Below is an translation of Section 5 of Sohmiya, T. and Sohmiya, K. (1976) entitled "Fundamental Study on Pattern Recognition by a New Experimental Method." Nagoya; Maruzen. [In Japanese with English abstract]; Translated from Japanese into English by Sohmiya Seiyu.

Figure Strength and Gestalt Laws

Sohmiya, T. and Sohmiya, K. (September 29, 1976)

1 Gestalt factors

Wertheimer (1923) maintained that when there are a number of stimuli in a field of vision, one does not see individual aspects equal to the number of their stimuli; instead one sees a figure as a whole whose configuration is most simple and regular. At the same time, he proposed the following criteria in terms of simple geometrical figures such as dots and lines.

(1) Factor of proximity If the other conditions are held constant, elements of the smallest interval are readily seen in grouping.

(2) Factor of similarity If the other conditions are held constant, similar elements are readily seen in grouping.

(3) Factor of closure If the other conditions are held constant, a closed region is readily seen in grouping.

(4) Factor of good continuity If the other conditions are held constant, elements connected continuously or smoothly are readily seen in grouping.

(5) Factor of good Gestalt If the other conditions are held constant, a single and regular pattern is readily seen in grouping.

(6) Factor of common fate Elements making similar movement and change are readily seen in grouping.

(7) Factor of objective set If a stimulus is presented in series, elements shown in objective set are readily seen in grouping.

We consider that the Gestalt criteria of grouping are the most profound insight not only for visual perception but also for all mental phenomena of humans. Hence, we first examine quantitatively the Gestalt factors and then elucidate the mechanisms underlying perceptual grouping.

1.1 Factor of proximity

The test figure (TF) presented to the left eye was drawn in black ink on white cardboard. It consisted of a row of black circles 5 mm in a diameter whose alternate intervals were 7.5 mm and 20 mm. The flickering suppression figure (SF) to the right eye was two black parallel lines 90 mm long, 10 mm apart, and 2 mm wide [SF was also drawn in black ink on white cardboard].

The TF was adjusted to be located in the center of the SF. The subjects were asked to fixate the dot B as shown in Fig. 5.1 and to report each frequency of disappearance of dots B and A or dots B and C immediately after onset of the SF when each pair disappeared simultaneously and completely. We first measured the disappearance rate of TF (δ); [δ= frequency of complete disappearance of TF/frequency of presentations of SF]. Then, on the basis of the obtainedδvalues we introduced the concept of figure strength (F) and expressed it as F = log 1/δ. [ 0≦F≦∞; F is large in a figure difficult to disappear and small in a figure suppressed readily]. The F values were as follows;

　　　The F value of the single dot [B] = 1.05
　　　The F value of the closely spaced dots [A and B] = 0.66
　　　The F value of the widely spaced dots [B and C] = 1.15

That is, the F value of a pair seen in grouping was minimum.

1.2 Factor of similarity

The left-eye TF consisted of a row of black solid and outline dots of 5 mm diameter whose alternative intervals were 10 mm. The SF was two black parallel lines identical to that used in Factor of proximity.

As shown in Fig. 5.2, the F values were as follows;

The F value of the solid dot[B] = 1.05
The F value of the outline dot[D] = 1.10
The F value of the pair of two black dots[A and B] = 0.74
The F value of the pair of two outline dots [C and D] = 0.82
The F value of the pair of solid and outline dots[B and C] = 1.15

The F value of the pair of black solid dots seen as a group was minimum. Also, the value for the pair of outline dots was lower than those of each single dot and the pair of dots not seen in grouping.

1.3 Factor of closure

The left-eye TF was composed of an outline square 10 mm wide and a convex lens-pattern 10 mm long. The right-eye SF was two black parallel lines 90 mm long, 12 mm apart, and 2 mm wide.

As shown in Fig. 5.3, the F values were as follows;

The F value of (A+B) = 0.85
The F value of (C+D) = 0.74
The F value of A = 1.40
The F value of C = 2.40
The F value of D = 1.22
The F value of (A+C) = 2.70
The F value of (B+D) = 2.70

The F values of the square and the lens-pattern seen in grouping were minimum, respectively.

1.4 Factor of good continuity

The left-eye TF was composed of a sinusoid of 40 mm long, high 6 mm intersected by a slant line 20 mm long. The right-eye SF was two black parallel lines 90 mm long, 40 mm apart, and 2 mm wide.

As shown in Fig. 5.4, the F values were as follows;

The F value of A or B = 0.85
The F value of C or D = 0.89
The F value of (A+B) = 0.52
The F value of (C+D) = 0.66
The F value of (A+C) = 0.92
The F value of (B+C) = 1.00
The F value of (A+B+C) = 1.30

The F values of (A+B) for the slant line and (C+D) for the sinusoid seen as a group were minimum, respectively.

