the vertical–horizontal illusion revisited: quantitative
TRANSCRIPT
J. Psy. Sci. 38(2): 214-226 (2020)
a, b, * b
a b
contact position, orientation, and monocular/binocular visions
Hiroki Oharaa, b, * and Satoru Kawaib
aMinatogawa College bTezukayama University
Despite numerous Vertical–Horizontal Illusion (VHI) studies conducted since that of Adolf Fick in 1851, VHI has yet to attain a uniformly accepted consensus due to conflicting conclusions. As a result, a re-examination of VHI was undertaken focusing on contact position of a vertical (mast) line on a horizontal (base) line, orientation of the VHI stimulus, and viewing conditions, i.e., monocular vs. binocular-vision. In pseudorandom fashion on a comput- er, 35 adults adjusted mast lines of varying length and contact position in reference to a 50-mm base line to the same perceived length as the base line. The Point of Subjective Equality (PSE) was measured over 168 trials (two trials of 7 contact positions×4 orientations×3 viewing conditions). Perceived lengths were significantly affected by contact position in an M-shaped manner (Marma et al., 2015) rather than V-shaped (Künnapas, 1955a), and PSE was short- er when the baseline was horizontal rather than vertical, confirming the anisotropy in vertical–horizontal axis (Kün- napas, 1955a).
Ke y words: Vertical–Horizontal Illusion VHI, contact position, orientation, monocular vision, binocular vision
– Vertical–Horizontal Illusion; VHI T ⊥L Fick,
1851; Oppel, 1855; 2005; 2005, 2010 Fick 1851Fick
illusion 2005
1909;
1911 1927 1935 1933; Oyama, 1975 1971; 1972; 1977, 1978;
Oyama & Morikawa, 1985; Fujita, Blough, & Blough, 1993 1963, 1966; 1982 VHI
⊥ 2 VHI
The Japanese Journal of Psychonomic Science 2020, Vol. 38, No. 2, 214–226
J-STAGE First published online: April 21, 2020
215–
1955a, 1957b; Suto, 1960; Mikellidou & Thompson, 2013;
Marma, Bulatov, & Bulatova, 2015 Ritter, 1917; Finger & Splet, 1947; Künnapas,
1955a; 1959; Morinaga, Noguchi, & Ohishi, 1962; Be-
gelman & Steinfeld, 1967; Avery & Day, 1969; Schiffman &
Thompson, 1975; Hamburger & Hansen, 2010; Marma et al.,
2015∠ Suto, 1960; Morinaga et al., 1962; Cormack & Cor-
mack, 1974; Wolfe, Maloney, & Tam, 2005
von Collani, 1985b; 2014 Meyer, 1986 McBride,
Risser, & Slotnick, 1987VHI Valentine,
1912a Künnapas, 1955b,
1957a, 1959; 1959; Mankin, 1969; Houck, Mefferd, &
Greenstein, 1972; von Collani, 1985a; Li & Durgin, 2017 Ritter, 1917; Künnapas, 1957b; Avery & Day,
1969; 1998; Hamburger & Hansen, 2010 Fraisse & Vautrey, 1956; Piaget,
Bang, & Matalon, 1958 Vallentine, 1912a; Künnapas, 1957c;
Prinzmetal & Gettleman, 1993 Kün-
napas, 1957b, Pearce & Matin, 1969; Thompson & Schiffman,
1974 Künnapas, 1958b; Piaget et al., 1958 Ritter, 1917; Künnapas, 1958a; 1959; Morinaga et
al., 1962; Avery & Day, 1969; Avery, 1970; Prinzmetal & Get-
tleman, 1993; 1997 Day & Avery, 1970;
Deregowski & Ellis, 1972; Wong, Ho, & Ho, 1974; Wong, 1977;
Heller, Calcaterra, Burson,& Green, 1997; Taylor, 2001 von Collani, 1979; Heller et al., 1997; Millar & Al-At-
