Motion estimator apparatus and methods are presented in which a fully constrained nonlinear system of equations combining forward and backward displaced frame difference equations with a plurality of displacement vector invariant equations is solved using the input data from two image frames without approximation and without any additional constraints or assumptions to obtain an estimated displacement field. Also presented is an adaptive framework for solving a system of motion estimation equations with an integer valued block size defining a number of node points within an image, the number of node points being less than or equal to a number of pixels within the image, and a cost function based on a nonlinear least-squares principle. A system of iteration equations for the motion field on node points is solved using an iterative technique, and a degree of over-constraint can be progressively relaxed by selectively reducing the block size during the iteration.