Intermediate Flow Field Filtering in Energy Based Optic Flow Computations

The Euler-Lagrange framework and splitting based methods are among the most popular approaches to solve variational optic flow problems. These methods are commonly embedded in a coarse-to-fine strategy to be able to handle large displacements. While the use of a denoising filter inbetween the warping is an important tool for splitting based approaches, such a practice is rather uncommon for the Euler-Lagrange method. The question arises, why there is this surprising difference in optic flow methods. In previous works it has also been stated that the use of such a filtering leads to a modification of the underlying energy functional, thus, there seems to be a difference in the energies that are actually minimised depending on the chosen algorithmic approach. The goal of this paper is to address these fundamental issues. By a detailed numerical study we show in which way a filtering affects the evolution of the energy for the above mentioned frameworks. Doing so, we not only give many new insights on the use of filtering steps, we also bridge an important methodical gap between the two commonly used implementation approaches.