Perceptual Grouping as a Function of Proximity

This study was an attempt to quantify Wertheimer's law of proximity in perceptual grouping. The stimuli were 4 X 4 matrices of black 5-mrn. dots drawn in India ink on white cards. In the V-series, the vertical distance between the edges of dots was varied from 5 mm. to 35 mm. by 2-mm. steps, while the horizontal distance was fixed at 15 mm. The vertical-horizontal relationship was reversed in the H-series. The stimulus card was presented behind the square aperture, 22 X 22 cm., on a white vertical screen, 85 X 85 cm., standing on a table 115 un. from S, and illuminated by two 60-w daylight bulbs, which were placed above and behind S. The illuminance on the stimulus surface was about 5 ft.-c. Each of four Ss was instructed to continue to fixate binocularly the center of the stimulus pattern during 120 sec. and to press one of two telegraph keys when the stimulus matrix was perceived spontaneously as four horizontal rows and the other when vertical columns were seen. He was to press neither key when he saw other modes of grouping, e.g., four rectangles, a large and a small rectangle, etc., or in the absence of clear percepmal organization. Rest periods of 3 min. were inserted between observations. Each S observed the 15 patterns of the two series twice in the six sessions. The total time for pressing the key that corresponded to the direction of the constant distance was designated T , and that corresponding to the direction of variable distance, T,. As the measure of dominance, the ratio, TJT, was computed from average T , and T, under each condition. Fig. 1 shows log (T,/Tc) as a function of log (D,/D,), in which D, is the variable distance and D, the constant distance. Good linearity is observed both for the empty and filled dots in Fig. 1, which represent the results of the Vand H-series, respectively. A regression formula, log(T,/Tc) = log a + b log(D,/D,), was fitted to these data by the method of least squares. The constant a was 1.82 in V-series and 0.858 in H-series, while b was -2.88 and -2.87 (r = 0.987 and 0.972). From these results i t may be concluded that the relative dominance of each of two modes of perceptual grouping, measured by the time ratio of occurring, varies as a power function of the ratio of spatial separation, and the power ( b ) is about -3. The difference of the value a between Vand H-