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 ?(vx, vy) is calculated by an analytical method. ??(vx, vy)/?vx=0 and ??(vx, vy)/?vy=0 may be derived by partial derivatives of the objective function ?(vx, vy) with respect to vx and vy, and Equation 4 may be obtained by solving the two equations as simultaneous equations. s1vx(i,j)+s2vy(i,j)=?s3 s4vx(i,j)+s5vy(i,j)=?s6??[Equation 4]
In Equation 4, s1, s2, s3, s4, s5, and s6 are given as shown in Equation 5.