Let’s look at an example of this.
Suppose we have an image in which H(x,y) = y. That
is, the image will look like:
11111111111111
22222222222222
33333333333333
And suppose there is optical flow of (1,1). The new image will look like:
-----------------------
-1111111111111
-2222222222222
I(3,3) = 2. H(3,3) =
3. So It(3,3) = -1. GRAD I(3,3) = (0,1). So
our constraint equation
will be: 0 = -1 + <(0,1), (u,v)>, which is 1 = v. We recover the v component of the optical flow, but not
the u component. This is the aperture problem.