1.5 Factor of good Gestalt

The TF to the left eye consisted of an outline circle of 14 mm diameter and an outline diamond of 10 mm side. The flickering SF to the other eye was two black parallel lines 15 mm apart.

As shown in Fig. 5.5, the F values were as follows;

The F value of A = 2.30
The F value of C = 2.15
The F value of (A + B) = 0.59
The F value of (C + D) = 0.77
The F value of (A +D) = 1.15
The F value of (C + B) = 1.22
The F value of (A+C) = 2.00

Both the F values of (A+B) for the circle and (C+D) for the outline diamond seen in grouping were less than those of the other patterns not seen as a group.

2 Theoretical foundation of perceptual grouping

2.1 Law 11 Figure strength periodically oscillates.

Experiment 27

The left-eye TFs was drawn in black ink on white cardboard. They were black filled circles 3 mm and 10 mm in diameter under Conditions 1 and 2, respectively. The right-eye SF was a black 1 mm wide outline circle. The SF was adjusted to locate concentrically to the TF.

Fig. 5.6 shows the temporal sequence of suppression and non-suppression of each TF immediately after each onset of the SF. The δvalues for the black circles 3 mm and 10 mm in diameter were 20% and 78%, respectively. On the other hand, both the frequencies of disappearance for the small and large circles oscillate clearly in spite of theδvalues differ between the two. Such regular oscillations of suppression and non-suppression always appeared for all of various features under the suppression method.

Fig. 5.7 shows our explanation for the obtained experimental results on the basis of the following postulates:

1. The figure strength of TF, which is presented continuously and for a long time,
oscillates periodically.

2. The amplitude of oscillation increases with increasing figure strength of TF.

3. The suppression strength of SF depends on a maximum of figure strength immediately after each appearance [of SF] and hence is held constant.

4. According to Law 10 [Contour effect is a monotonic decreasing function of
both distances within a visual field of one eye and between visual fields of the two eyes], the suppression strength of SF is a monotonic decreasing function of a distance between TF and SF. Hence, under Condition��
　　　　　Ss of SF under Condition �� > Ss of SF under Condition �
[Where Ss is suppression strength.]

5. As Condiions �歛nd � for lights are equal, Ground effects that are independent of figure effect are as follows;
　　　　　Ground effect under Condition�� = Ground effect under Condition �

6. TF disappears
　　　　　when figure strength of TF < Ss [of SF]
　TF keeps appeaing
　　　　　When figure strength of TF > Ss [of SF]

Thus, if the figure strength of TF oscillates periodically, we can predict the following phenomena [as illustrated in Fig. 5.9] for the TF immediately after each removal of only the SF or both of the SF and its ground, as shown in Fig. 5.8. For the circle of 3 mm diameter whose duration of disappearance is short, when the SF is removed the probability of its appearance depends on the timing of the removal of the SF. The probability of appearance should be as follows;

1. Immediately after the disappearance of TF, the probability of its appearance is extremely low.

2. At 1 sec. after the disappearance of TF, the probability of its appearance is high.

If both the two kinds of effects on suppression of TF are removal, it is expected that the TF always appear regardless of a timing of the removal of SF. On the other hand, for the dot 10 mm in diameter whose duration of disappearance is long, when only the SF is removed the probability of its appearance depends on each timing of the removal of SF are as follows;

1. Just after the disappearance of TF, the probability of appearance of SF =100%

2. At 1 sec. after the disappear of TF, the probability of appearance of SF decreases.

3. At 2 sec. after the disappearance of TF, the probability of appearance of SF = 0%.

4. At 3 sec. after the disappearance of TF, the probability of appearance of SF increases.

5. At 4 sec. after the disappearance of TF, the probability of appearance of SF = 100%.

When both the figure and the ground effects are removed, the TF should always appear irrespective of the timing of the removal of SF.

Experiment 28

The left-eye TFs were black solid circles 3 mm and 10 mm in diameter. The SF was a black outline circle of 10 mm diameter. For the TF 3mm in diameter, only the SF and both of the SF and GF were removed just and at 1 sec after the disappearance of TF, respectively. On the other hand, for the TF of 10 mm diameter the two kinds of suppression effects were removed after 1, 2, 3, and 4 sec., respectively. The obtained results indicated good agreement with the theoretical predictions as shown in Table 5.1.

2.2 Explanation of perceptual grouping on the basis of synchronous oscillations of figure strength

As shown in Figs. 5.1 - 5.5, the F values of patterns seen in grouping are always less than those of patterns not seen in grouping.

Figs, 5.10 and 5.11 give each explanation concerning Factors of proximity and similarity based on t ren that oscillate periodically. The duration that both the figure strengths of the two dots become less than the suppression level (L1) decreases with increasing the difference in phase between the dots. On the other hand, its duration reaches a maximum when the phases synchronize. So, the figure strength defined as an inverse function ofδis minimal when the two phases synchronize. In addition, it is considered that Factors of closure, continuity, and good Gestalt also enhance synchronization of phases.

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