tar, 2000 Ritter, 1917; Armstrong & Marks,
1997 Valentine, 1912b; 2015 Fraisse & Vautrey, 1956; Thompson & Schiffman,
1974; Brosvic et al., 1993; Blanusa & Zdravkic, 2015 Valentine, 1912b; Ritter, 1917; Heller & Joyner,
1993; Renier, Bruyer, & De Volder, 2006; Savazzi, Posteraro,
Veronesi, & Mancini, 2007; de Montalembert & Mamassian,
2010 Finger & Spelt, 1947; Wolfe
et al., 2005; Hamburger & Hansen, 2010
VHI de Montalembert & Mamassian, 2010;
Hamburger & Hansen, 2010; Mamassian & de Montalembert,
2010; Mikellidou & Thompson, 2013 VHI
2005 “ ”
n10 Wolfe et al., 2005; Hamburger & Hansen,
2010 VHI Ex. Oyama, 1960; Gregory, 1963, 1997; Coren & Gir-
gus, 1978 TL
216 38 2
al., 2005; Charras & Lupiáñez, 2010; Marma et al., 2015 Figure 1 V A: Künnapas,
1955a B: Wolfe et al., 2005 M C: Marma et al., 2015 ⊥90 Figure
1-A: Künnapas, 1955a VHI T
⊥ baseline mast line ⊥
Künnapas 1957c Harrington
1981 1 M Marma et al. 2015
Ritter, 1917; Künnapas, 1957b; Avery & Day, 1969; 1998; Hamburger & Hansen, 2010 Künnapas, 1955b, 1957a, 1959; 1959; Mankin, 1969; Houck et al., 1972; von Collani, 1985a; Li
& Durgin, 2017 Künnapas, 1957a Mankin,
1969 von Collani, 1985a Houck et al., 1972
Figure 1. Quantitative VHI Magnitude Variations. A; Künnapas, 1955, p. 136, Figure 4, B; Wolfe et al., 2005, p. 971, Figure 4-D, C; Marma et al., 2015, p. 71, Figure 2-a. “V-shaped” curves were obtained as a function of contact position by Kün- napas A; 1955a and Wolfe et al. B; 2005 while a “M-shaped” curve was reported by Marma et al. C; 2015. In A, the curves were maintained as “V-shaped” regardless of orientation of the VHI figures Künnapas, 1955a. Referential lines were 50 mm A, 27.3 mm B, and 66 minarc C, respectively. The figures were modified to make comparisons easier. Permissions for citations were also obtained for all figures.
217–
Prinzmetal & Gettleman 1993 Marma et al. 2015 Künnapas 1955a 210×210 mm p. 135, Wolfe et al. 2005 96 cd/m2
Prinzmetal & Gettleman (1993)
Marma et al. (2015) M 2
⊥ PSE100 VHI anisotropyFick 1851 Finger & Spelt, 1947; Künnapas, 1955a;
Gardner & Long, 1960; Hamburger, Hansen, & Gegenfurtner,
2007; Hamburger & Hansen, 2010; Mamassian & de Mon-
talembert, 2010 3Künnapas
1957c 1977
28-05
Figure 2 VHI
Marma et al.
2015 Windows 7 Fig-
ure 2-AVisual Studio 2012 Microsoft
Figure 2. Experiment Schematic. In a darkened room 1.0 lx, a stimulus generated through the master computer A was presented on the monitor B
placed 500 mm from the subject. Figure C consists of a baseline 50 mm and a mast line of varying lengths connected to one of seven contact points. This illustration indicates an example of a trial for the Up ⊥ condition with a horizontal baseline and 2 contact position for the baseline. The subject adjusted the perception of the mast line to be the same length as the baseline by operating the button and the joystick E of the controller D.
218 38 2
15 inchLL-
T15G4-H, Japan; cf. Wolfe et al., 2005 50 mm 172 pixel3 mm 10 pixel Figure 2-B 3 mm, 7 Figure 2-C 30–70 mm
