If you haven't seen or don't know what a random dot stereogram looks like, click here.  Random dot stereograms make use of the fact that humans have two eyes that provide slightly different views of the world -- we call this binocular vision.  The view of a scene projected to the retina of the left eye is offset relative to the view projected to the right eye.  Because the views of the left and right eyes overlap, the visual system faces the problem of how to combine the two views to create a unified image.  The big problem for vision is that there is no direct way to align the views of the left and right eye.  The image falls on different parts of the two retinas and the correspondence of the images depends on how far away an object is from the observer.  Objects that are closer to the observer will be farther apart in the two images, whereas objects that are more distant will be closer together. Click here to see an example of this linear perspective depth cue.

    For people with normal vision, the information is projected to visual cortex where the 2-D views of the left and right eye are combined.   The combination process is very interesting, because it solves an extremely complex problem using massive parallel neural computation.  To explain how the correspondence is solved, it is first useful to understand that there are binocular depth cells in visual cortex that are sensitive to different disparities between the two eyes.  These cells respond best to stimuli that fall on points separated by a specific angle of disparity in the two retinas.  Click here to see an example of the response of a single binocular depth cell in the visual cortex of a monkey (these recordings were made by Hubel & Wiesel in 1970).  This particular disparity cell fires maximally when the image in the right eye (RE) and the image in the left eye (LE) are separated by 30' of visual angle.   The binocular disparity cells are interconnected in such a way that cells at different disparities tend to inhibit each other, whereas cells at the same disparity tend to reinforce one another.  David Marr and Tomaso Paggio developed a simplified constraint satisfaction " neural network" model for stereo vision that illustrates these inhibitory and facilitatory interconnections.  Over time, the activations in the network reverberate until the network settles into a stable depth state.  Phenomenologically, you can feel this settling process as the 3-D image fades into view.

    An interesting property of this recovery of depth information is that the 3-D image can be different from the single 2-D images.  An elegant example of this is the random dot stereogram, in which the monocular (one eye) view is just a random set of dots, but the binocular view is combined to create a meaningful 3-D pattern.  The algorithm for building random dot stereograms is relatively straightforward.  First, a repeating pattern is needed so that the same image will be presented in the left and right eyes.   If you want objects appear to be closer to (or farther away from) the observer, spaces are added so that the separation between the repeating pattern will be greater.  If you want objects to appear farther away from (or closer to) the observer, spaces are removed so that the separation between the repeating patterns will be smaller.  Note that closer vs farther dependes on whether your eyes converge or diverge.   Click here to see a simple stereogram I built that adds spaces between repeating patterns.

   Many people have difficulty seeing random dot stereograms.  Because normal binocular vision is a prerequisite, a quick test for people who have problems seeing random dot stereograms is to see if they can see the 3-D perspective in a child's hand-held Viewmaster.  If someone cannot see the 3-D perspective in a Viewmaster, they probably do not have normal stereo vision and will be unable to see the random dot stereograms.  Note that this does not imply that these people can't see in depth -- there are about a dozen visual cues that underlie depth perception.  If you can see the 3-D image in the Viewmaster, then patience and practice are in order.  Often it helps to relax your eyes and not try to force the effect.  Try to focus your eyes in front of or behind the image by converging or diverging your eyes.

    For more information on how random dot stereograms work, consult Steven Pinker's (1997) book: How the Mind Works (pp. 214-242). Norton & CO, New York.