiyoshi Kitaoka of Ritsumeikan University. Notethat Kitaoka states that the strawberries depicted in the illusory image appear to
be red, but this is not caused by our knowing that strawberries appear to be red(Figure 2-2).
Thus, it is important to remember that the external world that we take for
granted is in fact a fiction created by the brain. Normally, when investigating
visual information processing in the human brain, it would be impossible froman ethical point of view to directly measure and manipulate the inner workings of the visualsystem. If we define illusion as described in section 2.1, it can be interpreted
as a discrepancy between the input and output of the brain. By investigating
this discrepancy between input and output (i.e. external stimuli and brain
perception), it is possible to estimate the behaviour of the brain's information
processing mechanisms and algorithms. Even if we exclude ethical considerations,the input-output relationship we usually perceive, such as a constant mapping,
does not provide clues to the mechanism when investigating the mechanisms of thevisual system. This is also where optical illusions are useful. Input-Studies of brain algorithms are carried out by using optical illusions that
produce a displacement between outputs, and by quantitatively measuring andanalysing the displacement that occurs.
8Figure 2-2 Illusion based on colour constancy. The strawberry in the left image
above does not have red pixels due to the light blue filter, but appears
to be red due to brain compensation. In addition, the strawberry in theright image appears to be blue, though it has no blue pixels due to theyellow filter.
(Cited from: https://www.ritsumei.ac.jp/research/radiant/heart/story10.html/ Last
accessed.
24/01/2023)

2.3

About the viewing angle

When observing the illusion images used in this study, it is important to know
which size of the illusion image is being observed. The visual angle is explainedin this section. The visual angle is the angle formed when an observed object isprojected onto the retina (Fig. 2-3)
. If the visual angle is equal, the size ofthe image projected onto the retina is
The brain perceives the same size because the sizes are equal. In addition, each
degree of visual angle is referred to as a unit visual angle andCalled. The viewing angle is determined by the following equation.

𝑉=

360
𝜋

𝑠
𝑎𝑟𝑐𝑡𝑎𝑛 ,2𝑑0

1 unit: °2

Using the above equation, the viewing angle during the observation of the
optical illusion in this research experiment was calculated (Table 2-1)
. The
observation distances D were 50 cm and 100 cm, and the size of the observed object
9

(illusory image) was 8.0 cm, which is the size on the actual PC display.

10

Observation
distance D

Observables.
size (i.e. sadistof a plant)

Figure 2-3.

Visual
angle
V

retin
a

Schematic diagram of the viewing angle.

Table 2-1. Size of the visual angle in eachexperiment.
Experiment
1-1.
Visual angle
(°)

9.147

Experiments 1-2
2-1

Experiment

Experime
nt 2-2.

4.581

9.147

9.147

11

2.4

Spatial frequency characteristics of vision andcontrast sensitivity functions.

The illusion used in this study (Fig. 3-5) is a mask image with a highfrequency component of light-dark contrast. Spatial frequency is defined as thenumber of cycles of light and dark sinusoids within a unit viewing angle (2.3),
and its unit is cycle/degree = cpd (cycles per degree). In general, the spatial
frequency response has either a band-pass characteristic, which passes both
high and low frequencies, or a low-pass characteristic, which passes low
frequencies, with maximum sensitivity around 10 cpd (J.G. Robson, 1966). Under low
luminance, the sensitivity in the low spatial frequency band is also depressed.

Figure 2-4

Contrast sensitivity function. Contrast sensitivity isplotted on an arbitrary logarithmic scale against spatial frequency.
(Cited by J.G. Robson, 1966)

12

2.5

hybrid image

In relation to the spatial frequency properties of vision described in section
2.4, in 2006 Oliva, Torralba and Schyns
Hybrid images with two different views depending on the viewing distance were
proposed by(Oliva.A et al. 2 0 0 6 ). It was created by compositing two images, one with a highspatial frequency and the other with a low spatial frequency. The hybrid image
is an optical illusion that makes use of the fact that when people perceive an
image, they adopt a spatial frequency band that depends on the size of the viewing
angle. Specifically, when perceiving this image at close range, i.e. when theviewing angle is small, only the high-frequency component image is seen. On theother hand, at a distance, i.e. when the viewing angle is large, only the lowfrequency component image is seen and an effect occurs. Furthermore, in 2012,
Arai et al. at Waseda University reported a super-hybrid image in which three
types of visibility exist depending on the distance (Arai and Arai, 2012).

(A)

Figure 2-5.

(B)

Hybrid image by Oliva, A. Einstein when observed at close

range. Marilyn Monroe is visible when observed at a distance.
(cited at: http://olivalab.mit.edu/hybrid_gallery/gallery.html)
24/01/2023)

13(Last accessed3 Chapter
3.1

Experimental overview Summary

About PsychoPy

There are several reasons for using Python to create perceptual experiments,
but the main reason is that Python has a number of packages oriented towards
perceptual and psychological experiments. A package is something that extends thefunctionality of Python by incorporating it into Python, and by combining various
packages, you can create experiments that suit your needs.
PsychoPy is one of the packages of the Python library, and is a tool thatallows psychological experiments to be easily created on a personal computer(PC). The introduction of PsychoPy into experiments makes it possible to automaticallycontrol operations that are too complicated to be carried out manually, suchas recording the reaction time of each subject and accumulating the resultant
data, in perceptual experiments, using a PC. In addition, PsychoPy can be used tocreate experiments with relative ease, even when multiple conditional branches
and dynamic processing are involved, as in this experiment.
There are two main ways to create experiments in PsychoPy. The first is
Psychopy Coder, where you write the Python code yourself to create the experiment, andthe second is Psychopy Builder, where you can easily create experiments by arranging
icons on the GUI app. Psychopy Coder requires the creator of the experiment towrite the Python code themselves, which requires some familiarity with Python
programming. Psychopy Builder, on the other hand, allows users to construct andcreate experiments by simply rearranging icons on the GUI application, so eventhose who have never written a Python programme can create experiments moreeasily than with PsychoPy Coder. However, if the experiments to be created arecomplex, it is difficult to handle the creation of experiments using only
Psychopy Builder. Thus, by introducing PsychoPy and using PsychoPy Coder andPsychoPy Builder separately or in combination as necessary, it is possible tocreate experiments appropriately.

