Many theories have been created to explain why vertical lines appear longer than horizontal lines. Kunnapas (1957) proposed the framing theory. This theory predicts that a visual fields asymmetric shape is to blame for the misinterpretation of line length. Kunnapas believed that since a visual fields horizontal range is longer than its vertical range one will see the horizontal line as shorter than the vertical line. Experiments to test this theory were done by Prinzmetal and Gettleman (1993). They tested the vertical-horizontal illusion with monocular vision versus binocular vision to see the results of a symmetrical visual field versus an asymmetrical visual field. The results of this experiment showed that monocular vision resulted in a reduction of the vertical-horizontal illusion.
Another theory that describes the vertical-horizontal illusion is Emmerts Law, which states that size and distance are directly related in the perception of objects. Therefore, if the perceived distance of an object is increased then it will appear larger. Girgus and Coren (1975) tested this theory by measuring the amount of perspective convergence photographs triggered when depth cues were present. Their experiment showed that pictures with depth cues caused perspective convergence, which affected the subjects size scaling mechanisms. According to this data, if one were to put a horizontal and vertical line into a picture with depth cues the vertical-horizontal illusion should become stronger. Ward, Porac, Coren, and Girgus (1977) did a follow up experiment that showed slight evidence of pictures eliciting depth information making various illusions like the Sandler parallelogram, Muller-Lyer, Zollner, and Ehrenfels variant of the Ponzo illusion stronger. They found no evidence of depth perception affecting illusions like the normal form of Ponzo, Poggendorf, or the vertical-horizontal illusion. They concluded that depth processing affects some, but not all illusions.
However, many other experiments have given contrasting results. When studying the vertical-horizontal illusion with depth perception and hand movement, Toni, Gentilucci, Jeannerod, and Decety (1996) found that target localization was affected, increasing the strength of the vertical-horizontal illusion.
Von Collani (1985) found that imposing the vertical-horizontal illusion on a two-dimensional picture with appropriate depth cues increases the vertical-horizontal illusion. He explained that the illusion grew stronger because the vertical line seemed to flow into the distance of the picture, making it look longer than it really was. The horizontal line did not seem to flow into the distance, therefore, its size was not affected.
Depth cues are not the only way to increase the vertical-horizontal illusion with perspective. Higashiyama (1988) ran an experiment which gave evidence that perceived distance and perspective is affected by retinal, visual, and gravitational orientations.
However, if the vertical-horizontal illusion is placed in a photograph with depth cues and size-scaling cues (things that give a comparable size for both the vertical and horizontal lines) a person should be able to reduce the size of the illusion because they have something to compare the illusion against. Conversely, if the vertical-horizontal illusion is imposed in a two-dimensional photograph that gives a good three-dimensional perspective the illusion should increase if it looks like it is part of the picture. This experiment is going to test these last two factors.
Methods
Participants: Twenty-one Alma College students between the ages of eighteen to twenty years old participated in this experiment. The participants consisted of ten women and twelve men. All of the subjects were unpaid volunteers.
Stimulus: This experiment had two types of stimuli. The first type (depth cues) consisted of three real photographs with a vertical-horizontal line imposed into the pictures in such a way that the vertical lines looked like they traveled into the distance of the pictures (Figure 1 below). The vertical-horizontal lines were always at a ninety degree angle in an L shape. The second type (size constancy) consisted of three real photographs that gave size-scaling cues as to how big the vertical lines were in relationship to the horizontal lines (Figure 2 below). Once again the vertical-horizontal lines were always in a ninety degree angle with an L shape. The control for this experiment is a vertical-horizontal line on a white background with no images in the background to give depth or size-scaling cues. These seven trials were randomly shown by using the multiple staircase method so participants were not aware of the extent that they manipulated the line size. The pictures and stimuli were shown on Eye Lines software (Beagley, 1996). The apparatus that presented the stimuli was a 2006 Apple Macintosh computer with a twenty inch flat panel screen.
Outside Hallway Hallway Ground View
Figure 1. Perspective Images
Tiles Vent Brick Wall
Figure 2. Size Constancy Images
Procedure: The subjects were then asked to sit in a chair that was nineteen inches above the ground and told to sit upright while participating in the experiment. If the subjects thought the vertical line was longer they would press the a key and if they thought the vertical line was shorter they would press the z key. The step size was set at 3 mm in the subsequent staircase. Cycles of six were required in each staircase and the two stimuli were presented in random order. When the subject pressed the a key to indicate the vertical line was longer, the computer made the next vertical line shorter. This process was reversed when the z key was pressed. The next image was always shown in random order after the subjects evaluated the vertical line length by pressing the a or the z key. The experiment was run in an incandescent lit room and the photographs were in color. The presentation of the stimuli was controlled by the computer program, but the participants were able to control when the next picture would be shown. The time it took to test an individual subject was approximately seven minutes.
