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A variational approach is presented to the estimation of turbulent fluid flow from particle image sequences in experimental fluid mechanics. The approach comprises two coupled optimizations for adapting size and shape of a Gaussian correlation window at each location and for estimating the flow, respectively. The method copes with a wide range of particle densities and image noise levels without any data-specific parameter tuning. Based on a careful implementation of a multiscale nonlinear optimization technique, we demonstrate robustness of the solution over typical experimental scenarios and highest estimation accuracy for an international benchmark data set (PIV Challenge).