Studies and tests

To understand how autostereograms work and to be able to recreate them, one has to understand the mechanism of human eyes. This page explores the topic of 3D vision and why people see dimensions. And finally, presents simple tests everyone can do at home to understand how autostereograms work.

scientific context

Human eye anatomy is very similar to the camera structure, which is no surprise as the first cameras closely mimicked eye mechanisms. Therefore, the most approachable way of describing eye anatomy is by the juxtaposition of the two. The figure below highlights the most important parts of the human organ of sight. Homo sapiens, just like many other mammals, have two eyes, which share one common area of view. Thanks to this vision intersection area people can perceive depth and recognise shapes much better than other species. This physical attribute is called binocular vision, which, as opposed to monocular vision, involves two eyes.

Eye anatomy compared to camera structure. Credit: W. Szczypinska
Representation of binocular and monocular vision. Credit: Created by W. Szczypinska

Depending on the distance of the object, its image on the retina is projected in a different place and scale. Moreover, each eye creates a different projection of the same object on the retina. This can be observed when looking at a distant target and closing one eye at a time; the object will change its position and angle depending on which eye is opened. So when looking with both eyes we end up with two different images, how is it possible we see only one? This is thanks to our brain, which looks for similarities in the two images from two retinas and merges objects that appear to be the same (Tricart, 2017, 4), this phenomenon gives the illusion of depth but also allows to trick our brains into seeing unreal things.

Representation of retinal disparity. Credit: Created by W. Szczypinska
Representation of vergence. Credit: Created by W. Szczypinska

Another important aspects of 3D vision are vergence and lens accommodation. The former can be defined as the movement of the eyes that allows both eyes to converge at the fixation point (at the point we are looks at); the wider the vergence angle, the closer the object. Accommodation, however, is the ability of the lens to squash and stretch depending on the distance between the lens and the object, which allows for a change in focus. Accommodation and vergence are controlled subconsciously and are closely linked – one triggers the other, however, one can learn to control the muscles and separate the two. This ability is what makes autostereograms possible. (Burt and Julesz, 1980) By separating vergence from accommodation one can look at an object in a distance at the same time focusing the eyes at a point closer to the retina. By decreasing the vergence angle (looking at a distance as close to infinity as possible), one can almost entirely separate two eyes (get two completely different images, similar to a panoramic view). Then, while still maintaining the same vergence, one can focus on two close 2D images to see the stereoscopic illusion.
Due to having twice as much information to process, the brain can calculate 3D space more precisely, however, this ability alone is not enough. Studies have found that stereoscopic vision is more accurate if the brain and eyes receive certain stereoscopic cues. (Brewster, 1844) There are two groups of cues – monocular (perceived with one eye) and binocular (requiring two eyes). Monocular cues are frequently used in cinematography to give the feeling of depth; the most important ones include perspective, ambient occlusion, or atmospheric effects.

Depth Cues for Monocular and Binocular Vision. Credit: Created by Wiktoria Szczypinska

The brain needs one or more cues to read depth, but if we eliminate all monocular cues it must rely solely on vergence and retinal disparity. One of the first experiments eliminating optical cues was conducted by Adelbert Ames in the early twentieth century, “he hoped to achieve an environment with a minimum of monocular depth cues”. (Pepin, 2003, 296) To see depth, the viewer had to rely primarily on the binocular cues, which was later used for the creation of autostereograms. This phenomenon has laid the ground for random dot autostereograms, and later for 3D glasses and Virtual Reality.

The Leaf Room. Credit: Ames, circa 1939

understand how it works by doing simple tests

All that theory might seem a bit overwhelming, so it is best to understand the mechanisms behind 3D perception by conducting several simple experiments.

understanding Diplopia

Hypothesis: one can separate vision for each eye by looking at a distance
Test (chopsticks):
1. Place two chopsticks in front of you, one in front of the other and aligned with each other, the distance should be bigger than 20 cm (as shown in the image on the right)
2. Look at the chopstick farther away Findings: when looking at the second chopstick, one can see a double image of the first chopstick
Conclusion: diplopia can be used to separate the vision in two eyes

Binocular vision

Hypothesis: the brain generated a new image based on the two images from each eye
Test (tube):
1. Place your left hand in front of you
2. Hold the cylinder in your right hand (as shown in the image on the right) and place it next to your left hand
3. Look through the cylinder with both eyes opened
Findings: a circular hole can be seen in the left hand
Conclusion: the brain can be easily tricked when given an insufficient amount of information; even when not given enough data, the brain still tries to combine the images given by two retinas

Monocular cues

Hypothesis: depth recognition without binocular cues is less accurate
Test (2 people and chopsticks):
1. Each person must be on the opposite side of a table
2. Ask your partner to hold two chopsticks behind a table (as shown in Figure 36)
3. Move your head so that you can only see the top part of the chopsticks
4. Close your eyes
5. Ask the partner to place one chopstick farther than the other, but ensure their top parts are aligned
6. Keep the head perfectly steady and open one eye
7. Guess which chopstick is closer
8. Repeat the test several times
Findings: when covering one eye, one has more difficulties perceiving distance
Conclusion: the brain has troubles recognising depth when given an insufficient number of binocular cues

Vergence and Accommodation

Before doing the test, you will have to learn how to view autostereograms. If you cannot see them, please fo back to the “Autostereogram: viewing techniques” page.

Hypothesis: autostereograms can be viewed when vergence and accommodation are separated
Test (“Magic Eye” image):
1. Hold the image in front of your eyes
2. Look at the point above the image twice as far as the book, slowly start moving your eyes to the book, but without focusing on it, can you see the image?
3. Now look at the point 4 times as far as the book, slowly start moving your eyes to the book, but without focusing on it, how did the image change?
4. Next, look at a point in front of the book, at half of the distance between your eyes and the book (you can use the chopstick to help), slowly start moving your eyes to the book, but without focusing on it, how did the image change? Findings: when looking at the point 2 as far as the book, the 3D image can be easily seen; when looking 4 times as far, the image is duplicated; and when looking at a 0.5 distance, the image is reversed (extrusions are holes and vice versa)
Conclusion: autostereograms use uncrossed diplopia and the best way to view them is by looking at a point twice as far as the book; when viewing autostereograms one is forcing their eyes to look beyond the image, which can be a good exercise and can have a positive impact on their eyes