In the one-dimensional case, Equation (15) can be solved directly, without any further constraints, and we obtain:
for the velocity estimate. The solution is, of course, undefined in regions of
constant brightness. To overcome this problem it might be advantageous to
calculate the flow within a small window and to consider a weighted average of
the flow estimates, excluding locations where 
. Similar to the
two-dimensional case, this method is less accurate for larger displacements
and yields best results when applied iteratively as described in
Section 3.3.1.
In the sense that 1D optical flow makes use of partial derivatives in
the x and t directions, the above method is closely related to
the concept of gradient-based 2D orientation estimation. In particular,
the ratio 
is directly analogous to the quantity the arctangent
of which provides us with 
in Kass and Witkin's method.
Although orientation estimates normally do not have a direction associated
with them, in the specific case that one dimension is time, an arrowhead
pointing in the direction of t>0 can be assumed.