HORIPAD FPS PLUS,
Japan Figure 2-D L1 R1 4 Figure 2-E R1 R1PSE
3 pixel 1 pixel 0.29 mm Wundt, 1897 Heller et al.,
1997
PSE
2011 Künnapas, 1955a; Wolfe et al., 2005 Chin-rest cf.
Marma et al., 20151 2 ⊥ 3 500 mm 4 50 mm
219–
50 mm0 3
25 mm2 16.6 mm1 8.3 mm 0 0 mm 1 8.3 mm2 16.6 mm3 25 mm7 ⊥ Up180 Down90
Right 90 Left 2
41
14 7×2 ×56 14×4 3 168 56×3 1 1 1010 160
80–100
PSE;
mm 100 PSE 100PSE 100120 2085 15
Excel IBM SPSS Statistics 22 Win-
dows 7 2 PSE 1 2 3 7×4×2 5 p.05 2010
Table 1VHI 4 Up, Down, Right, Left 7×4×2 F3.53, 120.1722.06, p.001,
ηp 2.39 F2.00, 67.8242.36, p.001, ηp
2
.01, n.s., ηp 2.00×
F8.92, 303.331.69, n.s., ηp 2.05×
F6, 204.37, n.s., ηp 2.01×
F3, 1021.64, n.s., ηp 2.05
× × F10.78, 366.59.82, n.s., ηp
2.02 Figure 3⊥ Up Mon-
ocularPSE100 Bonferroni0 2 112 3 21 2 p
.05 Figure 4PSE 100 ⊥ Up Down Right Left M
220 38 2
Bonferroni Up vs. Right, Up
vs. Left, Down vs. Right, Down vs. Left p.053 Right vs. Left
p.05
Down90°270° RightLeft M M
Table 1. Mean values and standard deviations of illusion strength as a function of contact point, orientation, and viewing conditions.
Figure 3. Mean PSE values as a function of contact point.
The data shown was obtained from the Up ⊥ con- dition with monocular vison. The PSE obtained by ad- justing a mast line is expressed as a percentage for the referential baseline 50 mm. Thus, the PSE on a dot- ted line is equal to the baseline, indicating no illusion. Accordingly, a negative illusion PSE100 occurs above the dotted line, while a positive illusion PSE 100 occurs below it.
Figure 4. Mean PSE values as a function of orientation. The data shown is that obtained from the Up , Down , Right , and Left conditions based on monocular vision respectively. The magni- tudes of PSE are greater toward a direction in which the mast line is perceived longer than the baseline in Right and Left conditionswhere the baseline is verti- cally positionedthan those in Up and Down condi- tions where it is horizontally positioned.
221–
PSE100 PSE 97 PSE 107
Figure 5⊥ Up PSE100 PSE VHI M
1
Künnapas, 1955a; Wolfe et al.,
2005; Marma et al., 2015 V Figure 1-A; Künnapas, 1955a V Figure 1-B; Wolfe et al., 2005 M Figure 1-C; Marma et al., 2015 Künnapas,
1957a; Mankin, 1969; Houck et al., 1972; von Collani, 1985a Prinzmetal & Gettleman 1993Marma et al.
2015 Künnapas 1955a Prinzmetal & Get-
tleman (1993)Marma et al. (2015) 1 VHIM
Table 1,
Purves 2002 Fig-
333° 80°
25,0002 5° step M 2 M
Figure 5. Mean PSE values as a function of monocular/ binocular vision.
The data was obtained from monocular vision and binocular vision conditions based on the Up ⊥ condition, respectively. No significant differences
were observed between the monocular and binocular conditions.
222 38 2
Luckiesh, 1922 Künnapas, 1957b; Pearce & Mat-
in, 1969; Restle & Merryman, 1969; Prinzmetal & Gettleman,
1993 Oppel, 1855; Künnapas,
1955a; Girgus & Coren, 1975; Wolfe et al., 2005; Charras & Lu-
piáñez, 2009, 2010 Wood-
worth, 1938
Gregory, 1963, 1973, 1997 Lei-
bowitz, 1965; Day, 1972; Schiffman & Thompson, 1975; von
Collani, 1985a,b; 2010 Williams & Enns, 1996
Wolfe et al., 2005 Hamburger &
Hansen, 2010; Mamassian & de Montalembert, 2010;
Mikellidou & Thompson, 2013 Craven, 1993; Mamassian &
Landy, 2001; Howe & Purves, 2002; Wolfe et al. 2005 VHI
M
VHI Wolfe et al. 2005Howe & Purves 2002 M Top-downVHI VHI Künnapas, 1955a; Wolfe et al., 2005; Marma
et al., 2015 V Künnapas, 1955a; Wolfe et al., 2005M
Marma et al., 2015 Marma et al. 2015 M1 Marma et al. 2015 Figure 1-C M TM Figure 1
Künnapas, 1955a Wolfe et al.,
2005 Marma et al., 2015
2 VHIM
Marma et al. 2015
Figure 1-C, Figure 4 ⊥ Up/
Down
Figure 6. Examples of “M-shaped” variations in the magnitude of the PSE Howe & Purves, 2002, p. 13186, Figure 3-C
The horizontal axis shows the viewing angle. The verti- cal axis indicates Cartesian/polar coordinate ratio λ. Permissions for citations were also obtained for all fig- ures.
