Here, (i′, j′) denotes the positions of the pixels in the mask Ω. For example, when M=2, the mask has a shape as shown in
In order to estimate the optical flow (vx, vy) of each pixel (i, j) in the block, a solution which minimizes the objective function Φ(vx, vy) is calculated by an analytical method. ?Φ(vx, vy)/?vx=0 and ?Φ(vx, vy)/?vy=0 may be derived by partial derivatives of the objective function Φ(vx, vy) with respect to vx and vy, and Equation 4 may be obtained by solving the two equations as simultaneous equations.