Global Optimization

As a possible solution to the corrspopndence problem, Julesz suggested ``global stereopsis'' as a process where all of the many possible matches between the two sets of dots on the right and left retinas are evaluated and then only one selected according to certain criterion. Specifically, if there are n random dots in the scene, then there are $n!=n(n-1)(n-2)\cdots 1$ different ways their images on the right and left retinas can be matched, corresponding to n! possible configurations of the n dots of different depths in the 3D space. The global stereopsis is assumed to select among all these possible configurations the one with most consistent disparities, or minimal number of different depths as the solution. While this could explain the random dots experiment, it does not help the first example of n=2 dots as either of the n!=2!=2 configurations represents the same number (two) of depths. This idea of global optimization is straight forward to implement mathematically but very costly computationally. Moreover, it may be hard to find a biologically plausible implementation for this method.