A closed-form solution for optical flow by imposing temporal constraints

We present a well-constrained formulation for estimation of optical flow in a video sequence, which yields a closed-form solution. Unlike other existing closed-form approaches, our solution does not require second order spatial derivatives. It relies only on first order and cross-space-time derivatives which can be computed more reliably. Instead of the commonly used spatial smoothness constraint, we propose a temporal smoothness constraint which has a clear physical interpretation. Our formulation also allows for accurate analysis of sources of error and ill-conditioning, leading to a more tractable implementation and mathematically justifiable thresholding values.