14

Figure3-1

Operational images of PsychoPyCoder and PsychoPy Builder. As

shown above, PsychoPy Coder requires the experiment creator to write thePython scripts themselves. In PsychoPy Buil der, on the other hand,
PsychoPy creates the Python scripts for you, making it easier to create
experiments.
(cited at: http://www.s12600.net/psy/python/ppb/PsychoPyBuilderBook.pdf) (Last
accessed 24/01/2023)

15

Figure 3-2 Initial screen of PsychoPy Coder, where experiments are created fromscratch by writing Python code directly.

Figure 3-3 PsychoPy Builder experiment creation screen. It consists of threepanes, where the stimuli etc. selected in the component pane are placedin the routine pane, and the order of the routines is determined in theflow pane.
16

Figure3-4

PsychoPyRunner experiment add screen.When an experiment isselected and the Run button on the right is clicked, a window forentering the subject name and session appears and the experiment starts.

17

3.2

Experimental environment and subjects

The subjects were 18 male and 18 female adults, all of whom had clear eyes(including those with corrective glasses, contact lenses, etc.). Before thestart of the experiment, the subjects were given instructions on how to operate the
PC and the structure of the experiment in the experiment manual (see p.) displayedon the display, so that each subject could operate the experiment appropriately.
To ensure fairness in the results, subjects were not informed of the purpose of
the experiment. The experiment was conducted over a two-week period from 1 to 15
December 2022, all in a room in the Science Research Building at Yokohama City
University. Furthermore, to ensure that the subjects could concentrate on theexperiment in a quiet state, they were not spoken to more than necessary.

3.3

Experimental equipment and vanishing illusions

The display size of the PC (MacBook Retina, 12-inch, 2017) used in this study was 12 in.
The Cambodia is 28.05 cm wide and 19.65 cm high, with a width of 28.05 cm and a height of
19.65 cm (2304 x 1440).
Figure 3-5 shows the illusion image used in this study. This illusion, theexistence of which was suggested by Akiyoshi Kitaoka of Ritsumeikan University,
is that when a mask image with high spatial frequency components is superimposedon a background image of letters or illustrations, the background image is hiddenby the mask image and is difficult to be seen. Quantitative measurement of theillusory effect of this illusion has not yet been conducted, and the mechanism of
the generation of the illusory effect of this illusion has not been clarified.
In the experiment, a square with one side of 8.0 cm was displayed on the rightside of a PC display. The spatial frequency of this illusory figure varied fromexperiment to experiment. In Experiments 1-1.2-1 and 2-2, the distance between thesubject and the display was 50 cm, so the viewing angle was obtained as shown in
Table 2-1 and the spatial frequency was 8.7460 cpd. On the other hand, inExperiments 1-2, the distance between the subject and the display was set to 100
cm, so the spatial frequency was 17.492 cpd based on the same calculation.
18

Figure 3-5 Structure of the vanishing illusion image used in this study. As
shown

above,

theillusion

effectiscreatedbysuperimposingabackground image with text strings or illustrations and a mask image withhigh spatial frequency components, adjusting the transparency.

19

3.4

experimental configuration
Subjects were subjected to four types of experiments. These experiments can beclassified into two types: static and dynamic illusions. In the experiment withthe static illusion, (1-1) the distance between the subject and the PC display was fixed at
50 cm. (1-2) The distance between the subject and the PC display is fixed at 100 cm. We
measured how the illusory effect of the illusory image on the subject changed
with each observation distance. In the experiment using the stationary illusion,mask images with five different spatial frequency characteristics (Fig. 3-6) wereused, so that the illusory effects between the mask images were compared at the sametime. In the experiment using the dynamic illusion, (2-1) only the mask image ismade to drift at a specific temporal frequency. (2-2) The entire illusory image
is subjected to a single oscillation in two directions, horizontally andvertically, at a specific time frequency.
The effect of the illusion was measured. Changes in the illusory effect caused by
the above two operations were measured.

(A)

(B)

(C)

(E)

(D)

Figure 3-6 Five mask images used in experiment (1).(A) vertical stripe, (B) horizontal stripe,(C) checkerboard ( D ) , right oblique stripe, (E) left oblique stripe. （The spatial
frequency of the (A ) ,( B ) ,( D ) ad(E) stripes was 80 Hz;thnespatial frequency of the20(C) checkerboard pattern was set at 50 Hz intervals between t h evertical and horizontal stripes.

21

3.5

experimental procedure

The experiment was conducted on PsychoPy on a PC according to the experimental
operation manual (Figure 3-7) shown to the subjects. First, subjects were asked
to sit on a chair facing the experimental PC display on their desk. The
subjects were then familiarised with the experimental manipulations by means of
the manual before starting the experiment. The operation itself was simple, as
the subjects only had to click on three buttons on the screen during theexperiment. Subjects adjusted the transparency so that the target text image(left of the experimental screen), which was displayed with random densities,
and the text image in the illusion image (right of the experimental screen) wereperceived as equally dense. This manipulation was repeated in Experiment 1-1
described in section 3.4
to 2-2 were carried out in sequence.

The density of the text
is displayed at
random.

The illusion side also
has an initial value of
Displayed at random( i i ) Clicking on the + makes the text
darker.

( i ) Initial screen of
the experiment( i v ) T h e left and right forms should
be of equal density.

( i i i ) Clicking on - causes the text tofade.

