Continuum theory provides two constraints on the velocity field generated by a deforming body.
Computation of the velocity field using these two constraints is an ill-posed problem which may be regularized using a smoothness term. We define a penalty function as a weighted sum of the two constraining terms and the smoothness term. Minimization of this function yields the desired velocity field. It is shown that, under certain conditions on the image, a unique minimizer of the penalty exists. Via variational calculus, it can be shown that the solution minimizing the penalty satisfies the Euler-Lagrange equations for this problem.