Caroline Van Zeeland and Angela Nelson, Effects of Local Visual Cues on the Tilt Illusion.

Our experiment on the tilt illusion provides information about the perceptual mechanisms related to orientation in space.    The tilt illusion is demonstrated when a subject�s horizontal alignment of two dots on a computer screen is distorted by the presence of slanted background lines. The tilt-constancy theory states that the tilt illusion is a misperception of orientation due to local visual context. If the tilt-constancy theory is also used to account for other illusions such as the Poggendorff illusion, then certain apparent conflicts in existing data must be reconciled. Specifically, the tilt illusion is greatest when the inducing lines depart from the horizon by 10 to 20 degrees, while the Poggendorff illusion is most potent with large angles (50 degrees) with respect to the horizon. Earlier student research found that the magnitude of the tilt illusion is greatest with steeper angled lines when the inducing lines have a gap in the center, as does the slanted line in the Poggendorff illusion. We hypothesize that it is not the gap itself that changes the angle associated with the strongest illusion, but the proximity of the dots to the edge of the background lines on which they are superimposed. We varied the slope of the background lines and the distance of the dots from the edge of the region containing the inducing lines. The illusion increased with increasing slope, for the dots located at the edge of the inducing lines. This is the same as the relationship between line slant and illusion magnitude for the Poggendorff illusion. When the dots are superimposed on the lines and were located farther away from the edge, the magnitude of the illusion decreases with increasing slope.

Visual illusions are more than amazing curiosities. Explanations of illusions may lead to a better understanding of the mechanisms of normal visual perception. The study of tilt-induced effects may be valuable in learning about perceptual spatial orientation. Gibson�s (1937) subjects judged that a vertical line viewed against a background of slanted lines appears to tilt in the opposite direction (See Figure 1). Shimamura and Prinzmetal (1999) described a new method for studying tilt-induced effects in both the vertical and horizontal axis. To examine horizontal tilt effects, their subjects moved an adjustable dot on a computer screen to match the height of a fixed dot. When these dots were presented on a background of slanted parallel lines, the subjects� judgments of height was distorted, i.e., they tended to move the adjustable dot so that a straight line drawn between the dots would tilt in the same direction as the inducing lines (see Figure 2).

Shimamura and Prinzmetal (1999) offered the Orientation framing theory (OFT) to account for the tilt-induced illusion as well as other geometric illusions including the Ponzo, rod-frame, Poggendorff, Wűndt-Hering, and Zőllner illusions. OFT claims that visual processing is important in establishing spatial frames of reference. The four basic principles of OFT are; 1) orientation frames are established in terms of perceived vertical and horizontal axes, 2) perceived frames are affected by local visual cues and there may be multiple orientation frames at multiple levels, concurrently, 3) Misperception of the true gravitational axis distorts many aspects of perceptual processing, and 4) Orientation frames contribute to higher-level spatial representations.

Prinzmetal, Shimamura, and Mikolinski (2001) refer to the OFT as the Tilt Constancy theory which states that the tilt-induced effect results from a misperception of orientation due to visual context. Prinzmetal, Shimamura, and Mikolinski (2001) present a series of experiments on the Ponzo illusion that support the Tilt Constancy theory compared to other explanations, e.g., relative size judgments and the pool-and-store model. Prinzmetal, Simamura, and Mikolinski (2001) claim that the Tilt Constancy theory can also account for the Poggendorff illusion. Figure 3 illustrates the Poggendorff illusion, which consists of two vertical lines with an oblique line with the center occluded. Tilt Constancy theory predicts that the oblique lines will appear to be tilted toward the horizontal axis. This apparent tilting of the line segments make the left end of the right line appear higher and the right end of the left line segment appear lower. The result is the two line segments no longer appear collinear. The two lines appear to be parallel with the right segment higher than the left.

One difficulty with the claim that the same underlying mechanism can explain both the Poggendorff illusion and the tilt-induced effect is the finding that the optimal line slopes for the tilt-induced illusion and the Poggendorff illusion are not the same. While the Poggendorff illusion is quite strong (Weintraub & Krantz, 1971) with a steeply sloping oblique, e.g. 45 to 60 degrees, the tilt-induced illusion is greatest with inducing lines that deviate from the axis of judgment by only about 10 to 20 degrees, with relatively small illusions at 45 degrees (Shimamura & Prinzmetal, 1999).

An obvious difference between the tilt-induced and the Poggendorff illusions is that the slanted line in the Poggendorff illusion is interrupted, or is composed of two line segments, while the background for the tilt-induced illusion is composed of parallel continuous lines. A second difference is that the locations to be compared are at the ends of lines in the Poggendorff and are in the middle of slanting lines in the tilt-induced illusion.

In our investigation, we evaluated the tilt-induced illusion where the dots to be compared were located on two rectangular fields made up of slanting lines. The two fields of slanted lines were separated by a vertical gap as in the Poggendorff illusion (see Figure 4). The size of this gap varied so that the dots would be located various distances from the inner edge of the fields. We predicted that the maximum illusory effect would be obtained with steeply slanting lines when the dots were located at the edges of the fields. When the dots are located farther onto the fields (away for the center gap) we predicted that the greatest illusion would be obtained with line slants of 5 to 20 degrees, as is found with the tilt-induced illusion with continuous lines.

Twenty-eight undergraduates (8 male, 20 female) enrolled in an Introductory Psychology course at the University of Wisconsin-Stevens Point participated in the experiment. The students partially fulfilled a course requirement by participating in this study. Students also had the option of writing a short research report or participating in other studies to satisfy the requirement.

