Single Image Random Dot Stereograms are 2-D pictures made up of computer generated randomly placed dots. The earliest examples consisted of black and white random dots, but more recent developments have led to colorful and complex 3-D images (Burder, 1994). In order to view the 3-D image, several techniques may be used. One involves crossing one's eyes, and another involves blankly staring "through" the paper until the image appears. Seeing 3-D images from 2-D pictures began around the 19th centruy when Victorian researchers found that looking through a stereoscope of photographs of an object taken by 2 cameras a few inches apart resulted in a 3-D illusion (Zimmer, 1999). A century later, psychologist Dr. Bela Julesz created a sterogram consisting of two identical fields of randomly scattered dots. Dr. Julesz was the first to use the sterogram concept for studying depth perception in human beings (N.E. Thing Enterprises, 1993). The following experiment will also utilize sterograms to explore depth perception in human subjects. This experiment was designed to determine the just noticeable difference (JND) between depth levels. The JND, or difference threshold, is the smallest detectable difference between two stimuli (Goldstein, 1999).
Participants were 25 college students ages 18-23. Upon questioning, all answered that they were able to see 3-D images in sterograms either "fairly easily" or "easily." Both males and females participated.
Magic Bitmap 3 was the computer program used to create the sterograms. The program made sterograms from 2-D grayscale pictures. The grayscale pictures were created on Presto! Imagefolio LE. Depth levels were controlled by the brightness of the grays. Brightness ranged from white to black, with white numbered 255 and black numbered 0. Lighter colored objects appeared further back in the 3-D image; darker colored objects appeared to pop out at the viewer.
Using the program, one sample and eleven stimuli were created. The background of all the pictures was white. In each stereogram, the control bar was a simple rectangular bar. The brightness of the bar was set at 127, directly between white and black. The independent variable in this experiment was a second bar directly below the control bar in each picture. The second bar had the same dimensions and was positioned parallel and roughly one centimeter below the control bar (see Figure 1). In each of the eleven sterograms, the second bar was set at a different brightness level. The brightness ranged from 117-137 in increments of 2. The images with a lighter gray shade appeared further back in the page, and darker images appeared closer. The stereograms were printed in black and white ink on standard white 8 1/2" x 11" sheets of paper. For experimenters' use, each of the stereograms was identified with its own four-letter code word.
During the experiment, subjects were first shown the sample stereogram. Once they saw the 3-D image, they were then asked two questions: "Did the image pop out or sink back into the page?" and "Would you say you see 3-D images in stereograms fairly well or easily?" The first question was necessary to interpret the results; when the paricipant saw the sample image sinking into the page, the inverse of the answers given was tallied. Then the subjects were briefed on what the next 11 stimuli contained and asked to determine whether the bottom bar popped out in comparison to the top control bar. The stimuli were then presented to the participant in random order. If the subjects thought that the bottom bar stuck out more than the control bar, then the experimenter recorded the result as "yes." If the subjects thought that the bar sunk into the page or that it was equal to the top bar, then that result was entered in as "no."
The number of "yes" answers for each of the eleven stimuli were totaled and the percentage of "yes" answers per stimuli were calculated. The JND was found using the graph seen in Figure 2. The JND was the depth level at which subjects answered "yes" 50% of the time. Therefore, the JND was shown to be seven depth levels (127-120).
From the graph (Figure 2), one can see that the majority of the subjects noticed the depth difference between stimuli of depth level 120 and 127. So, the JND was shown to be seven depth levels. Basically, this number meant that the subjects were able to see a difference between two bars when the depth difference between them was at least seven levels.
It was discovered during the experiment, that depth perception was harder to perceive when comparing depth levels that sunk behind the control bar. Subjects easily determined 117 to be popping out from the control 127 bar, but it was harder to see a depth difference at 137 compared to 127. A better experiment would explore the JND for both "popping out" and "sinking in" stimuli.
The coding on each page allowed this to be a double-blind experiment, which strengthened its validity. The real JND could have been detected more easily if more stereograms had been used over a wider range of settings, using increments of one shade between sets.
Burder, David (1994). Super Stereogram. San Francisco, CA: Cadence Books.
Goldstein, E. Bruce (1999). Sensation & Perception (5th ed.). Pacific Grove, CA: Brooks/Cole Publishing Co.
N.E. Thing Enterprises (1993). Magic Eye: A New Way of Looking at the World. Kansas City: Andrews and McMeel.
Zimmer, Carl. (1995, January). Wallpaper for the mind. Discover, 16, 80.
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