PerceptualandMotorSkilk, 1990, 70, 515-522. O Perceptual and Motor Skills 1990
M E T H O D FOR REPRESENTING QUANTITATIVELY W H O L E PROPERTIES O F VISUAL PATTERNS ' TAMOTSU SOHMIYA AND KAZUKO SOHMIYA Sohmiya Institute of Psychology Summary.-It was assumed that there is a variable, named "strength of fusion," underlying binocular fusion and rivalry. The strength of hsion is the resistance of the fused left- and right-eye patterns to separation. The first task was to obtain a measure of the strength of fusion and the second to examine the strength of fusion as a h n c tion of various differences of the patterns. The experiments showed that the angular separation only in the temporalward direction could be used as an appropriate measure of the strength of fusion and its value was maximum when the patterns were identical and decreased as the difference increased. This result supports the assumption about the strength of fusion.
When the two eyes view binocularly identical patterns, binocular fusion occurs between the patterns. When the eyes view quite different patterns, binocular rivalry occurs but not binocular fusion. This indicates that there is a variable whose value is maximum when the patterns are identical and decreases when their difference increases. It will be c d e d "strength of fusion." We assume that the strength of fusion is defined as the resistance of the fused left- and right-eye patterns to separation. The purpose of this study was twofold. The first was to find an appropriate measure of the strength of fusion. The second purpose was to examine the strength of fusion as a function of various differences of the patterns.
GENERAL METHOD Subjects Two subjects, TS (man) and KS (woman), who had normal or corrected-to-normal vision and extensive experience in observing binocular fusion, ~articipatedin the experiments. Both subjects showed no significant difference between their two eyes in visual acuity and time threshold for form when the interocular distance was 62 mm. Apparatus The basic apparatus was a haploscope having a rectangular prism imrnediately in front of each eye (Fig. 1). Left- and right-eye patterns were mounted on the left and right arms of haploscope which could independently be moved, respectively. ~ a c hpattern was illuminated from above by three tungsten bulbs. The illumination was 500 lx. 'Reprint requests should be sent to Tamotsu Sohmiya, Sohmiya Institute of Psychology, 2-1002, Ohtakadai, Midori-ku, Nagoya 459, Japan.
T. SOHMIYA & K. SOHMIYA
FIG.1. Schematic of apparatus. LE: left eye; RE: right eye; LP: left-eye pattern; RP: righteye attern; P: prism; 8,: angular separation in temporalward direction; 8.: angular separation in nasJward direction. A convergence angle of 6 . 2 O was adopted as the starting point of pulling.
Procedure Sohmiya ( 1 9 7 8 ) , who attempted to examine quantitatively whole properties of patterns, used the sum of the temporalward (8,) and nasalward separations (6,) as a measure of the strength of fusion; 8, and 0, were measured by pulling the fused patterns temporalward and nasalward in the visual field until fusion was lost, respectively. This measure has the demerit of requiring considerable training of subjects to control extreme convergence motion of the eyes in the nasalward direction, while it has the merit of being independent of the position of the starting point of the pulling. In this study, the angular separation only in the temporalward direction, O,, was adopted as a measure of the strength of fusion. The subject was seated with his head placed firmly in a chinrest. First, the left- and right-eye patterns were presented at 57.3 cm in front of each eye. Next, the patterns were moved nasalward to each convergence distance of 57.3 cm, with the interocular distance of 62 mm subtending 6 . 2 O of convergence angle so that they were almost always fused. If the patterns were not fused, the same process was repeated until fusion occurred. Finally, each subject was instructed to view the center of the fused patterns with as passive an attitude as possible, and then the patterns were pulled apart by moving them slowly and symmetrically temporalward. The total of the temporalward separations of the patterns was noted. This separation was always sudden and well defined as has been pointed out by Fender and Julesz (1967).