Figure 3-7

When adjusted, click next to continue.

Operation manual shown to subjects at the start of theexperiment. The actual experimental screen was also shown on a similar
PC display.

22

4 Chapter 3: Results
illusion effects.
4.1

and

analysisofvisualVerification of illusion effects with static
illusions.

4.1.1 In Sections 4.1.1 and 4.1.2, the illusory effects of stationary illusory images
were measured; in Section 4.1.1, the results of the comparison of illusory
effects for each of the five types of mask images are presented, and in
Section 4.1.2, the experimental results of the illusory effects at changes inobservation distance are presented.

4.1.1

Comparison of the illusion effect of each masked
image

The experimental results for each of the five mask images are shown below.
Figure 4-1 shows the results at an observation distance of 50 cm. In each illusion
image, the mask images were (A) verticalstripes,(B) horizontalstripes,(C) checkerboard ( D ) ,rightoblique stripes a(E) left oblique stripes. The horizontal axis of each scatterdnplot took the actual intensity of the letters displayed on the left side of theexperimental screen, while the vertical axis took the intensity perceived by the
subject. The red dashed line in the diagram represents the straight line withslope 1. In other words, the point on the red dashed line is the point where theintensity of the target text image actually displayed equals the intensity ofthe text in the illusion image perceived by the subject. The area above thedashed line is the area where the subject has difficulty perceiving the text inthe background due to the illusory effect of the mask image. On the other hand,
the lower area of the line is the area where the text appears darker rather than
the actual text intensity. Figure 4-1, (a) in Figure 4-2~.
（In (e), in the part of the image where the abscissa value is less than 0.1,
many of the points are located in the region above the dashed line. This
indicates that the illusion effect occurs in this region. Conversely, when theintensity of the displayed text exceeds 0.1, the illusion effect is reduced andthe points are plotted in the region below the dashed line. The tests ofnormality

and

equal

variance

between

each

mask

image

yieldedp>0.05,

respectively, and the null hypothesis was adopted. The results of one23

dimensional

ANOVA

without

correspondence

showedp<0.05,indicatingthat

differences in mask images may have an influence on the illusion effect.
Following the one-dimensional ANOVA, multiple comparisons were conducted using
Tukey's test to investigate which mask images had significant differences. As aresult, significant differences in the illusion effect were found in thechequered pattern - horizontal stripes, chequered pattern - right oblique
stripes and chequered pattern - left oblique stripes (Table 4-1).

24

Figure 4-1 Comparison for each of the five mask images. (A) vertical stripes, (B) horizontal
stripes, (C) checkerboard ( D ) , right oblique stripes,(E) left oblique
stripes. The horizontal axis represents the intensity of the actual
displayed letter, while the vertical axis represents the subject's
perceived intensity of the letter. The red dashed line in the diagram
25

represents the straight line with slope 1.

26

Figure 4-2 Graph with the vertical axis of Figure 4-1 changed to the difference fromthe horizontal axis. The red dashed line in the figure is the actual text
This is the line where the difference between the intensity of the lettersperceived by the subject and the intensity of the letters is 0. In otherwords, the illusion effect occurs at points in the upper region of this line.
The blue line in the figure is the approximate straight line of the27measured values.

28

Table 4-1.
Results of Tukey's multiple comparison test between eachmasked image. Significance level 0.05
Mask image 1

Mask image 2

p-valuevertical stripes

horizontal stripes

0.6387

vertical stripes

checkerboard

0.3865vertical stripes

right oblique stripe

0.8691

vertical stripes

oblique left stripe

0.5266

horizontal stripes

checkerboard

0.0148horizontal stripes

right oblique stripe

0.9937

horizontal stripes

oblique left stripe

0.9998checkerboard

right oblique stripe

0.0495checkerboard

oblique left stripe

0.0085right oblique
stripeoblique left stripe

0.976829

4.1.2

Relationship between observation distance andillusion effect.

The results when the illusory images were observed from a distance of 50 cm
and at a distance of 100 cm were superimposed on the graphs.（
neach of the maskI
images (A)~(E), the subject's perceived intensity decreased at an observation
distance of 100 cm more than at an observation distance of 50 cm (Fig. 4-3).
Furthermore, the linear approximation for 50 cm and 100 cm respectively isevident from the overall shift of the straight line downwards (Fig. 4-4). Basedon Figure 4-4, a histogram was created. Based on this histogram, a t-test was
performed between the observation distances of 50 cm and 100 cm. As a result,significant differences were found between the observation distances of 50 cm
and 100 cm for all mask images (Table 4-2).

30

Figure 4-3

Comparison of results at an observation distance of 50 cm(blue) and 100 cm (orange).
(A) vertical stripes,(B) horizontal stripes,(C)chequered pattern,(D) right oblique stripes,(E) left oblique stripes. For
all mask images, the perceived intensity is reduced at an observation
distance of 100 cm compared to an observation distance of 50 cm.
31

Figure 4-4 Graph with the vertical axis of Figure 4-3 changed to the difference
from the horizontal axis. In each of the approximate lines, the solidorange line of the 100 cm approximate line is also shifted downwards
more generally than the solid blue line of the 50 cm approximate line.

32

Figure 4-5.
Histogram created from Figure 4-4.
(A)~(E) for each masked image at an
observation distance of 50
The observation distance of 100 cm (orange) is shifted to the left
compared to 100 cm (blue).

33

Table 4-2 Results of t-tests for 50 cm and 100 cm observation distances.
Significance level 0.05
Type of mask image

p-value

Vertical stripes

0.031

horizontal stripes

0.008

chequered pattern

1.70e-05

Right diagonal stripe

0.001

Left diagonal stripe

5.00e-04

34

4.2

Verification of illusion effects by dynamic
illusions.

