Distance and an illusion of length of line.

Restle, Frank; Merryman, Coleman T.

doi:10.1037/h0027738

Cited by 27 publications

(18 citation statements)

References 6 publications

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“…The discrepancy between the measured length of a spatial interval and its perception has been rationalized in several different ways in the past, including asymmetries in the anatomy of eye (8,10,11,17), the ergonomics of eye movements (5, 32), and cognitive compensation for the foreshortening of vertical lines (12,(14)(15)(16). In the last of these theories, which is the one most often cited, vertical lines in the image plane are assumed to be objects on the ground plane that extend in depth; horizontal lines, on the other hand, are taken to be objects parallel to the frontal plane.…”

Section: Discussionmentioning

confidence: 99%

Range image statistics can explain the anomalous perception of length

Howe

Purves

2002

Proc. Natl. Acad. Sci. U.S.A.

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A long-standing puzzle in visual perception is that the apparent extent of a spatial interval (e.g., the distance between two points or the length of a line) does not simply accord with the length of the stimulus but varies as a function of orientation in the retinal image. Here, we show that this anomaly can be explained by the statistical relationship between the length of retinal projections and the length of their real-world sources. Using a laser range scanner, we acquired a database of natural images that included the three-dimensional location of every point in the scenes. An analysis of these range images showed that the average length of a physical interval in three-dimensional space changes systematically as a function of the orientation of the corresponding interval in the projected image, the variation being in good agreement with perceived length. This evidence implies that the perception of visual space is determined by the probability distribution of the possible real-world sources of retinal images.A s the orientation of a linear stimulus in the retinal image changes, so does its apparent length. Thus, a line that projects vertically appears to be longer than the same line presented horizontally, the maximum length being seen when the stimulus is oriented 20-30°from the vertical axis (refs. 1-4; Fig. 1). This variation is evidently a particular manifestation of the general tendency to perceive the extent of any spatial interval differently as a function of its orientation in the retinal image. For instance, the apparent distance between a pair of dots varies systematically with the orientation of the imaginary line between them (5), and a perfect square or circle appears to be slightly elongated along its vertical axis (6, 7). Despite extensive study of these phenomena during the past 150 years (8-19), neither a quantitative explanation of these effects nor a generally accepted biological rationale has been forthcoming.The explanation we have examined here is that the variable perception of length as a function of stimulus orientation represents a solution to the problem presented by the inevitable ambiguity of retinal projections, namely that retinal images cannot uniquely specify their physical sources (20). Thus, a given line in the retinal image could have been generated by an infinite number of real-world objects with different lengths, located at different distances and in different 3D orientations. The physical source of a retinal stimulus nonetheless is what the observer must respond to with appropriate visually guided behavior. One solution to this dilemma would be to generate percepts according to the probability distribution of the possible physical sources of the retinal stimulus. To test this hypothesis with respect to the perception of visual space, the arrangement of objects in the physical world must be related to their projected images. Accordingly, we used a laser range scanner (21, 22) to acquire a database of natural scenes that included the location in 3D space of every pixe...

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Section: Discussionmentioning

confidence: 99%

Range image statistics can explain the anomalous perception of length

Howe

Purves

2002

Proc. Natl. Acad. Sci. U.S.A.

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“…Moreover, alternative theoretical notions might do as well or better in explaining aspects of the data. Restle and Merryman (1969) have a version of adaptation-level theory that considers distances between elements of a displayas well as the size of contextual elements. Pressey (e.g., Pressey & Murray, 1976) has proposed assimilation theory, which incorporates a construct called the attentive field.…”

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confidence: 99%

Fragments of Delboeuf and Ebbinghaus illusions: Contour/context explorations of misjudged circle size