EXPERIMENT 1 This experiment was designed to examine the strength of fusion as a
517
WHOLE PROPERTIES OF VISUAL PATTERNS
function of perimeter and area of the fused left- and right-eye patterns under the condition in which the patterns were identical.
Method The left- and right-eye patterns were solid white figures on bIack cardboard. They were constructed in three different ways as shown in Fig. 2 below; (a) the perimeter of the patterns increases progressively while the area
(A) P = Variable A = Constant
(B) P = Constant A = Variable
P,A TS KS
4,l 8.04 5.08
8, 4 7.92 5.28
16, 16 8.26 5.08
32, 64 8.50 5.14
64, 256 8.14 5.12
(C) P = Variable A = Variable
FIG.2. Strength of fusion as a function of perimeter and area. P: perimeter (mrn); A: area (mm'). The left- and right-eye patterns are identical. remains constant, (b) the area increases while the perimeter remains constant, and (c) both increase. In the series of A and B, each pattern was constructed within a 3 x 3 square matrix whose side was 9 mm. At 57.3 cm, the viewing distance used for the present study, 10 mm subtends l o of visual
angle. In Series A, the perimeter (rnm) and area (rnrn2) were (30, 45), (36, 4 3 , (42, 4 3 , (48, 4 3 , and (60, 4 3 , respectively. In Series B, they were (36, 27), (36, 45), (36, 63), (36, 72), and (36, 81). The patterns in Series C were squares with sides of 1, 2, 4, 8, and 16 mrn, respectively, and hence their perimeters and areas were (4, 11, (8, 4), (16, 16), (32, 64), and (64, 256). Each 8, is the average, based on 10 trials. The order of the different conditions in each series was randomized within each subject.
Results Fig. 2 shows 8, as a function of perimeter and area of the fused leftand right-eye patterns under the condition in which the patterns are identical. An analysis of variance was performed on the data for each subject. The effects of pattern were not significant ( p > .05): for Subject TS for each 0, of Series A, B, and C (F,,,, = 2.25, 2.00, and 2.67, respectively); for Subject KS for each 8, ( F , , , = 2.27, 1.52, and .466). This indicates that the strength of fusion is independent of the perimeter and area of the fused patterns, provided the patterns are identical.
EXPERIMENT 2 This experiment was designed to examine the strength of fusion as a function of various aspects of the left- and right-eye patterns under the condition in which the patterns were different. Method The left- and right-eye patterns were solid white figures on black cardboard except A-C in Fig. 3 below, which was a solid black figure on white cardboard. There were four sets: (A) the left-eye pattern was a white circle of .6O diameter and the right-eye patterns were (a) a circle identical to the left-eye pattern, (b) a white ring having . 6 O in inner diameter by .lo in width, and (c) a black circle .6O in diameter. In Set (B) the left-eye pattern was a vertical line 3.2O in length by . l o in width and the right-eye patterns were (a) a vertical line identical to the left-eye pattern, (b) a 9-dashed line 3.2O in length by .loin width, and (c) a fine line 3.2O in length by .05O in width. In Set (C) the left-eye pattern was a . I 0 x . I 0 square and the right-eye patterns were vertical lines of . l , .2, .4, .8, and 1.6O in length, respectively, by . I 0 in width. And, in Set (D) the left-eye pattern was a dot .2O in diameter and the right-eye patterns were (a) a dot identical to the left-eye pattern, (b) a vertical 3-dot pattern adding two dots to the fused central dot, ( c ) an horizontal 3-dot pattern, (d) a 5-dot pattern with four nearby dots, and (e) a 9-dot pattern with eight nearby dots. Each area between dots was S o . Measurements of angular separations were made fusing left-eye pattern with each central part (dot) of the right-eye patterns. 8, for each pattern in Sets A and B was based on 10 trials. To minimize temporal changes from fatigue, each 0, in Sets C and D with different right-eye pat-
WHOLE PROPERTIES O F VISUAL PATTERNS
FIG.3. Strength of fusion as a function of various differences of left- and right-eye patterns. L: length of vertical line (deg.). The left-eye pattern is fused with each central part (dot) of the right-eye patterns.