223–
Right/Left
Figure 4 Künnapas 1955a Figure
1-AKünnapas 1955a Table 1 50 mm
Up/DownPSE94.26–94.43 47.23–47.13 47.18 mm
50 mm
Right/Left PSE 104.64–
105.00 50.25–50.23 50.24 mm 47.18 mm50.24 mm106.5 Finger & Spelt 92.8, 1947, Ham-
berger et al. 93.4, 2007, Hamberger & Hansen 93.54,
2010Mamassian & de Montalembert 94.0, 2010 Künnapas 86.98, 1955aGardner & Long
71.7, 1960 anisotro-
pyFick 1851 VHI VHI Valentine, 1912b; Avery &
Day, 1969; Thompson & Schiffman, 1974 Begelman & Steinfeld, 1971 Bayer & Pressey,
1972 Kün-
napas, 1955b, 1957a, b; Prinzmetal & Gettleman, 1993 Craven,1993;
Howe & Purves, 2002 – Künnapas 1955a 2
1 : 1 1 : 1.06 Finger & Spelt, 1947;
Hamburger et al., 2007; Hamburger & Hansen, 2010; Mamas-
sian & de Montalembert, 2010 Fick, 1851 PSE100 PSE100Figure
4Right Left Up ⊥Down Künnapas Figure 1-AV L
3 VHI
Künnapas 1957c
3.8, 4.2, 4.0Harrington 1981 24 Künnapas 1957c Table 1, Figure 5 M VHI Julesz 1971
4 VHI Marma et al. 2015
224 38 2
Fick 1851 M V VHI 1997
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2019.5.272020.1.28
a, b, * b
a b
contact position, orientation, and monocular/binocular visions
Hiroki Oharaa, b, * and Satoru Kawaib
aMinatogawa College bTezukayama University
Despite numerous Vertical–Horizontal Illusion (VHI) studies conducted since that of Adolf Fick in 1851, VHI has yet to attain a uniformly accepted consensus due to conflicting conclusions. As a result, a re-examination of VHI was undertaken focusing on contact position of a vertical (mast) line on a horizontal (base) line, orientation of the VHI stimulus, and viewing conditions, i.e., monocular vs. binocular-vision. In pseudorandom fashion on a comput- er, 35 adults adjusted mast lines of varying length and contact position in reference to a 50-mm base line to the same perceived length as the base line. The Point of Subjective Equality (PSE) was measured over 168 trials (two trials of 7 contact positions×4 orientations×3 viewing conditions). Perceived lengths were significantly affected by contact position in an M-shaped manner (Marma et al., 2015) rather than V-shaped (Künnapas, 1955a), and PSE was short- er when the baseline was horizontal rather than vertical, confirming the anisotropy in vertical–horizontal axis (Kün- napas, 1955a).
