Horn-Schunck Algorithm

The Horn-Schunck method is an algorithm for estimating optical flow across an entire image at once, rather than only at a sparse set of chosen points, by combining the same basic brightness-constancy assumption used in local methods with an added global smoothness assumption that neighboring flow vectors should vary only gradually. That combination is expressed as a single energy function balancing how well a candidate flow field matches the observed brightness changes against how smoothly it varies from point to point, and the algorithm solves for the flow field that minimizes this energy across the whole image simultaneously, an approach that fills in plausible motion even inside broad, texture free regions where a purely local method has no direct information to work with. Berthold Horn and Brian Schunck published the method in 1981, in the same year as the competing local, sparse approach of Lucas and Kanade; the tradeoff for Horn-Schunck's dense coverage is a greater sensitivity to noise than local methods typically show.