520
T.SOHMIYA & K. SOHMIYA
terns of five each was based on five trials. The order of the different conditions in each set was randomized within each subject.
Results Fig. 3 shows 8, as a function of vari6us differences of the fused leftand right-eye patterns. Each 8, had a maximal value when the patterns were identical and decreased when the patterns were different. It decreased, moreover, as the difference in length increased (Set C) and as the number of nearby dots increased (Set D). An analysis of variance for each set also indicated the effects of pattern to be significant ( p < . 0 1 ) . For Subject TS for Sets A, B, C, and D, F,,,, = 254 and 62.1, and F = 66.7 and 41.1, respectively. For Subject KS for Sets A, B, C, and D, F,,,, = 66.0 and 13.1, and F4,,,=21.0 and, 8.05. According to Sohmiya (1978, 1979), who used 6 = 6 , + 0, as a measure of the strength of fusion, similar results have been obtained by changing various aspects of patterns such as.illuminance, reflectance, color, form, and contoui
,,,,
This experiment was designed to examine the strength of fusion as a function of position of the fused figure.
Method The left- and right-eye patterns were solid white figures on black cardboard. The left-eye pattern was a circle of So diameter and the right-eye pattern was a square pattern of %dot. Each dot had a diameter of . 5 O and each area between dots was 1 . 2 O . Measurements of the angular separation were made fusing the left-eye pattern with each dot of the right-eye pattern. Each 6, was based on five trials. The order of the different conditions was randomized within each subject. Results Fig. 4 shows 8, for each dot of the 9-dot square pattern. For each subject, 8, was minimum .at the center of the pattern and greater at the corner RP
FIG.4. Strength of fusion as a £unction of position. The left-eye pattern is fused with each dot of the right-eye pattern.
WHOLE PROPERTIES OF VISUAL PATTERNS
52 1
parts than at the middle parts. An analysis of variance also indicated that the effects of position were significant (p
M E T H O D FOR REPRESENTING QUANTITATIVELY W H O L E PROPERTIES O F VISUAL PATTERNS ' TAMOTSU SOHMIYA AND KAZUKO SOHMIYA Sohmiya Institute of Psychology Summary.-It was assumed that there is a variable, named "strength of fusion," underlying binocular fusion and rivalry. The strength of hsion is the resistance of the fused left- and right-eye patterns to separation. The first task was to obtain a measure of the strength of fusion and the second to examine the strength of fusion as a h n c tion of various differences of the patterns. The experiments showed that the angular separation only in the temporalward direction could be used as an appropriate measure of the strength of fusion and its value was maximum when the patterns were identical and decreased as the difference increased. This result supports the assumption about the strength of fusion.
When the two eyes view binocularly identical patterns, binocular fusion occurs between the patterns. When the eyes view quite different patterns, binocular rivalry occurs but not binocular fusion. This indicates that there is a variable whose value is maximum when the patterns are identical and decreases when their difference increases. It will be c d e d "strength of fusion." We assume that the strength of fusion is defined as the resistance of the fused left- and right-eye patterns to separation. The purpose of this study was twofold. The first was to find an appropriate measure of the strength of fusion. The second purpose was to examine the strength of fusion as a function of various differences of the patterns.
GENERAL METHOD Subjects Two subjects, TS (man) and KS (woman), who had normal or corrected-to-normal vision and extensive experience in observing binocular fusion, ~articipatedin the experiments. Both subjects showed no significant difference between their two eyes in visual acuity and time threshold for form when the interocular distance was 62 mm. Apparatus The basic apparatus was a haploscope having a rectangular prism imrnediately in front of each eye (Fig. 1). Left- and right-eye patterns were mounted on the left and right arms of haploscope which could independently be moved, respectively. ~ a c hpattern was illuminated from above by three tungsten bulbs. The illumination was 500 lx. 'Reprint requests should be sent to Tamotsu Sohmiya, Sohmiya Institute of Psychology, 2-1002, Ohtakadai, Midori-ku, Nagoya 459, Japan.