4.2 Section 4.2.1 shows the results when the mask image (vertical and horizontal
stripes) in the illusion image is made to drift at a specific frequency, andSection 4.2.2 shows the results when the whole illusion image is made to oscillate in
two directions (horizontal and vertical). The results are shown in Section 4.2.2.

4.2.1

Illusionary effects associated with drift in mask
images.

Experimental results are shown below when two types of mask images, vertical andhorizontal stripes, were drifted at a specific time frequency. The temporal changeof the mask image was changed by drifting the phase of the mask image; PsychoPy
has a function that allows n Hz drift by setting n*t to the phase of the stimulus.
Here n Hz is the number of cycles per unit time. In the present study, the time
frequencies of the drift in the mask image were (A) 2 Hz,(B) 4 Hz, (C) 5 Hz, (D) 6
Hz and (E) 7 Hz.
(C) 8 Hz ad(D) 16 Hz were prepared and tested. When vertical stripes were used asnthe mask image, significant differences from the stationary illusion image wereobserved at all frequencies (Table 4-3). In the case of horizontal stripes,
significant differences were observed at 8 Hz and 16 Hz (Table 4-4). Significant
differences between the vertical and horizontal stripes were only observed when
the drift frequency was 4 Hz (Table 4-5).

35

Fig. 4-6

Experimental results when the mask image of the vertical

stripes is shifted in time. Mask image frequencies (A) 2 Hz (B) 4 Hz,(C) 8
Hz a(D) 16 Hz.
dn36

Figure 4-7.

Graphs with the vertical axis of the graph in Figure 4-6 changed tothe difference from the horizontal axis.
(A) 2 Hz,(B) 4 Hz, (C)(C) 8 Hz,(D) 16 Hz.

Table 4-3 Results of t-tests between static and drift illusion images (vertical
stripes). Significance level 0.05
Time-frequency

fp value

2 Hz

0.002

4 Hz

4.69e-05

8 Hz

4.22e-06

16 Hz

2.07e-0837

Figure 4-8

Experimental results when the mask image of the horizontal

stripe is shifted in time.
(A) 2 Hz,(B) 4 Hz,(C) 8 Hz a(D) 16 Hz.
dn38

Figure 4-9.

Graphs with the vertical axis of the graph in Figure 4-8 changed tothe difference from the horizontal axis.
(A) 2 Hz,(B) 4 Hz,.

(C) 8 Hz,(D) 16 Hz.
Table 4-4 Results of t-tests between static and drift illusion images (horizontal
stripes).
Time-frequency

fp value

2 Hz

0.22

4 Hz

0.82

8 Hz

0.003

16 Hz

8.05e-0939

Figure 4-10 Overlaid graphs of Figures 4-6 and 4-8. (A) 2 Hz (B) 4 Hz (C) 8 Hz (D) 16
Hz. for both vertical (blue) and horizontal (orange) stripes, theillusion effect decreases as the temporal frequency of the mask
image drift increases.

40

Figure 4-11 Vertical axis of the graph in Figure 4-10 as a difference from thehorizontal axis.
(a) 2 Hz,(b) 4 Hz,(c)
8 Hz,(d) 16 Hz.

Table 4-5 Results of t-tests between drift illusion images of vertical andhorizontal stripes. Significance level 0.05
Time-frequency

fp value

2 Hz

0.48

4 Hz

0.001

8 Hz

0.56

16 Hz

0.32

41

4.2.2Illusion effect by single oscillating illusion
images.

The experimental results when the whole illusory image is changed with time
are shown below. Figure 4-12 shows the results of the experiment in which theentire illusory image of vertical and horizontal stripes was subjected tosin(2t),sin(4t),sin(8t) andsin(16t) single

oscillations

in

two

directions(horizontal and vertical). The respective movement periods are shown in Fig. 412, with the periods becoming shorter in the order from (A) to (D).
Figure 4-13. In Fig. 4-12, it is difficult to understand the change of the illusion
effect by the change of the period, but Fig. 4-13 shows that the four
approximate lines are divided into two parts, the upper and lower parts. In
Figures 4-14 and 4-15, the results are plotted for each mask image (vertical andhorizontal stripes) and direction of movement (vertical and horizontal). Figures
4-14 and 4-15 show that when the mask image is a vertical stripe, the illusion
effect decreases when the illusion image is moved horizontally in a single
oscillation, and when the mask image is a horizontal stripe, the illusion effectdecreases when the mask image is moved vertically in a single oscillation. The
common point among them is that the direction of the stripes of the high-spatial
frequency component of the mask image and the direction of movement areorthogonally related. Furthermore, t-tests were conducted between the stationary
and single-vibration illusion images. Significant differences were found between
the vertical stripes and the stationary illusion image at all frequencies whenthe vertical stripes were subjected to a single oscillation in the horizontal
direction (Table 4-6)
. When the horizontal stripes were single-vibrated in thevertical direction, significant differences were found at all frequencies
between the horizontal stripes and the stationary illusion image (Table 4-9)
f
o
c
r
i
d
t
n
e
h
W
.
stripes in the mask image was parallel to the direction of the single oscillation,
no significant differences were found at all frequencies (Tables 4-7 and 4-8).

42Figure 4-12

Experimental results of single oscillation of the wholeillusion image at each period.Thefrequencies of single oscillation are (A)f = 2/π,(B) f = 4/π,(C) f = 8/π a(D) f = 16/π, respectively; each plot in thednfigure shows the vertical shift of vertical stripes (blue), horizontal
shift of vertical stripes (orange), vertical shift of horizontal
stripes (green) and horizontal shift of horizontal stripes (red).

43

Figure 4-13 The vertical axis of the graph in Figure 4-12 is the difference from thehorizontal axis. It can be read that the illusion effect decreases whenthe mask image (vertical or horizontal stripes) and the direction of
movement (vertical or horizontal movement) are orthogonal.

