Contributions to the Horn-Schunck optical flow equations-part II: Decoupling via linear transformations

Abstract

The Horn-Schunck optical flow equations, as a coupled system of partial differential equations, are proved to not be decouplable under linear transformations. This negative result, on one side, forbids any further attempt in this direction, on the other side, motivates our alternating algorithms which are in decoupled form at each single iteration, as will be carried out in the third part. Both the consequence and limitations are discussed. © Springer-Verlag 2013.