Ke y words: Vertical–Horizontal Illusion VHI, contact position, orientation, monocular vision, binocular vision
– Vertical–Horizontal Illusion; VHI T ⊥L Fick,
1851; Oppel, 1855; 2005; 2005, 2010 Fick 1851Fick
illusion 2005
1909;
1911 1927 1935 1933; Oyama, 1975 1971; 1972; 1977, 1978;
Oyama & Morikawa, 1985; Fujita, Blough, & Blough, 1993 1963, 1966; 1982 VHI
⊥ 2 VHI
The Japanese Journal of Psychonomic Science 2020, Vol. 38, No. 2, 214–226
J-STAGE First published online: April 21, 2020
215–
1955a, 1957b; Suto, 1960; Mikellidou & Thompson, 2013;
Marma, Bulatov, & Bulatova, 2015 Ritter, 1917; Finger & Splet, 1947; Künnapas,
1955a; 1959; Morinaga, Noguchi, & Ohishi, 1962; Be-
gelman & Steinfeld, 1967; Avery & Day, 1969; Schiffman &
Thompson, 1975; Hamburger & Hansen, 2010; Marma et al.,
2015∠ Suto, 1960; Morinaga et al., 1962; Cormack & Cor-
mack, 1974; Wolfe, Maloney, & Tam, 2005
von Collani, 1985b; 2014 Meyer, 1986 McBride,
Risser, & Slotnick, 1987VHI Valentine,
1912a Künnapas, 1955b,
1957a, 1959; 1959; Mankin, 1969; Houck, Mefferd, &
Greenstein, 1972; von Collani, 1985a; Li & Durgin, 2017 Ritter, 1917; Künnapas, 1957b; Avery & Day,
1969; 1998; Hamburger & Hansen, 2010 Fraisse & Vautrey, 1956; Piaget,
Bang, & Matalon, 1958 Vallentine, 1912a; Künnapas, 1957c;
Prinzmetal & Gettleman, 1993 Kün-
napas, 1957b, Pearce & Matin, 1969; Thompson & Schiffman,
1974 Künnapas, 1958b; Piaget et al., 1958 Ritter, 1917; Künnapas, 1958a; 1959; Morinaga et
al., 1962; Avery & Day, 1969; Avery, 1970; Prinzmetal & Get-
tleman, 1993; 1997 Day & Avery, 1970;
Deregowski & Ellis, 1972; Wong, Ho, & Ho, 1974; Wong, 1977;
Heller, Calcaterra, Burson,& Green, 1997; Taylor, 2001 von Collani, 1979; Heller et al., 1997; Millar & Al-At-
tar, 2000 Ritter, 1917; Armstrong & Marks,
1997 Valentine, 1912b; 2015 Fraisse & Vautrey, 1956; Thompson & Schiffman,
1974; Brosvic et al., 1993; Blanusa & Zdravkic, 2015 Valentine, 1912b; Ritter, 1917; Heller & Joyner,
1993; Renier, Bruyer, & De Volder, 2006; Savazzi, Posteraro,
Veronesi, & Mancini, 2007; de Montalembert & Mamassian,
2010 Finger & Spelt, 1947; Wolfe
et al., 2005; Hamburger & Hansen, 2010
VHI de Montalembert & Mamassian, 2010;
Hamburger & Hansen, 2010; Mamassian & de Montalembert,
2010; Mikellidou & Thompson, 2013 VHI
2005 “ ”
n10 Wolfe et al., 2005; Hamburger & Hansen,
2010 VHI Ex. Oyama, 1960; Gregory, 1963, 1997; Coren & Gir-
gus, 1978 TL
216 38 2
al., 2005; Charras & Lupiáñez, 2010; Marma et al., 2015 Figure 1 V A: Künnapas,
1955a B: Wolfe et al., 2005 M C: Marma et al., 2015 ⊥90 Figure
1-A: Künnapas, 1955a VHI T
⊥ baseline mast line ⊥
Künnapas 1957c Harrington
1981 1 M Marma et al. 2015
Ritter, 1917; Künnapas, 1957b; Avery & Day, 1969; 1998; Hamburger & Hansen, 2010 Künnapas, 1955b, 1957a, 1959; 1959; Mankin, 1969; Houck et al., 1972; von Collani, 1985a; Li
& Durgin, 2017 Künnapas, 1957a Mankin,
1969 von Collani, 1985a Houck et al., 1972
Figure 1. Quantitative VHI Magnitude Variations. A; Künnapas, 1955, p. 136, Figure 4, B; Wolfe et al., 2005, p. 971, Figure 4-D, C; Marma et al., 2015, p. 71, Figure 2-a. “V-shaped” curves were obtained as a function of contact position by Kün- napas A; 1955a and Wolfe et al. B; 2005 while a “M-shaped” curve was reported by Marma et al. C; 2015. In A, the curves were maintained as “V-shaped” regardless of orientation of the VHI figures Künnapas, 1955a. Referential lines were 50 mm A, 27.3 mm B, and 66 minarc C, respectively. The figures were modified to make comparisons easier. Permissions for citations were also obtained for all figures.
