The mean-integral representation of rectangles

Abstract

To assess perceptual interaction between the height and width of rectangles, we used an accuracy variant of the Gamer paradigm. Wemeasured the discriminability of height and width (baseline tasks) and size and shape (correlated tasks). From the d' values in these conditions, we estimated perceptual distances and inferred a mean-integral representation in which height and width corresponded to nonindependent dimensions in a perceptual space. This model accounted well for performance in these two-stimulus conditions, and it also explained 70% -80%of the decline in performance in selective and divided attention. In a second experiment, conducted for purposes of comparison with the rectangle discrimination Experiment, we studied the discrimination of horizontal and vertical line segments connected in an L-shape. In size discrimination, observers were equally good with line pairs and rectangles,suggesting holistic perception; but in shape discrimination, they appeared to combine information from the two line-pair components of the rectangle independently. The mean-integral model was again successful in relating performance in the Gamer tasks quantitatively.Rectangles are among the simplest visual forms, and the manner in which they are perceived is of some importance in visual perception. In addition, many studies of rectangles have been motivated by psychophysical considerations. Complex perceptual objects (faces, say, or speech) are often said to be "multidimensional," meaning that such objects depend perceptually on several characteristics, and rectangle perception has provided a workshop for trying out alternative realizations of the multidimensional idea.As illustrated by the minimal set in Figure 1, rectangles can differ in height (vertical axis), width (horizontal axis), size (along the minor diagonal), and shape (along the major diagonal). Any or all of these dimensions may be psychologically important, and a critical research question has been whether height and width, or size and shape, are the defining dimensions for perception. A second question has been whether the dimensions used in the representation interact, or whether they are independent. As Schonemann (1990) has pointed out, there has not been full agreement; the answers have depended in part on the psychophysical methodology used to ask the questions.One useful experimental approach has been to measure identification (absolute judgment) of sets of rectangles. Weintraub (1971) combined 15 values ofheight and 15 values ofwidth to form a group of225 forms. Subsets of 15, one for each possible height, were constructed in a variety ofways, and stimuli within each subset were preThis research was supported by NSF grant DBS 92-12043 and a PSC-CUNY award to the first author. A preliminary report of the data was presented at the Psychonomic Society meetings in Washington, DC, November 1993. We are grateful to John Kingston and Todd Maddox for their comments on an earlier draft. Please address correspondence to N. A. Macmillan, Department of Psychology, Br...

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