When New Views Meet Old Assumptions
Stereopsis: An underappreciated sense, especially in the long view.
Posted Nov 30, 2013
In Hans Christian Andersen’s fable, “The Emperor’s New Clothes”, two swindlers, posing as weavers, come to town boasting that they can make clothes so wonderful and magical that only the wise can see them. Although they pretend to work hard at their loom, they don’t make anything. There are no real clothes. But the emperor and all his subjects hear their claim so many times that they come to believe it. They don’t see any actual clothes being made, but to reveal that they see nothing, suggests that they are unwise. No one wants to admit that to themselves or to others so they convince themselves that the clothes are real. Finally the emperor dons these virtual clothes and parades down the street. Everyone cheers, exclaiming about the beauty of the new robes, except for one innocent child who cries, “But he hasn’t got anything on.”
When, at age 48, thanks to vision therapy, I first began to see in 3D, I often felt like the child in “The Emperor’s New Clothes.” As a neurobiology professor, I had taught my students the mechanics of stereopsis (3D vision) and had parroted what I had read in many textbooks – that stereopsis is helpful for close viewing and for eye-hand coordination but has little impact on our distant vision. I had read these statements so many times that I didn’t question them. So, I was floored when I began to see the world in stereo. The whole landscape inflated. I could see the pockets of space between objects near to me but also some distance away. If stereopsis was only good for close viewing, it should not have created such an impact on my worldview. So like the child in Andersen’s fable, my vision told me something that conflicted with the common beliefs of the day.
So I looked into the phenomenon of stereopsis further and discovered why we have not appreciated the impact of stereopsis on our global view. When we look at an object, call it object A, we aim or fixate both eyes at that object, so that its image falls on the central part of the retina of both eyes. This central region is called the fovea. Since the image of the object falls on the fovea of both retinas, it falls on corresponding retinal points. However, a second object, call it object B, located in front or behind object A casts its images on non-corresponding points. The image of object B falls some fraction of a degree to the right or left of the fovea, and this location is different for the two eyes. The difference in the location of the retinal image between our two eyes is called retinal disparity. The further away in depth object B is from object A, the greater the disparity of its images on our two retinas. The bigger the disparity (up to a certain limit), the more volume or depth we see between object A and B.
As we look further and further away, we need more distance between two objects to tell with stereopsis which object is closer and which is further away. Indeed, the amount of the distance between objects that is necessary to judge their relative depth increases rapidly, with the square of the viewing distance. As a result, we assume that we don’t use stereopsis very much in assessing depth in a distant view. Instead, we use cues that can be seen with only one eye, such as perspective or object occlusion (i.e. a closer object will block our view of an object further away.) But this assumption doesn’t take into account the exquisite sensitivity of stereopsis, of just how small a retinal disparity we can use to judge depth.
Stereoacuity is a measure of the smallest retinal disparity a person can use to see things in depth. For people with normal vision, stereoacuities are in the range of 10 to 40 arc seconds. (One arc second is 1/3600 of a degree.) This means that an object can cast an image on one retina that is located at a point only 10 to 40 arc seconds different than its location on the other retina for a person to see it in stereo depth. My stereoacuity isn’t quite up to normal standards since I need a disparity of 70 arc seconds to see things in depth.
But what a boon to my vision is my subnormal, 70 arc second stereoacuity! As I look out my kitchen window, I can see birds alighting on the branches of small trees and vines at the edge of the woods 16 feet (5 meters) away. The branches are all a jumble, way too mixed up for me to judge which branch is in front of the other by object occlusion. Yet, with my stereovision, I can see the pockets of space between the branches and can tell which branch is closer to me and which is further away. The small gray birds no longer disappear among a flat mess of branches. Instead, I see them as solid, round beings landing on solid, little twigs. Using the equation printed at the end of this post, I have calculated that, at a viewing distance of 16 feet, I can distinguish which branch is closer to me and which is further away for branches only 6 inches apart. If I had normal stereoacuity, this distance would shrink to 2 inches.
I can look up into the sky at the higher branches of oaks and maples and can judge which branches are closer to me. The whole tree canopy no longer looks flat but is round instead. Oaks and maples grow up to 80 feet (24 meters) tall. At this height, I should be able to judge which of two branches is closer to me for branches that are 4 feet apart. If you have normal stereoacuity, you could make this judgment for branches only 1 foot apart.
I was delighted to find a paper recently which explored people’s stereo perception for distant views in the dark. For this study, people were tested in a disused steam railway tunnel. The whole area was dark except for two LED lights, one placed 65.6 feet (20 meters) away and a second placed, in each trial, at one of 6 different locations 0.8 to 23 feet (0.24 to 7 meters) more distant. The distances created retinal disparities of 7.9 to 184.5 arc seconds, and, under these conditions, stereopsis provided the only depth cue. Nevertheless, subjects were able to rank order the relative depth of the 6 more distant lights. The same experiment was repeated with the closest light being 131 feet (40 meters) and the 6 more distant lights located 26 to 814 feet (7.8 to 248 meters) further away. Subjects could still rank order the depth of the six more distant lights. They did not judge the actual distance between the close and more distant light accurately, but they could make comparisons between the volume of space existing between the closer and more distant lights. This paper confirmed my own experiences. At night, I am aware now of the pockets of space between street lights in a long row or among a cluster of city lights, and all the lights together produce a wonderful texture to the landscape. Stereopsis is so sensitive that we do indeed use it when viewing large distances. It’s no wonder then that my view of the landscape transformed when I began to see in stereo depth.
Equation used to calculate retinal disparities of more distant object when fixating the closer object:
Disparity = I(ΔD)/(D2 + D(ΔD))
Disparity is measured here in radians. To convert to arc seconds, multiply the result by 206,265.
I = interocular distance (distance between 2 pupils; 64 mm on average, 58 mm for me)
D = fixation distance (distance, in this case, of closer object)
ΔD=distance between closer and further object
See: Howard I, Rogers B. Seeing in Depth, vol 2. Ontario, Canada: I. Porteous, 2002.