44

Figure 4-14 Results for each mask image (vertical stripe, horizontal stripe) andmovement direction (vertical movement, horizontal movement). (A)Horizontal shift of vertical stripes, (B) vertical shift of vertical stripes,(C) horizontal shift of horizontal stripes, (D) vertical shift ofhorizontal stripes. The plots in each graph are colour-coded according to
the frequency of the illusion image, showing (blue) f = 2/π,(orange) f = 4/π,
(green) f = 8/π a(red) f = 16/π.
dn45Figure 4-15

vertical axis of the graph in Figure 4-14 is the differenceehTbetween the horizontal axis and. (a) horizontal shift of vertical
stripes,(b) vertical shift of vertical stripes,(c) horizontal shift ofhorizontal stripes,(d) vertical shift of horizontal stripes. The plots ineach graph are colour-coded for each frequency of the illusion image,
showing (blue) f = 2/π,(orange) f = 4/π,
(green) f = 8/π a(red) f = 16/π.
dnApproximate straight lines are drawn for each colour.

46

Table 4-6.
Results of t-tests between illusion images of the static illusion
and the horizontal single oscillation illusion (vertical stripes).
Significance level 0.05
fp value

Time-frequency
2/π Hz2.327e-05

4/π Hz7.108e-09

8/π Hz5.596e-07

16/π Hz1.485e-05

Table 4-7.
Results of t-tests between illusion images of thestatic illusion andthe longitudinal single oscillation illusion (vertical stripes).
Significance level 0.05
Time Frequency fp-value2/π Hz0.365

4/π Hz0.732

8/π Hz0.850

16/π Hz

0.567

47

Table 4-8.
Results of t-tests between the static and lateral single oscillation
illusion images (horizontal stripes).
Significance level 0.05
Time Frequency fpvalue2/π Hz0.78824/π Hz0.50208/π Hz0.178616/π Hz0.1790T a b l e 4-9. Results of t-tests between illusion images of the static illusion
and the longitudinal single oscillation illusion (horizontal stripes).
Significance level 0.05
fp value

Time-frequency
2/π Hz9.030e-05

4/π Hz4.674e-06

8/π Hz9.946e-06

16/π Hz

2.677e-05

48

4.3 consideration
From Sections 4.1 and 4.2, the illusory effect of the illusion image decreased
when the viewing distance was increased, when the mask image of the illusion
image was made to drift, and when the illusion image was made to oscillate
perpendicularly to the mask image in the illusion image. When t h e v i e w i n g
distance of the illusory image was converted into the visual angle, the visual
angle was 9.147° at an observation distance of 50 cm and 4.581° at 100 cm. The
spatial frequency of the mask image at an observation distance of 50 cm is 80
cycles/9.147 degrees = 8.746 cpd and that at 100 cm is 80 cycles/4.581 degrees = 17.49 cpd.
The contrast sensitivity of the human eye is known to reach its maximum value
around 10 cpd, as described in section 2.4, so it can be assumed that the 50 cm
v i e w i n g distance is more affected by the contrast of the stripes in the mask
image. The high contrast sensitivity at an observation distance of 50 cm is also
considered to be a strong effect of lateral inhibition. Lateral inhibitionrefers to the inhibition of the neuronal activity of other neurons in the periphery,
which are less responsive to sensory stimuli, by neurons that respond to sensory
stimuli in the centre of the receptive field via surrounding inhibitory neurons(Barlow, 1953; Barlow, 1953). (Barlow,1953)（Lateral suppression in the retina has been reported by (Kuffler, 1953) et al.
In section 4.2, the illusion effect was reduced by physically moving the illusion
image. First, in section 4.2.1, the mask image was drifted. The illusion effect was
reduced by the drift of the mask image for both vertical and horizontal stripes. Also.
In section 4.2.2, the illusion effect was reduced when the whole illusion image
was subjected to a single vibration in the direction orthogonal to thedirection of the stripes in the mask image. The common feature of both
operations is that the spatial frequency in the illusory image perceived by the
subject is perceived to be higher than it actually is (Fig. 4-16). (Fig. 4-16)
Thus, it is considered that this temporary perception due to the drift of themask image cancelled the effect of the aforementioned lateral suppression, andas a result, the illusion effect was reduced. In other words, this result
suggests that the spatial frequency of the mask image is a major factor in thedisappearance illusion.

49

position

tt +ΔtpercepTime

tualposition

tt +ΔtTime

Figure 4-16 Integration of temporal information on perception. When the relationshipis orthogonal to the direction of the stripes, the spatial frequency isperceived to have increased (top figure). On the other hand, when the
direction of movement coincides with the direction of the stripes, theperceived spatial frequency does not change (bottom figure).

50

5 Chapter
5.1

Neural circuit simulation

Hodgkin-Huxley Model (HH Model )Neural circuit simulation is the numerical simulation of the behaviour ofneural circuits in the brain on a computer. At present, the algorithms of
information processing in the whole brain have not yet been elucidated and there
are many unknowns. However, when it comes to the single neurons that make up thebrain, numerous studies have been conducted and their behaviour can be
specifically described by differential equations. Since differential equations
can be solved numerically using computers, the programmes can be used toreproduce the human brain on a supercomputer.
The world's first mathematical model of a single neuron was formulated byAlan L. Hodgkin and Andrew F. Huxley in 1952; Hodgkin and Huxley found that the action
potential of a neuron is generated by transient changes in cell membrane
permeability to sodium (Na+ ) and potassium ions (K+ ) They found that this iscaused by changes They then analysed the electrical properties of the plasma
membrane and proposed the Hodgkin-Huxley model (hereafter HH model). This HH
model is the basis of all neuronal models and is expressed by the following
equation (Gerstner, W & Kistler 2002) (Hodgkin(A. & Huxley A. 1952).