T. SOHMIYA & K. SOHMIYA
FIG.1. Schematic of apparatus. LE: left eye; RE: right eye; LP: left-eye pattern; RP: righteye attern; P: prism; 8,: angular separation in temporalward direction; 8.: angular separation in nasJward direction. A convergence angle of 6 . 2 O was adopted as the starting point of pulling.
Procedure Sohmiya ( 1 9 7 8 ) , who attempted to examine quantitatively whole properties of patterns, used the sum of the temporalward (8,) and nasalward separations (6,) as a measure of the strength of fusion; 8, and 0, were measured by pulling the fused patterns temporalward and nasalward in the visual field until fusion was lost, respectively. This measure has the demerit of requiring considerable training of subjects to control extreme convergence motion of the eyes in the nasalward direction, while it has the merit of being independent of the position of the starting point of the pulling. In this study, the angular separation only in the temporalward direction, O,, was adopted as a measure of the strength of fusion. The subject was seated with his head placed firmly in a chinrest. First, the left- and right-eye patterns were presented at 57.3 cm in front of each eye. Next, the patterns were moved nasalward to each convergence distance of 57.3 cm, with the interocular distance of 62 mm subtending 6 . 2 O of convergence angle so that they were almost always fused. If the patterns were not fused, the same process was repeated until fusion occurred. Finally, each subject was instructed to view the center of the fused patterns with as passive an attitude as possible, and then the patterns were pulled apart by moving them slowly and symmetrically temporalward. The total of the temporalward separations of the patterns was noted. This separation was always sudden and well defined as has been pointed out by Fender and Julesz (1967).
EXPERIMENT 1 This experiment was designed to examine the strength of fusion as a
517
WHOLE PROPERTIES OF VISUAL PATTERNS
function of perimeter and area of the fused left- and right-eye patterns under the condition in which the patterns were identical.
Method The left- and right-eye patterns were solid white figures on bIack cardboard. They were constructed in three different ways as shown in Fig. 2 below; (a) the perimeter of the patterns increases progressively while the area
(A) P = Variable A = Constant
(B) P = Constant A = Variable
P,A TS KS
4,l 8.04 5.08
8, 4 7.92 5.28
16, 16 8.26 5.08
32, 64 8.50 5.14
64, 256 8.14 5.12
(C) P = Variable A = Variable
FIG.2. Strength of fusion as a function of perimeter and area. P: perimeter (mrn); A: area (mm'). The left- and right-eye patterns are identical. remains constant, (b) the area increases while the perimeter remains constant, and (c) both increase. In the series of A and B, each pattern was constructed within a 3 x 3 square matrix whose side was 9 mm. At 57.3 cm, the viewing distance used for the present study, 10 mm subtends l o of visual
angle. In Series A, the perimeter (rnm) and area (rnrn2) were (30, 45), (36, 4 3 , (42, 4 3 , (48, 4 3 , and (60, 4 3 , respectively. In Series B, they were (36, 27), (36, 45), (36, 63), (36, 72), and (36, 81). The patterns in Series C were squares with sides of 1, 2, 4, 8, and 16 mrn, respectively, and hence their perimeters and areas were (4, 11, (8, 4), (16, 16), (32, 64), and (64, 256). Each 8, is the average, based on 10 trials. The order of the different conditions in each series was randomized within each subject.
Results Fig. 2 shows 8, as a function of perimeter and area of the fused leftand right-eye patterns under the condition in which the patterns are identical. An analysis of variance was performed on the data for each subject. The effects of pattern were not significant ( p > .05): for Subject TS for each 0, of Series A, B, and C (F,,,, = 2.25, 2.00, and 2.67, respectively); for Subject KS for each 8, ( F , , , = 2.27, 1.52, and .466). This indicates that the strength of fusion is independent of the perimeter and area of the fused patterns, provided the patterns are identical.
