Variational estimation of experimental fluid flows with physics-based spatio-temporal regularization

Abstract

We present a variational approach to motion estimation of instationary experimental fluid flows from image sequences. Our approach extends prior work along two directions: (i) the full incompressible Navier–Stokes equation is employed in order to obtain a physically consistent regularization which does not suppress turbulent variations of flow estimates; (ii) regularization along the time axis is employed as well, but formulated in a receding horizon manner in contrast to previous approaches to spatio-temporal regularization. This allows for a recursive on-line (non-batch) implementation of our variational estimation framework. Ground-truth evaluations for simulated turbulent flows demonstrate that due to imposing both physical consistency and temporal coherency, the accuracy of flow estimation compares favourably even with advanced cross-correlation approaches and optical flow approaches based on higher order div–curl regularization.