Fusion & Float
Is the presence of disparities in fused binocular images sufficient for stereopsis?
An email conversation with Susan Barry
Many of you who are interested in 3D perception have heard of Susan Barry, and may have read the remarkable account of her recovery of binocular vision at age 48, which was published in a highly acclaimed popular science book titled Fixing My Gaze. I recently wrote to Dr. Barry to share some of the work being done in our lab on 3D perception. Dr. Barry, in response, kindly shared some additional details of her experience with vision therapy that are relevant to a new theoretical proposal regarding the function and cause of stereopsis.
Stereopsis is the special vivid effect of depth and 3D perception that typically occurs with 2-eye viewing, for example, when you watch a 3D movie. In the optometric literature, the phenomenology of stereopsis is also called ‘float’ or ‘projection’ and refers to the fact that when one obtains the 3D effect, objects seem to float or stick out in space in front of you, with a sense of real separation between the object and background. See, for example, Scheiman & Wick (2013).
Briefly, our paper proposes that stereopsis, the vivid perception of depth and ‘float’, is not simply the outcome of the successful fusion of the images from two eyes, but instead, is dependent on how well disparity information from fused binocular images can be scaled by distance information to derive what is called ‘absolute depth’: the estimate your brain has of the actual distances between the things you are looking at. One prediction of this proposal is that the impression of stereopsis might not occur even if binocular disparities are present in fused binocular images, if these disparities cannot be properly scaled by distance information (for example, from the vergence posture of the eyes).
Dr. Barry’s account, as well as documentation on best practice in therapy in behavioural/developmental optometry which she shared with me, suggest some interesting anecdotal support for this prediction. As Dr. Barry points out: “I couldn’t appreciate stereopsis until I found a way to correlate vergence, disparity, and distance”. Below is a quote from Dr. Barry’s emails:
“… learning to converge, fuse images, and gain access to retinal disparity information wasn’t enough to see with stereopsis. I needed one more step to see in depth. Let me explain this by describing my experiences with the quoits vectogram. Quoits refers to a rope ring. This vectogram consists of two polarized sheets, each with an image of the quoits, which are then viewed while wearing polarized glasses. Due to the polarization, each eye sees only one of the quoits images which can then be fused. The quoits vectogram can be seen in the attached figure which shows the two images partially overlapping with one another.
The Quoits Vectogram (Photo by James Gehrt)
If I slid the sheets apart in the “base-out” direction, the image for the right eye went to the left and the image for the left eye went to the right. As a result, I had to converge my eyes to maintain fusion. If I slid the sheets in the opposite “base-in” direction, the right image moved rightward and the left image moved leftward, requiring me to diverge to maintain fusion. Finally, I could make sure that the virtual image resulted from fusion of the two eyes’ images by looking at the suppression check. This consisted of the letters, A and B, in the boxes on the left-hand side of the sheets. Each letter was only seen by one eye so, after fusion, I checked to make sure I could simultaneously see both letters appearing in their boxes, one right on top of the other.
Using the quoits vectogram, I started to build up a pretty good fusion range. I could slide the sheets apart by many prism diopters and still maintain fusion. However, I wasn’t seeing much depth. Initially, the fused image did not appear to float off the polarized sheets. So my optometrist gave me another procedure. I hung a tennis ball from the ceiling so that it could swing toward and away from me. Then I stood in front of the ball while looking through the quoits vectogram. If I slid the vectogram sheets in the base-in direction, I had to diverge my eyes to maintain fusion and the fused quoits image should have appeared to float behind the polarized sheet, further away from me. I did not see this until I put the ball in motion. As the ball swung forward but remained behind the vectogram sheets, I got the uncanny impression that the ball went right through the fused image of the quoits! The motion of the ball gave me some sense of distance and depth, and this was what I needed to get that sense of float, the sense that the fused quoits image was floating behind the polarized sheets.
Still, my sense of float was shallow so I came up with a second procedure. I hung a string across my dining room so that the length of the string was parallel to the ceiling and floor. (I did this by attaching one end of the string to the window frame and suspending the center and free end of the string from the ceiling with long threads.) Now, when I walked into my dining room, I encountered the free end of the string at eye level, with the rest of the string extending the length of the room. As I looked along the length of the string, I saw two images of the string which converged at the point where my two eyes were aiming and then separated into two string images, diverging from there. This is similar to the exercise with the Brock string that I describe in my book. The image of the string looked like an X where the center of the X marked the crossing point of the line of sight of the two eyes, that is, the distance in space where my two eyes were aiming. (See attached figure, where, on the Brock string in the figure, a bead is shown at the convergence point.)
Now I took my quoits vectogram and stood before the free end of the string. I slid the sheets in the base-in direction so that I had to diverge my eyes to maintain fusion. At the same time I could see the string through the center of the fused quoits. The crossing point of the string told me where my two eyes, which had fused the quoits, were aiming, and this should be the distance at which I should see the fused quoits image float. Initially, I saw the quoits image float only a little ways off the sheet. So I took a thin pole and probed the region in front of me, toward where the string images crossed. With practice over several weeks, I got the quoits image to float at the crossing point of the string images. I was learning to use vergence cues or the crossing point of the line of sight of the two eyes as a cue to absolute distance. And with this information, I gained a dramatic sense of the quoits floating in mid-air. As I mastered this exercise, I also noticed a much greater sense of stereopsis all around me- of solid, round images, each in their own space, with palpable negative space between them. I set up the string/quoits exercise in my dining room because several behavioral/developmental optometrists had told me that I would not see with stereopsis until I got “projection,” that is, the sense that the fused image was floating in space at a distance that correlated with vergence.”
“An additional technique, suggested by my optometrist, that I used to correlate disparity with distance was to take a pointer, pen, or pencil, and hold it vertically in front of me. I would then fuse the quoits vectogram and then move the pointer in front or behind the polarized sheets. If the pointer was located in space in front of or behind the crossing point of my eyes, then it would be seen as double. I could then probe the distance at which the pointer became single. This was distance in space where the fused image should float.”
(Susan Barry, via email, 26th and 28th May 2014)