Image Motion Estimation Algorithms Using Cumulants

A class of algorithms is presented that estimates the displacement vector from two successive image frames consisting of signal plus noise. In our model, the signals are assumed to be either non-Gaussian or (quasistationary) deterministic; and, via a consistency result for cumulant estimators, we unify the stochastic and deterministic signal viewpoints. The noise sources are assumed to be Gaussian (perhaps spatially and temporally correlated) and of unknown covariance. Viewing image motion estimation as a 2-D time delay estimation problem, the displacement vector of a moving object is estimated by solving linear equations involving third-order auto-cumulants and cross-cumulants. Additionally, a block-matching algorithm is developed that follows from a cumulant-error optimality criterion. Finally, the displacement vector for each pel is estimated using a recursive algorithm that minimizes a mean 2-D fourth-order cumulant criterion. Simulation results are presented and discussed.