217–
Prinzmetal & Gettleman 1993 Marma et al. 2015 Künnapas 1955a 210×210 mm p. 135, Wolfe et al. 2005 96 cd/m2
Prinzmetal & Gettleman (1993)
Marma et al. (2015) M 2
⊥ PSE100 VHI anisotropyFick 1851 Finger & Spelt, 1947; Künnapas, 1955a;
Gardner & Long, 1960; Hamburger, Hansen, & Gegenfurtner,
2007; Hamburger & Hansen, 2010; Mamassian & de Mon-
talembert, 2010 3Künnapas
1957c 1977
28-05
Figure 2 VHI
Marma et al.
2015 Windows 7 Fig-
ure 2-AVisual Studio 2012 Microsoft
Figure 2. Experiment Schematic. In a darkened room 1.0 lx, a stimulus generated through the master computer A was presented on the monitor B
placed 500 mm from the subject. Figure C consists of a baseline 50 mm and a mast line of varying lengths connected to one of seven contact points. This illustration indicates an example of a trial for the Up ⊥ condition with a horizontal baseline and 2 contact position for the baseline. The subject adjusted the perception of the mast line to be the same length as the baseline by operating the button and the joystick E of the controller D.
218 38 2
15 inchLL-
T15G4-H, Japan; cf. Wolfe et al., 2005 50 mm 172 pixel3 mm 10 pixel Figure 2-B 3 mm, 7 Figure 2-C 30–70 mm
HORIPAD FPS PLUS,
Japan Figure 2-D L1 R1 4 Figure 2-E R1 R1PSE
3 pixel 1 pixel 0.29 mm Wundt, 1897 Heller et al.,
1997
PSE
2011 Künnapas, 1955a; Wolfe et al., 2005 Chin-rest cf.
Marma et al., 20151 2 ⊥ 3 500 mm 4 50 mm
219–
50 mm0 3
25 mm2 16.6 mm1 8.3 mm 0 0 mm 1 8.3 mm2 16.6 mm3 25 mm7 ⊥ Up180 Down90
Right 90 Left 2
41
14 7×2 ×56 14×4 3 168 56×3 1 1 1010 160
80–100
PSE;
mm 100 PSE 100PSE 100120 2085 15
Excel IBM SPSS Statistics 22 Win-
dows 7 2 PSE 1 2 3 7×4×2 5 p.05 2010
Table 1VHI 4 Up, Down, Right, Left 7×4×2 F3.53, 120.1722.06, p.001,
ηp 2.39 F2.00, 67.8242.36, p.001, ηp
2
.01, n.s., ηp 2.00×
F8.92, 303.331.69, n.s., ηp 2.05×
F6, 204.37, n.s., ηp 2.01×
F3, 1021.64, n.s., ηp 2.05
× × F10.78, 366.59.82, n.s., ηp
2.02 Figure 3⊥ Up Mon-
ocularPSE100 Bonferroni0 2 112 3 21 2 p
.05 Figure 4PSE 100 ⊥ Up Down Right Left M
220 38 2
Bonferroni Up vs. Right, Up
vs. Left, Down vs. Right, Down vs. Left p.053 Right vs. Left
p.05
Down90°270° RightLeft M M
Table 1. Mean values and standard deviations of illusion strength as a function of contact point, orientation, and viewing conditions.
Figure 3. Mean PSE values as a function of contact point.
The data shown was obtained from the Up ⊥ con- dition with monocular vison. The PSE obtained by ad- justing a mast line is expressed as a percentage for the referential baseline 50 mm. Thus, the PSE on a dot- ted line is equal to the baseline, indicating no illusion. Accordingly, a negative illusion PSE100 occurs above the dotted line, while a positive illusion PSE 100 occurs below it.
Figure 4. Mean PSE values as a function of orientation. The data shown is that obtained from the Up , Down , Right , and Left conditions based on monocular vision respectively. The magni- tudes of PSE are greater toward a direction in which the mast line is perceived longer than the baseline in Right and Left conditionswhere the baseline is verti- cally positionedthan those in Up and Down condi- tions where it is horizontally positioned.