The Cognition Laboratory houses four experimental stations separated by office partitions. Each station consists of a Gateway 2000, P5-120 computer with a 17 in Vivatron monitor on a small table. The stimuli presented to the participants on the computer monitor consisted of 3 mm dots superimposed on two fields of parallel lines with a vertical gap separating the fields (see Figure 4). The parallel lines were separated by 10 mm. The two dots were located 100 mm apart, horizontally, and centered on the screen. By using the arrow keys, the participant could move the right dot up and down. The starting position of the adjustable dot was between 17.5 to 35 mm above, or 17.5 to 35 mm below the center of the screen.

Using the four experimental stations, up to four participants could be tested at one time. Each participant was asked to sit a comfortable distance away from the monitor and keyboard. They were instructed to use the arrow keys to move the height of the adjustable dot on the right until it appeared to be the same height as the fixed dot on the left. The participant ended the trial by pressing the enter key when they were satisfied that the two dots appeared to be equal in height. A new display was presented after a 1 sec delay. After each trial, the final position of the adjustable dot was recorded and the tilt of the line connecting the two dots was computed. On each trial the participant viewed a display consisting of a background of two fields of parallel slanted lines on which the dots were superimposed. The size of the gap separating the two fields varied so that the distance of the dots from the inner edge of each field was 0, 17.5, or 35 mm (see Figure 4). The background lines had either positive (counterclockwise tilts) or negative (clockwise tilts) slopes with respect to the horizontal axis. There were three line slopes, 15, 35, and 55 degrees. There were 18 different trial types produced by the combination of the three edge distances combined with the two directions of slope and the three line slopes. Each trial type was repeated seven times for a total of 126 trials. Each participant received the trials in a unique random order.

Figure 5 displays the tilt-induced illusions for the three edge distance conditions. As the illusions appear to be relatively symmetrical for the two directions of line slope, the line slope variable was divided into two variables, direction of slope (positive and negative) and absolute slope (15, 35, and 55 degrees). The magnitude of tilt-induced illusion, i.e., the degrees of tilt in the predicted direction, was submitted to a three-factor analysis of variance with distance from edge (0, 17.5, and 35 mm), direction of slope (positive vs. negative), and line tilt (15, 35, and 55 degrees) as factors. The main effect of distance from edge was significant, F(2, 54) = 104.53, Mse = .451, p < .001. When the dots were located on the edge of the fields the mean magnitude of the illusion was .34 degrees while the mean magnitude of the illusion was much stronger when the dots were 17.5 and 35 mm from the edge of the fields, 1.13 and 1.34 degrees, respectively. The main effect of direction of slope was not significant, suggesting that the illusion was the same for positively and negatively sloped lines. Although the main effect of slope was not significant, there was a significant edge X slope interaction, F(4, 108) = 19.62, Mse = .1617, p < .001. No other interaction was significant.

Figure 6 plots the magnitude of the tilt-induced illusion as a function of line slants for the three edge conditions. When the dots were located on the edge of the inducing fields the magnitude of the illusion increased with the slope of the inducing lines. In contrast, the magnitude of the illusion decreased with increasing slope for the dot farthest from the field edge. Illusion magnitude was stable across slopes when the dot was an intermediate distance from the field edge.

We found that the horizontal, tilt-induced effect was observed when the two dots to be horizontally aligned were superimposed on two lateral fields of slanting lines separated by a vertical gap. When the dots were located well onto the fields, 35 mm from the inner edges, the tilt-induced effects was comparable to the effect reported by Shimamura and Prinzmetal (1999). In both cases, the size of the effect was greatest with shallow inducing lines, 15 degrees, and decreased with increasing line slope. The central gap dividing the fields of lines had little affect on the tilt-induced effect compared to the tilt-induced effect with continuous lines.

When the dots were located at the inner edge of the fields of lines, the size of the tilt-induced illusion was reduced. In addition, there was a direct relationship between line slope and the size of the tilt-induced illusion. This form of the tilt-induced illusion is similar to the Poggendorff illusion in that the points that are compared are at the ends of slanted lines. In both cases there is a direct relationship between line slope and the strength of the illusion. The distortions of spatial orientation appear to be different in the center of a field of slanting lines than toward the perimeter.

Gibson, J. J., (1937). Adaptation, after-effect, and contrast in the perception to tilted lines. II. Simultaneous contrast and the areal restriction of the after-effect. Journal of Experimental Psychology, 20, 553-569.

Prinzmetal, W. Shimamura, A. P., & Mikolinski, M. (2001). The Ponzo illusion and the perception of orientation. Perception and Psychophysics, 63, 99-114.

Shimamura, A. P. & Prinzmetal, W. (1999). The mystery spot illusion and its relation to other visual illusions. Psychological Science, 10, 501-507.

Weintraub, D. J. & Krantz, D. H. (1971). The Poggendorf illusion: Amputations, rotations, and other perturbations. Perception and Psychophysics, 10, 257-264.

Figures

Figure 1

Example of Gibson�s (1937) tilt-induction effect where the vertical line appears to tilt in the direction opposite the induction lines.

Figure 2

Figure 3

The Poggendorff illusion can be considered a form of the tilt-induced effect. The oblique lines do not appear to be collinear, because the oblique lines appear to tilt toward the horizon.

Figure 5

Tilt-induced illusion as a function of line slope and distance of dots from the edge of the field of lines.

Figure 6

Magnitude of the tilt-induced illusion as a function of absolute line slant and distance of dots from the edge of the field of lines.

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