Motion estimation revisited: an estimation-theoretic approach

The present paper analyzes some previously unexplored aspects of motion estimation that are fundamental both for discrete block matching as well as for differential `optical flow´ approaches à la Lucas-Kanade. It aims at providing a complete estimation-theoretic approach that makes the assumptions about noisy observations of samples from a continuous signal of a certain class explicit. It turns out that motion estimation is a combination of simultaneously estimating the true underlying continuous signal and optimizing the displacement between two hypothetical copies of this unknown signal. Practical schemes such as the current variants of Lucas-Kanade are just approximations to the fundamental estimation problem identified in the present paper. Derivatives appear as derivatives to the continuous signal representation kernels, not as ad hoc discrete derivative masks. The formulation via an explicit signal space defined by kernels is a precondition for analyzing e.g. the convergence range of iterative displacement estimation procedures, and for systematically chosing preconditioning filters. The paper sets the stage for further in-depth analysis of some fundamental issues that have so far been overlooked or ignored in motion analysis.