Optical flow as a smoothness problem
Berthold Horn and Brian Schunck showed that velocity cannot be computed locally: at each point there is one measurement and two unknowns. They added a second condition — that the velocity field vary smoothly almost everywhere — and reduced motion estimation to minimising a single functional over the whole image. The paper appeared in August 1981.
Why it matters
Motion in video stopped being a matching of patches between frames and became a problem with one solution over the whole field at once. Together with the local method of Lucas and Kanade from the same year, these are the two halves of how motion is still computed: densely under a smoothness constraint, or sparsely in windows.
The figures the paper actually gives are errors on synthetic sequences. With a single time step and many iterations, few changes occur after 32 iterations and the velocity vectors carry errors of about 10 percent. With one iteration per time step convergence is faster: after 16 steps the error is about 7 percent, and the average over the whole image is within 1 percent of the correct value. The record does not claim "convergence in 100 iterations" and does not claim a "mean angular error under 1.5 degrees". Neither number is in the paper; 1.5 degrees is a figure from later comparative work on evaluating optical flow, not a result of this one. The paper was received in March 1980. The MIT AI Laboratory memo exists separately and is not used here: the server holding it could not be read.