6.1.2 Stereo depth cues

Figure 6.8: The horopter is the loci of points over which the eyes can converge and focus on a single depth. The T curve shows the theoretical horopter based on simple geometry. The E curve shows the empirical horopter, which is much larger and correspond to the region over which a single focused image is perceived. (Figure by Rainer Zenz.)
\begin{figure}\centerline{\psfig{file=figs/horopter.ps,width=4.0truein}}\end{figure}

As you may expect, focusing both eyes on the same object enhances depth perception. Humans perceive a single focused image over a surface in space called the horopter; see Figure 6.8. Recall the vergence motions from Section 5.3. Similar to the accommodation cue case, motor control of the eye muscles for vergence motions provides information to the brain about the amount of convergence, thereby providing a direct estimate of distance. Each eye provides a different viewpoint, which results in different images on the retina. This phenomenon is called binocular disparity. Recall from (3.50) in Section 3.5 that the viewpoint is shifted to the right or left to provide a lateral offset for each of the eyes. The transform essentially shifts the virtual world to either side. The same shift would happen for a stereo rig of side-by-side cameras in the real world. However, the binocular disparity for humans is different because the eyes can rotate to converge, in addition to having a lateral offset. Thus, when fixating on an object, the retinal images between the left and right eyes may vary only slightly, but this nevertheless provides a powerful cue used by the brain.

Furthermore, when converging on an object at one depth, we perceive double images of objects at other depths (although we usually pay no attention to it). This double-image effect is called diplopia. You can perceive it by placing your finger about $ 20$cm in front of your face and converging on it. While fixating on your finger, you should perceive double images of other objects around the periphery. You can also stare into the distance while keeping your finger in the same place. You should see a double image of your finger. If you additionally roll your head back and forth, it should appear as if the left and right versions of your finger are moving up and down with respect to each other. These correspond to dramatic differences in the retinal image, but we are usually not aware of them because we perceive both retinal images as a single image.

Steven M LaValle 2016-12-31