221–
PSE100 PSE 97 PSE 107
Figure 5⊥ Up PSE100 PSE VHI M
1
Künnapas, 1955a; Wolfe et al.,
2005; Marma et al., 2015 V Figure 1-A; Künnapas, 1955a V Figure 1-B; Wolfe et al., 2005 M Figure 1-C; Marma et al., 2015 Künnapas,
1957a; Mankin, 1969; Houck et al., 1972; von Collani, 1985a Prinzmetal & Gettleman 1993Marma et al.
2015 Künnapas 1955a Prinzmetal & Get-
tleman (1993)Marma et al. (2015) 1 VHIM
Table 1,
Purves 2002 Fig-
333° 80°
25,0002 5° step M 2 M
Figure 5. Mean PSE values as a function of monocular/ binocular vision.
The data was obtained from monocular vision and binocular vision conditions based on the Up ⊥ condition, respectively. No significant differences
were observed between the monocular and binocular conditions.
222 38 2
Luckiesh, 1922 Künnapas, 1957b; Pearce & Mat-
in, 1969; Restle & Merryman, 1969; Prinzmetal & Gettleman,
1993 Oppel, 1855; Künnapas,
1955a; Girgus & Coren, 1975; Wolfe et al., 2005; Charras & Lu-
piáñez, 2009, 2010 Wood-
worth, 1938
Gregory, 1963, 1973, 1997 Lei-
bowitz, 1965; Day, 1972; Schiffman & Thompson, 1975; von
Collani, 1985a,b; 2010 Williams & Enns, 1996
Wolfe et al., 2005 Hamburger &
Hansen, 2010; Mamassian & de Montalembert, 2010;
Mikellidou & Thompson, 2013 Craven, 1993; Mamassian &
Landy, 2001; Howe & Purves, 2002; Wolfe et al. 2005 VHI
M
VHI Wolfe et al. 2005Howe & Purves 2002 M Top-downVHI VHI Künnapas, 1955a; Wolfe et al., 2005; Marma
et al., 2015 V Künnapas, 1955a; Wolfe et al., 2005M
Marma et al., 2015 Marma et al. 2015 M1 Marma et al. 2015 Figure 1-C M TM Figure 1
Künnapas, 1955a Wolfe et al.,
2005 Marma et al., 2015
2 VHIM
Marma et al. 2015
Figure 1-C, Figure 4 ⊥ Up/
Down
Figure 6. Examples of “M-shaped” variations in the magnitude of the PSE Howe & Purves, 2002, p. 13186, Figure 3-C
The horizontal axis shows the viewing angle. The verti- cal axis indicates Cartesian/polar coordinate ratio λ. Permissions for citations were also obtained for all fig- ures.
223–
Right/Left
Figure 4 Künnapas 1955a Figure
1-AKünnapas 1955a Table 1 50 mm
Up/DownPSE94.26–94.43 47.23–47.13 47.18 mm
50 mm
Right/Left PSE 104.64–
105.00 50.25–50.23 50.24 mm 47.18 mm50.24 mm106.5 Finger & Spelt 92.8, 1947, Ham-
berger et al. 93.4, 2007, Hamberger & Hansen 93.54,
2010Mamassian & de Montalembert 94.0, 2010 Künnapas 86.98, 1955aGardner & Long
71.7, 1960 anisotro-
pyFick 1851 VHI VHI Valentine, 1912b; Avery &
Day, 1969; Thompson & Schiffman, 1974 Begelman & Steinfeld, 1971 Bayer & Pressey,
1972 Kün-
napas, 1955b, 1957a, b; Prinzmetal & Gettleman, 1993 Craven,1993;
Howe & Purves, 2002 – Künnapas 1955a 2
1 : 1 1 : 1.06 Finger & Spelt, 1947;
Hamburger et al., 2007; Hamburger & Hansen, 2010; Mamas-
sian & de Montalembert, 2010 Fick, 1851 PSE100 PSE100Figure
4Right Left Up ⊥Down Künnapas Figure 1-AV L
3 VHI
Künnapas 1957c
3.8, 4.2, 4.0Harrington 1981 24 Künnapas 1957c Table 1, Figure 5 M VHI Julesz 1971
4 VHI Marma et al. 2015
224 38 2
Fick 1851 M V VHI 1997
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