Weintraub

Schneck

1986

Perception & Psychophysics

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Variants ofthe Delboeuf (concentric circle) display and the Ebbinghaus display (four large nonconcentric inducing circles) were produced by systematically eliminating fractions of the circumferences of the outer inducing circles. For the Ebbinghaus display, various amounts of the inner arcs and/or outer arcs were preserved; a series of dots was sometimes substituted for missing contours. Results are described by the following statements: Contours attract. Larger nonconcentric circles induce size contrast. Rotating an Ebbinghaus variant by 45°alters size misjudgments. The larger the horizontal (or vertical) extent of the inducing configuration, the smaller the judged size of the test (center) circle. A figural aftereffect of the inducing configuration acts to reduce the perceptual size of the comparison circle when eye movements are permitted between test and comparison circles.The term illusion, because of its connotations of magic and deception, neither of which is germane to the topic at hand, shall be restricted to the title. Informativeness requires its inclusion in the title. At issue are explanations of the Delboeuf anomaly, size misjudgments of a circle in the presence of a concentric circle, and the related Ebbinghaus (Titchener circles) anomaly, which depends upon the presence of nearby nonconcentric circles. The underlying problem is to understand the processes underlying misperceived circle size. The present investigation relies upon displays that are sometimes only distant cousins to Delboeuf and Ebbinghaus figures.The research was designed to explore elements of a theory proposed on the basis of relatively modest evidence (Cooper & Weintraub, 1970;Weintraub & Cooper, 1972) but more recently buttressed by extensive evidence (Weintraub, 1979). In barest outline, the contour/circle-context model asserts that contours attract and that context supplied by the larger or smaller size of nearby nonconcentric circles leads to size contrast. Contour attraction, then, predicts that exterior contours produce overestimation of Experiment 2 was based on research by the second author for his senior honors thesis in the Psychology Department, University of Michigan.

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“…One is based on the notion of contrast, in which differences between stimuli are perceptually enhanced. Thus, the distance near the small square (Distance B in Figure 1), which is a relatively large length, is judged in the context of the width of the small box, which is a relatively small length, and because of contrast, a phenomenal elongation of Distance B occurs (Baldwin, 1895;Restle & Merryman, 1969). A second interpretation is based on the concept of assimilation, in which differences between stimuli are perceptually reduced.…”

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confidence: 99%

The effects of location, orientation, and cumulation of boxes in the Baldwin illusion

Pressey

Smith

1986

Perception & Psychophysics

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Three experiments were conducted on variants of the Baldwin illusion. Experiment 1 showed that placing a box on each side of the standard line produced a larger illusion than placing both boxes on the same side of the line. These results failed to support the assimilation theory proposed by Brigell, Uhlarik, and Goldhorn (1977). In Experiment 2, the side of a rectangular box was varied when that side was either parallel or perpendicular to the standard line. The parallel rectangle produced a function that was similar to the one found with the classical Baldwin figure, but the perpendicular boxes produced a monotonically decreasing function with a reversal of illusion evident at the large sizes. The latter function did not support any version of the assimilation theory. The findings of Experiment 3 replicated previous findings that showed that cumulating contours as box size increased had no effect on the illusion. These findings explain two longstanding puzzles about the Miiller-Lyer illusion: why a multifinned form is not the sum of its single-finned parts and why the shrinkage form produces a smaller effect than does the expansion form.EXPERIMENT 1 (1977) argued that the critical causal variable in many illusions of length is the framing ratio, that is, the ratio of the length of the entire figure to the length of the standard line. Their explanation of the inverted-U function that relates illusion to box size was based on a neurophysiological model. According to Brigell et al., viewing a stimulus activates length-selective units in proportion to their sensitivities to thatlength. Eachunit responds to only a limitedrange of proximal stimulus lengths. The maximal overestimation of focal shaftlengthshould occur when thesame unitis mostsensitive tothetotal figure length and also is the rightmost unitin the distribution produced by thefocal shaftwhentheshaft is presented alone. (p. 116) Pressey's assimilation theory (e.g., Pressey & Dil.ollo, 1978) also focuses on the size of the contextual stimulus, which he calls the range Variable. The increasing portion of the inverted-U function is explained by the fact that the average of the focal and contextual stimuli increases as the size of the contextual stimulus (frame) increases. The decreasing portion is explained by the fact that the probability of averaging decreases, because (1) In the Baldwin configuration, shown in Figure 1, a bisected line is flanked by two squares of unequal size. The two portions of the bisected line do not appear equal. Rather, the part of the line near the small square appears longer than the part near the large square.

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Distance and an illusion of length of line.

Cited by 27 publications

References 6 publications

Range image statistics can explain the anomalous perception of length

Range image statistics can explain the anomalous perception of length

Fragments of Delboeuf and Ebbinghaus illusions: Contour/context explorations of misjudged circle size

The effects of location, orientation, and cumulation of boxes in the Baldwin illusion

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