1. A method for determining displacement by motion for a sequence of images, the method comprising: receiving an input image sequence comprising a plurality of image frames individually including multidimensional image data corresponding to a plurality of pixel locations at different times; providing a fully constrained nonlinear equation set including: a plurality of displacement vector invariant equations, a forward displaced frame difference equation using as input data from only two of the image frames at one time t.sub. 1 and an other time t.sub. 2 , respectively, and a backward displaced frame difference equation using as input data from only the same two image frames; using at least one processor, solving the equation set using an iteration equation and the image data of only the two image frames at times t.sub. 1 and t.sub. 2 to determine a displacement field describing the displacement vectors at pixel locations at the one time by solving displacement field values at the other time from the plurality of displacement vector invariant equation; and determining, using the at least one processor, displacement by motion for the sequence of images based on the solved equation set.