One problem we do have to worry about, however, is that we are only able to measure the component of optical flow that is in the direction of the intensity gradient. We are unable to measure the component tangential to the intensity gradient. This problem is illustrated in figure 4, and further developed below.

Denote the intensity by *I*(*x*,*y*,*t*). This is a function of three variables
as we now have *spatiotemporal* variation in our signal. To see how
*I* changes in time, we differentiate with respect to *t*:

Now, we assume that the image intensity of each visible scene point is
unchanging over time (for example, shadows and illuminations are
*not* changing due to any motion), so we have

*I*_{x}*u* + *I*_{y}*v* + *I*_{t} = 0,

This last equation is called the *optical flow constraint equation*
since it expresses a constraint on the components *u* and *v* of the optical
flow.

The optical flow constraint equation can be rewritten as

Thus, the component of the image velocity in the direction of the image intensity gradient at the image of a scene point is We cannot, however, determine the component of the optical flow at right angles to this direction. This ambiguity is known as theThere are two main approaches to reconstructing three dimensional motion from motion in the image plane:

- Convert the motion problem to a stereo problem and find the
correspondence between a number of points in the image at time
*t*to the image at time . - Computer the optical flow and use its geometrical properties to deduce three dimensional information about the scene and the motion.