Integration of the optical flow constraint equation for planar objects

It is shown that when the optimal flow velocity components are in terms of eight flow parameters, they can be substituted into the velocity terms in the optical flow constraint equation to obtain the integration form of the optical flow constraint equation by integration by parts. Due to this transformation, the values of the brightness function are used directly, not the derivative value of the brightness function at each pixel, so that the accentuation of the noise effect is eliminated in the numerical implementation. The integration form of the optical flow constraint equation is in terms of eight flow parameters and therefore determining the optical flow requires the integrating numerically of the equation over eight subregions of different areas on the image plane to give eight linear equations to solve for the eight flow parameters.<>