EXPERIMENT 2 This experiment was designed to examine the strength of fusion as a function of various aspects of the left- and right-eye patterns under the condition in which the patterns were different. Method The left- and right-eye patterns were solid white figures on black cardboard except A-C in Fig. 3 below, which was a solid black figure on white cardboard. There were four sets: (A) the left-eye pattern was a white circle of .6O diameter and the right-eye patterns were (a) a circle identical to the left-eye pattern, (b) a white ring having . 6 O in inner diameter by .lo in width, and (c) a black circle .6O in diameter. In Set (B) the left-eye pattern was a vertical line 3.2O in length by . l o in width and the right-eye patterns were (a) a vertical line identical to the left-eye pattern, (b) a 9-dashed line 3.2O in length by .loin width, and (c) a fine line 3.2O in length by .05O in width. In Set (C) the left-eye pattern was a . I 0 x . I 0 square and the right-eye patterns were vertical lines of . l , .2, .4, .8, and 1.6O in length, respectively, by . I 0 in width. And, in Set (D) the left-eye pattern was a dot .2O in diameter and the right-eye patterns were (a) a dot identical to the left-eye pattern, (b) a vertical 3-dot pattern adding two dots to the fused central dot, ( c ) an horizontal 3-dot pattern, (d) a 5-dot pattern with four nearby dots, and (e) a 9-dot pattern with eight nearby dots. Each area between dots was S o . Measurements of angular separations were made fusing left-eye pattern with each central part (dot) of the right-eye patterns. 8, for each pattern in Sets A and B was based on 10 trials. To minimize temporal changes from fatigue, each 0, in Sets C and D with different right-eye pat-
WHOLE PROPERTIES O F VISUAL PATTERNS
FIG.3. Strength of fusion as a function of various differences of left- and right-eye patterns. L: length of vertical line (deg.). The left-eye pattern is fused with each central part (dot) of the right-eye patterns.
520
T.SOHMIYA & K. SOHMIYA
terns of five each was based on five trials. The order of the different conditions in each set was randomized within each subject.
Results Fig. 3 shows 8, as a function of vari6us differences of the fused leftand right-eye patterns. Each 8, had a maximal value when the patterns were identical and decreased when the patterns were different. It decreased, moreover, as the difference in length increased (Set C) and as the number of nearby dots increased (Set D). An analysis of variance for each set also indicated the effects of pattern to be significant ( p < . 0 1 ) . For Subject TS for Sets A, B, C, and D, F,,,, = 254 and 62.1, and F = 66.7 and 41.1, respectively. For Subject KS for Sets A, B, C, and D, F,,,, = 66.0 and 13.1, and F4,,,=21.0 and, 8.05. According to Sohmiya (1978, 1979), who used 6 = 6 , + 0, as a measure of the strength of fusion, similar results have been obtained by changing various aspects of patterns such as.illuminance, reflectance, color, form, and contoui
,,,,
This experiment was designed to examine the strength of fusion as a function of position of the fused figure.
Method The left- and right-eye patterns were solid white figures on black cardboard. The left-eye pattern was a circle of So diameter and the right-eye pattern was a square pattern of %dot. Each dot had a diameter of . 5 O and each area between dots was 1 . 2 O . Measurements of the angular separation were made fusing the left-eye pattern with each dot of the right-eye pattern. Each 6, was based on five trials. The order of the different conditions was randomized within each subject. Results Fig. 4 shows 8, for each dot of the 9-dot square pattern. For each subject, 8, was minimum .at the center of the pattern and greater at the corner RP
FIG.4. Strength of fusion as a £unction of position. The left-eye pattern is fused with each dot of the right-eye pattern.
WHOLE PROPERTIES OF VISUAL PATTERNS
52 1
parts than at the middle parts. An analysis of variance also indicated that the effects of position were significant (p
