Variational dense motion estimation using a div-curl high-order regularization

In this paper, we present a variational approach to dense motion estimation of highly nonrigid structures in image sequences. Our representation of the motion vector field is based on the extended Helmholtz decomposition into its principal constituents: The laminar flow and two potential functions related to the solenoidal and irrotational flow, respectively. The potential functions, which are of primary interest for flow pattern analysis in numerous application fields like remote sensing or fluid mechanics, are directly estimated from image sequences with a variational approach. We use regularizers with derivatives up to third order to obtain unbiased high-quality solutions. Computationally, the approach is made tractable by means of auxiliary variables. The performance of the approach is demonstrated with ground-truth experiments and real-world data.