𝐶

𝑑𝑉
𝑑𝑡

= -𝑔

!"
#$

(𝑉(𝑡) - 𝐸%&.'() - 𝑔)# (𝑉, 𝑡)(𝑉(𝑡) -𝐸*'

) - 𝑔+ (𝑉, 𝑡)(𝑉(𝑡) - 𝐸+ ) + 𝐼&,- (𝑡)(5.1)

C is the capacitance of the membrane [µF/cm2 ]. t is the time [ms]. 𝑉(𝑡) is themembrane potential [mV]. 𝑔!"#$ is the leakage conductance [mS/cm2 ]. Here,conductance is the reciprocal of resistance [Ω] and represents the ease ofcurrent flow. 𝐸%&'( is the reversal potential of Cl- ions [mV]. 𝑔)# (𝑉, 𝑡) is thepotential dependent Na+ channel conductance [mS/cm2 ]. 𝐸*' is the reversal
potential of Na+ ions [mV]. 𝑔. (𝑉, 𝑡) is the potential dependent K +channel
conductance [mS/cm2 ]. 𝐸+ is the reversal potential of K+ ions [mV]. 𝐼&,- (𝑡) isthe external current injected from outside the cell [μA/cm2 ]. Note that thesevalues are normalised per unit area because the total capacitance of thecapacitor and the number of channels that determine the conductance value areproportional to the membrane area. To summarise the values of the constants in51

the equations, C= 1 µF/cm2 and normalised to 𝑔!"#$ = 0.3 mS/cm2 , 𝐸%&'( = 10.6 mV, 𝑔 )# = 120 mS/cm2
𝐸*' = 115 mV,𝑔. = 36 mS/cm2 and 𝐸+ = -12 mV.
Also, the Na+ conductance 𝑔)# (𝑉 , 𝑡) and K+ conductance 𝑔. (𝑉, 𝑡) in the equation arerespectively
Expressed by the formula.

52)#𝑔 (𝑉, 𝑡) = 𝑔*' 𝑚/ (𝑉, 𝑡)ℎ(𝑉, 𝑡). 𝑔 (𝑉, 𝑡) = 𝑔+ 𝑛

(5.2)

0 (𝑉, 𝑡)Note that these vary with time, where 𝑔*' and 𝑔+ are constant and maximum
conductance [mS/cm2 ] respectively. 𝑚(𝑉, 𝑡), ℎ(𝑉, 𝑡) and 𝑛(𝑉, 𝑡) in the equations aregate variables that depend on membrane potential V, respectively. The gate
variables represent the aperture of the ion channel and are updated by thefollowing equation.

𝑑𝑚
𝑑𝑡
𝑑ℎ
𝑑𝑡

(𝑉)D1 - 𝑚(𝑉, 𝑡)E -𝛽=𝛼1=𝛼(𝑉)𝑚(𝑉, 𝑡)

(5.3)

1

(𝑉)D1 - ℎ(𝑉, 𝑡)E - 𝛽 (𝑉)ℎ(𝑉, 𝑡)22𝑑𝑛(𝑉)D1 - 𝑛(𝑉, 𝑡)E - 𝛽 (𝑉)𝑛(𝑉, 𝑡)
=𝛼 3
3
𝑑𝑡
In the above equations 𝛼4 (𝑉) and 𝛽4 (𝑉) (x represents m, h and n) are defined by
the following equations, respectively. m is the activation parameter of the Na+
conductance, h is the inactivation parameter of the Na+ conductance and n is theactivation parameter of the K+ conductance. Note that these parameters arevalues based on experiments with giant axons of the Yari squid.

𝛼1(𝑉) =.

2.5 - 0.1𝑉
exp(2.5 - 0.1𝑉) - 1(5.4)

𝛽1(𝑉) = 4exp K-𝑉M
18
𝛼2 (𝑉) = 0.07exp K-𝑉M
20
1
𝛽 (𝑉) =.
2
exp(3 - 0.1𝑉) + 1
𝛼3 (𝑉) =0.1 - 0.01𝑉
exp(1 - 0.1𝑉) - 1

𝛽3 (𝑉) = 0.125exp K-𝑉M
80
Thus, the HH model is a non-linear dynamical system consisting of four
variables 𝑉(𝑡), 𝑚(𝑉, 𝑡), ℎ(𝑉, 𝑡) and 𝑛(𝑉, 𝑡), and by solving these differential
equations the behaviour of the neurons can be reproduced on the computer.
53

Membrane capacity Cm
Na-specificchannels

conductance
Equilibrium

1/!!"

potential of Na

"!"

film

K-specificcurrent#%

1/! #Equilibrium

extracelchannelpotential of K

"#

lular

intracellular

1/! $Other equilibrium
potentials"$

Other specificchannels

V

Figure 5-1.

Equivalent circuit model of the cell membrane in the HH

model (Hodgkin A. & Huxley A. 1952). In the parallel equivalent circuit
model of the cell membrane, the cell membrane of the neuron is replaced
by a capacitor and the ion channels embedded in the cell membrane by avariable resistance. Ion channels areatypeofmembrane transporter that
selectively allows certain ions to pass through. For each type of ion,
there are different ion channels. Ion channels also have different
conductances and equilibrium potentials, depending on the type of ion.
in the HH model,Na+ channels, K+ channels and other ion channels are
assumed. The other ion channels are channels that could not be identified
in 1952. It should be noted that most of these are now known to be Cl−
channels.

