## The influence of size and shape on visual intensity discrimination

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https://hdl.handle.net/2144/8334##### Abstract

Many experiments have been performed to determine the variables which affect the differential intensity threshold. These experiments have led to several theories which relate decreases in threshold to increases in size of the stimulus. The present study is an attempt to test these theories by determining the effect of size and shape on the differential threshold.
Host investigators state that threshold is some form of inverse function of the total area of the stimulus. Lamar, Hecht, Shlaer and Hendley, in contrast, state that the threshold is an inverse function of the "useful area", which is defined as the area within a specified distance from the edge of the stimulus. For a background intensity, I, of 17.5 footlamberts, the differential threshold, ΔI/I, is given by the following equation:
ΔI/I = .13 P^(2/3)/U.A.
where: P = perimeter of the stimulus
U.A. = useful area, the area within 1.5' from an edge.
The present experiment tests the following predictions from the above equation by varying the area, the useful area and the perimeter of series of rectangles.
Prediction I. There will be an inverse relationship between the differential threshold, ΔI/I, and area, for figures of lessthan a critical area and constant perimeter.
Prediction II. The differential threshold, ΔI/I, will be constant and independent of changes in area, for figures of more than a critical area and constant perimeter.
Prediction III. The differential threshold, ΔI/I, will increase as the perimeter is increased, for figures of constant area.
Prediction IV. The differential threshold, ΔI/I, can be predicted from the equation of Lamar et al. for stimuli composed of two figures.
The apparatus was designed so that size, shape and intensity of stimuli could be varied while presented against a constant background intensity of 17.5 footlamberts. The image of an evenly illuminated 30° background screen was reflected from a piece of plate glass. An increment in intensity, ΔI, was transmitted through the plate glass and appeared to be superimposed on the background. The amount of ΔI was varied by moving a light source to and from a piece of opal glass which acted as the secondary source. The size and shape of ΔI was changed by prepared slides which were placed in front of the opal glass.
The stimuli were made from razor blade edges which were arranged to permit the transmission of light in various sizes of rectangles. Slides 1-12 (perimeter of 40') varied from 10' by 10' to 19.9' by .1'. Slides 13-24 (perimeter of 80') varied from 20' by 20' to 39.9' by .1'. Slides B, C and D consisted of pairs of rectangles varying in size from 20' by 3' to 20' by 7' and in separation distance from 14' to 6'. The first slide, A, of this series, was a 20' by 20' square. Slides E, F, C and G were pairs of 20' by 5' rectangles differing in separation from 3' to 20'.
The dimensions of slides 7-12 and 19-24 were constructed in order that the useful area varied in the same way as the total area. According to Prediction I, these slides should have different thresholds. The dimensions of slides 1-6 and 13-18 were constructed in order that the useful area remained constant while total area was varied. According to Prediction II, these slides should have equal thresholds. According to Prediction III, slides of comparable area from 1-12 and 13-24 should have different thresholds because of differences in perimeter. Slides A-G, though varying in total area and separation distance, were predicted to have approximately equal thresholds, because they varied in perimeter and in useful area at about the same rate.
Thresholds for each of slides 1-24 were obtained from each of two paid subjects using the up-and-down method. Two thresholds, each based on fifty responses were obtained for each slide. Thresholds for each of slides A-G were obtained from one of the subjects using the same method. Five thresholds each based on twenty-five responses were obtained for each slide.
Comparisons of the thresholds based on each series of fifty responses, for slides 1-24, indicated that the measurements were reliable. Rank-order correlations between repeated measures of slides which were expected to vary in threshold as a function of area, were always equal to 1.00. Rank-order correlations of those slides which were expected to have equal thresholds were never significantly different from zero.
Predictions of the thresholds for slides 1-24 were made from the equation of Lamar et al. A trend analysis was then used to determine whether the equation predicted the data. The pattern of the data was correctly predicted by the equation but there was significant vertical displacement between the data and the predicted values. The vertical displacement refers to the value of the constant, .13, which determines the overall level of the threshold.
An analysis of variance was performed on the five repeated threshold measures of slides A, B, C and D. A significant F-ratio resulted which was attributable to the deviation of slide D. The other three slides had almost identical thresholds.
An analysis of variance was also performed on the five repeated threshold values of slides E, F, and C and G. A significant F-ratio resulted which was also attributable to the effects of a single slide, E, because the other slides had almost identical thresholds.
The first three predictions were verified by the thresholds of slides 1-24. As predicted, slides 7-12 and 19-24, which varied in useful area, differed in thresholds; slides 1-6 and 13-18, which did not vary in useful area, had equal thresholds; slides of comparable areas from 1-12 and 13-24. differed in perimeter and had different thresholds, furthermore, the equation as a whole was found to predict the data adequately. The fact that the constant differed, probably reflects nothing more than the individual differences in thresholds of subjects. Although the general concept of useful area was substantiated by the data, the data were too variable to state precisely if the value of 1.5' from an edge is the correct amount. Perhaps a value slightly larger might have resulted in better predictions. There was also some doubt about the adequacy of prediction for two of the narrowest rectangles. For one of the subjects, the thresholds for the narrowest rectangles were much larger than predicted. Similar findings were reported by Lamar et al. and the predictions may be inadequate for very small stimuli.
The predictions for slides composed of two figures were also verified, because slides A, B and C, and C, F and G had equal thresholds, indicating that there was no effect due to changes in total area or separation distance. However, slide D, which was composed of rectangles of 3' width, and sliae E, which was composed of rectangles separated by 3', were both found to have higher thresholds than the other slides. This is probably due to a decrease in the amount of useful area which strengthens the earlier suggestion that a value larger than 1.5' from an edge may be a more satisfactory definition of useful area.
In conclusion, the results of this experiment substantiate the theory of Lamar, Hecht, Shlaer and Hendley, which states that the judgment of contrast is made across the boundary of a stimulus rather than over its area.

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This item was digitized by the Internet Archive. Thesis (Ph.D.)--Boston University