Data: The results were compiled by averaging the amount of error each individual participant had for each picture. After each participants trials were averaged we took the mean of all the participants scores for an individual picture and averaged them together. The results in Figure 4 were compiled by averaging all the depth cue containing photographs together, then averaging all of the size-scaling photographs together.
Results
The results show that when subjects were shown the control (just the vertical-horizontal illusion) they misjudged the vertical line by an average of 1.775 mm (Figure 3 and Figure 4). The subjects misjudged the vertical line by 1.319 mm for the vent photo, 1.476 mm for the tile photo, and 2.819 for the brick photograph (Figure 3). The vent, tile, and brick photographs all contain size-scaling cues. When the size-scaling pictures were averaged together, the amount of error was slightly greater than the control group (.093 mm) (Figure 4). The subjects misjudged the vertical line by 4.124 for the ground view photo, 1.423 for the hallway photo, and 2.233 for the outside hallway photo (Figure 3). When the depth cue photographs were averaged together their error was .818 mm greater than the error of the control group (Figure 4).
Figure 3. Measure of the Vertical-Horizontal Illusion in mm
Figure 4. Average Error of Vertical-Horizontal Illusion in mm
During the course of this experiment we encouraged participant feedback. Three participants asked what to press if they thought the line was equal (which we had no button for) and one insisted that all of the initial lines were equal and so she said she would just guess if the vertical line was shorter or longer. Another interesting note was how some of the participants said they judged the vertical and horizontal lines. One male participant said he imagines the vertical and horizontal lines make triangles that tell him the size of the vertical line relative to the horizontal line. A female participant said she imagines that the vertical line is falling down on top of the horizontal line where she can measure them. These mechanisms for judging the vertical and horizontal line may suggest that improper eye movement may be another reason why the vertical-horizontal illusion occurs and should be taken into consideration when describing the vertical-horizontal illusion.
Discussion
The results supported our claim that depth cues would cause the vertical-horizontal illusion to grow stronger. The first two depth cue pictures, ground view and outside hall, elicited a stronger vertical-horizontal illusion. The picture of the hallway, however, did not elicit a stronger illusion. The hallway may not have elicited a stronger illusion because the hallway contained no vertical and horizontal lines to compare it to like the other photographs did. Without these lines the vertical-horizontal illusion may not have been superimposed in the photograph as in the previous depth containing photographs, which caused the vertical line to flow into the distance of the photograph and makes the illusion stronger (von Collani, 1985).
The second half of our results gave slight evidence that size-scaling pictures reduced the effect of the vertical-horizontal illusion. The first two size-scaling photographs, vent and tile, did reduce the illusion. However, the picture brickwall did not reduce the illusion. Brickwalls size-scaling mechanisms may be to blame for the increase in the illusion. The things in the picture that allowed the subject to compare the vertical and horizontal lines with were the bricks on the wall and the windows to the left and right of the illusion. The bricks may have been too small for the brain to accurately judge the vertical and horizontal lines by. Also, the windows next to the vertical-horizontal illusion had very long vertical lines and very short horizontal lines. If the subject was comparing the illusion to the window, they may have seen the vertical line as longer because they were comparing it to the long vertical lines of the window. When the size-scaling pictures were averaged together they were greater than the control because of the picture brickwall. If brickwall increased the illusion because of deceptive size-scaling cues then the size-scaling cues that gave accurate descriptions of the size of the vertical and horizontal lines (i.e. vent and tile) did reduce the illusion.
With this thought in mind it can be hypothesized that the vertical-horizontal illusion can either be reduced or increased based on size-scaling cues. If the cues give misleading information, like unequal vertical and horizontal lines, then the illusion may be increased due to the deception of the uneven vertical and horizontal lines. However, if the lines are equal and give accurate size-scaling mechanisms than the illusion should be decreased.
Girgus, J.S., & Coren, S. (1975). Depth cues and constancy scaling in the horizontal-vertical illusion: bisecting error. Canadian Journal, 29, 59-65.
Higashiyama, A., & Ueyama, E. (1988). The perception of vertical and horizontal distances in outdoor settings. Perception & Psychophysics, 44, 151-156.
Kunnapas, T.M. (1957). The vertical-horizontal illusion and the visual field. Journal of Experimental Psychology, 54, 405-407.
Prinzmetal, W. & Gettleman, L. (1993). Vertical-horizontal illusion: One eye is better than two. Perception and Psychophysics, 53, 81-88.
Toni, I., Gentilucci, M., Jeannerod, M., & Decety, J. (1996). Differential influence of the visual framework on end point accuracy and trajectory specification of arm movements. Experimental Brain Research, 3, 447-454.
von Collani, G. (1985). The horizontal-vertical illusion in photographs of concrete scenes with and without depth information. Perceptual and Motor Skills, 61, 523-531.
Ward, L.M., Porac, C., Coren, S., & Girgus, J.S. (1977). The case for misapplied constancy scaling: Depth associations elicited by illusion configurations. American Journal of Psychology, 90, 609-620.
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