54

5.2

Integral firing model (LIF model )Section 5.1 described the HH model, the first model of a single neuron. In
this paper, we describe a simpler form of the model than the HH model, theLeaky Integrate-and-fire (LIF) model, which has only one variable as a parameter and is
described by the following equation

𝜏𝑑𝑣= -(𝑣(𝑡) -𝑉
5&6-

𝑑𝑡

) +𝑅𝐼

&,-

(𝑡)

(5.5)

𝑣(𝑡) > 𝜃 ⟹ 𝑆(𝑡) = 1, 𝑣(𝑡) ← 𝑉7"8"9𝑣(0) = 𝑉:3:9
Where 𝑣(𝑡) [mV] is the membrane potential a t a time t. 𝜏[ms] is the time constantof the membrane potential. 𝑉7"89 [𝑚𝑉] is the resting potential. 𝑅[MΩ] is themembrane resistance. 𝐼"49 (𝑡)[𝑛𝐴] is the current flowing from the cell exterior at atime t. 𝜃[mV] is the threshold value. 𝑉7"8"9 [mV] is the reset potential. The initialpotential is given by 𝑉:3:9 [mV] In the LIF model, when 𝑣(𝑡) exceeds the thresholdvalue 𝜃, depolarisation occurs and the membrane potential increases and fires.
After firing, it is assumed that repolarisation occurs and the membranepotential decreases to the reset potential 𝑉7"8"9 . Thus, compared to the HH
model equation with four variables 𝑉(𝑡), 𝑚(𝑉, 𝑡), ℎ(𝑉, 𝑡) and 𝑛(𝑉, 𝑡), the LIF model
has a simpler expression with only membrane potential 𝑣(𝑡). Note that in the
LIF model, synapses are also current-based synapses in sets with neurons in thecurrent-based model. In the current-based synapse, the synaptic current 𝑔8;3 (𝑡) isused directly as the synaptic current. Note that a current-based model is amodel in which the conductance 𝑔(𝑉, 𝑡) is not explicitly described.
8;3𝐼 (𝑡) = 𝑤 ∙ 𝑔8;3 (𝑡)(5.6)

The coupling strength is denoted by w, with positive values of w indicating
excitatory coupling and negative values indicating inhibitory coupling. In thepresent study, simulations were performed using neurons of this LIF model andcurrent-based synapses.

55

5.3

ON Central retinal receptive field model

The bipolar cells that receive input from photoreceptor cells, as well as
retinal neurons and lateral optic tectal knee cells, have an ON-centre OFFperiphery type that responds excitably when bright light is received in thecentre of the receptive field and inhibitory when bright light is received in
the periphery, and an ON-centre ON-periphery type that responds inhibitively
when bright light is received in the centre and excitably when bright light isreceived in the periphery. OFF-centre ON-periphery type exists (Kuffeler, S.W. 1953).
As the central and peripheral parts of both types are concentrically arranged
and show opposite responses, this receptive field is called the centre-periphery
antagonistic receptive field. The central-peripheral antagonistic receptive
field can be divided into excitatory and inhibitory responses depending on how
the contrast stimulus is projected to the central and peripheral areas, so it canbe said to transmit information on the width and location of light/dark contrast.
In the visual cortex, in particular, in addition to the receptive fields
described above, there are also simple-type cells that recognise line segmentswith a specific position and slope, and complex-type cells that recognise line
segments with a specific slope regardless of their position (Hubel, D. & Wiesel,(T. 1962).
It is also known that the model of the peri-centre antagonistic receptive
field can be represented by the difference of two Gaussian functions (Rodieck, R.
1965). In the present study, therefore, the coupling strength of horizontal
coupling was assumed to be stochastically determined according to the distance
between neurons, with a Mexican hat-shaped function with excitatory coupling
dominance for short distances and inhibitory coupling dominance for long
distances. (Figure 5-2: light blue solid line)

𝐼 (𝑖 , 𝑗 ) = 𝑘< 𝑒𝑥𝑝b-|𝑖 - 𝑗|=2𝜎=<

e - 𝑘= 𝑒𝑥𝑝 b-|𝑖 - 𝑗|=2𝜎=
e =(5.7 )(aft
e
In the equation 𝑖 - 𝑗 is the distance between two neurons ir and j in the twoa
dimensional plane. Figure 5-2 illustrates the above equation.
The vertical axis isnothe coupling strength and the horizontal axis is the distance
between the neurons.
un
The red and blue wavy lines represent the coupling strength
between excitatory and,ainhibitory neurons. The width of the inhibitory coupling d is wider than the
je
c
56
ti
v
e,
e
t
c.

excitatory coupling, as the coupling through the inhibitory neuron reaches farther.
In the light blue solid line, the area where the coupling strength is negative meansthat the inhibitory input is indirectly provided via the inhibitory neurons.
The simulation in this study is a simplified one. When the illusion is observed at
a distance, the excitatory coupling is assumed to be at r+ of the Mexican hatshaped model, and when the illusion is observed at close range, the inhibitory
coupling is assumed to be outside r .+57

I(i , j)excitability
inhibitory
excitaBond
StrengthbilityInhibitory
differences
Local
r+.
excitability
area ofinteractionr+

Distance between neurons

Figure 5-2 Shape of horizontal connections of neurons. The vertical axis
represents the coupling strength and the horizontal axis represents the
distance between neurons. The width of inhibitory connections is wider
than

that

of

excitatory

connections,

as

it

is

consideredthatconnections reach farther through inhibitory neurons than between excitatoryneurons.

58

6 Chapter
Analysis
6.1

Simulation results and solutions

Simulation results

Assuming the model shown in Figure 5-2, the results of the neuron firing simulationare
The following are shown. The LIF model (Section 5.2) was adopted for the neurons.

FIGURE 6-1 Plot of membrane potentials of two non-synaptically coupled neurons.
Simulated conditions with only the text image observed without the mask
image. Firing rate: 28 Hz.

Figure 6-2 Plot of membrane potentials when two neurons are coupled at a currentbased exponential decay synapse. (A) Excitatory coupling dominance.
Simulated when the illusion is observed from a distance (observation
distance 100 cm). Firing rate: 30 Hz.
(B) For inhibitory coupling dominance.
59

Simulation

when

the

illusionisobserved(observation distance 50 cm). Firing rate:.
25 Hz.

