Panum's
fusional area

Consider two visual primitives positioned one in each of a left and right image. Let their positions correspond. When viewed monocularly no correspondence is initiated and the primitives remain distinct in the viewer's "sight". However when stereoscopically fused a correspondence is set up and the two primitives merge to form one. By holding the position of one of the primitives constant in one image while horizontally shifting the other primitive, stereoscopic fusion can be studied. There is a certain disparity value beyond which the two primitives will not fuse (referred to as diplopia) and the primitives are clearly seen in different positions. The range over which fusion has occurred is known as Panum's Fusional Area.

This classical notion was considered to place an absolute limit on the amount of disparity between primitives for fusion to occur regardless of the presence of neighbouring primitives. Recently studies have shown a need for the reformulation of the Panum idea. It now seems that neighbouring primitives do effect the fusion chances and so the idea of an absolute limit seems unlikely. With a great many of the accepted research works accepting the Panum notion as fundamental, there now seems a need to re-evaluate their results.

Therefore, the fusional limit is not absolute but corresponds to what has been called a disparity gradient. The disparity gradient uses primitive size and proximity in deciding whether fusion is possible or not. Experiments on human subjects showed that this limit was approximately 1.

To understand the disparity gradient idea a little better refer to the elementary two-dot stereogram in Figure 6, below.

Figure 6
Figure 6: A simple, two-dot stereogram

In the diagram both left and right images are shown together with the result of their stereoscopic fusion referred to as the cyclopean image. The disparity of the top pair of dots (when superimposed on the the same image plane (above) is d2. for the bottom pair it is d1. Hence The difference in disparity between the top and bottom dots is

From a right angled triangle,

A closer look at this formula reveals the reasoning behind the disparity gradient idea. Notice that increasing the disparity, while holding the separation constant, produces a tendency toward diplopia (taking the limit at 1). Again with constant disparity and decreasing cyclopean separation diplopia occurs. Fusion then is not guaranteed purely because the objects are close in proximity. A number of researchers have incorporated the disparity gradient into their algorithms in order to solve the stereo correspondence problem (e.g the PMF algorithm [Pollard et al, 1985]).


[ Random dot stereograms | A stereo vision system ]

Comments to: Sarah Price at ICBL.