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Apparatus and methods are presented for estimating the velocity field based on a multi-image frame sequence having an integer number M frames, M is greater than two, in which a set of M−1 displaced frame difference (DFD) equations is solved including a motion compensated prediction (MCP) equation, M−2 motion compensated interpolation (MCI) equations for solving a velocity field at a first time using a set of iteration equations to determine a velocity field, and 2×(M−2) conservative velocity constraint (CVC) equations for solving a velocity field at times t2, . . . , tM−1.