60

from

a

short

distance

6.2

consideration

Figure 6-1 shows a simulation of the firing of two neurons in an independent
state in which they are not connected to each other by synapses. It reproduces
a situation in which only the text image, excluding the mask image, is observed,
not the illusory image. The firing rate was 28 Hz. Figure 6-2 (a) reproduces thesituation when the illusion was observed from a distance (100 cm). The couplingstrength w w a s set to a positive value, reproducing the situation of excitatory
coupling dominance. On the other hand, Fig. 6-2 (B) shows the reproduction of
the illusion observed from a short distance (50 cm). The coupling strength w was
set to a negative value, reproducing the situation of inhibitory coupling
dominance. Comparing the firing rates of the two, the firing rate in Fig. 6-2(A)was 30 Hz, whereas in Fig. 6-2(B) it was 25 Hz. This compares to 28 Hz in the situation
without synaptic coupling, where the firing rate of 30 Hz in Fig. 6-2(A) was higher
than the simulation result of 28 Hz in Fig. 6-1, while the firing rate of 25 Hz in Fig. 62(B) was lower than that of 28 Hz. This is consistent with the results ofExperiment 1-2 (section 4.1.2). Therefore, it can be said that the present
simulation was able to qualitatively reproduce the behaviour of the firing of
neurons in the retinal receptive field when the distance of the illusory image
was varied and observed, albeit in a simplified manner.

61

7 Chapter

conclusion Theory

In this study, quantitative measurement of the illusion effect indisappearing illusion figures and analysis of the results were conducted in
Chapter 4, and simulation of the firing of neurons in the retinal receptive
field model during observation of illusion figures was conducted in Chapter 6.
in Section 4.1.1, a disappearing illusion was created using five types of mask
images with high spatial frequency, and the mask The illusion effect wasmeasured for each mask image. In all mask images, the illusion was generally
observed when the opacity was less than 0.1. The problem is that the shapes ofmask images ( D ) a(E) are different from those of the other three mask images duednto the specification of PsychoPy. In the future, it will be necessary to consider
other mask creation methods and conduct experiments in which the shapes of themask images to be compared are all the same.
In section 4.1.2, two patterns of observation distances were prepared: 50 cm(visual angle: 9.147°) and 100 cm (visual angle: 4.581°), and the illusion
effect at each observation distance was compared. As a result, the illusion
effect was reduced at an observation distance of 100 cm compared to that at an
observation distance of 50 cm for each mask image. A t-test was conducted, andsignificance was also found between the two groups. The problem is that only
two observation distances were used. In the future, it is necessary toconsider the correspondence between the continuous change in the observation
distance and the illusion effect by increasing the observation distance. In
addition, we would like to measure the illusion effect when the spatial
frequency of the mask image is continuously changed without changing theobservation distance.
4.2.1 In Section 3.2, the illusion effect during the drift of the mask image
in two directions, vertical and horizontal, was measured. As a result, as thetime frequency of the drift of the mask image in the vertical and horizontal
stripes increased, the illusion effect increased accordingly. A t-test was
conducted, and the difference from the static illusion image was observed attime frequencies of 4 Hz and above, except at 2 Hz.
4.2.2 In Section 3.2.2, the entire illusory image of vertical and horizontal stripes is shownas sin(2t),sin(4t),sin(8t) and sin(8t) in two directions (horizontal and vertical).
Single oscillation with sin(16t). As a result, Figures 4-12 and 4-14 were obtained. In
Figure 4-12, the single vibration
The results were summarised for each frequency of movement, and in Figure 4-14,62

the results were summarised for each mask image and movement direction. Figures
4-14 and 4-15 confirm that the illusion effect is reduced when the direction of
the stripe of the high spatial frequency component of the mask image and the
direction of movement are in an orthogonal relationship. The problem in theexperiments conducted in Sections 4.2.1 and 4.2.2 is that the temporalfrequencies of the drift and single oscillation of the mask image and theentire illusory image in both experiments are not consistent. In the future, itwill be possible to compare the illusion effects between Sections 4.2.1 and4.2.2 by aligning the time frequencies of the drift and single oscillation. In
addition, the time-frequency should be varied continuously so that the timefrequency and the illusion effect can be described in a more relevant way. The
overall experimental results suggest that the spatial frequency of the mask
image is a major factor in the disappearing illusion.
In Chapter 6, we considered an ON-centred receptive field model and simulated
the firing of neurons during observation of an optical illusion. Three patterns
were considered: when only the text image was observed, when the illusory
image was observed from a distance (100 cm) and when the illusory image wasobserved from a short distance (50 cm).

63

The simulation results, which are simple but consistent with the experimental
results, were successfully obtained by simulating the coupling strength atdifferent levels.

64

8 Chapter

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9 C h a p t e r Acknowledgements.
I would like to express my sincere gratitude to Professor Michelette for her
enthusiastic guidance during the course of this research. Without his sound advice
and support, this research would not have been possible and could not have been
compiled into this paper. Thank you very much.
I would also like to thank Mr Shunryo Yoshida of the laboratory for his kindand attentive guidance to me, as I had limited knowledge of programming andneural circuit simulation. He was always willing to answer my questions and gave
me numerous advices. Also, when my research did not go well and I was stuck, Mr
Yoshida's extensive knowledge of my research and his programming skills helped
me many times. Thank you very much.
I had many discussions with my classmates and other members of the laboratory
through weekly seminar activities. This stimulated me and I was able to makemeaningful progress in my research through friendly competition with everyone.
Thank you very much.
Last but not least, we would like to thank all the subjects who found time intheir busy schedules to conduct the experiments in this study and who willingly
agreed to participate in the experiments. Without your participation in theexperiment, we would not have been able to carry out this study. Thank you verymuch.

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