Variational Correlation Approach to Flow Measurement with Window Adaption

Cross-correlation constitutes the state-of-the-art method for measuring motion in PIV data. We present a novel variational approach to correlation-based fluid flow estimation, which determines the displacements via continuous optimisation. A Gaussian shaped window function is used, whose size, eccentricity and orientation can freely be chosen. We adapt the shape to the noise level and displacement gradients by minimising an error function that directly formulates the aim to minimise the motion estimation error. Displacement measurement and window adaption are performed simultaneously in a joint bi-level optimisation problem. The approach showed its ability to significantly improve accuracy also in the presence of high velocity gradients in synthetic data. Moreover, we tested our method with real PIV images. In comparison to a stateof-the-art cross-correlation implementation, the window adaption leads to smoother displacement fields in regions of homogenous motion, while gradients such as in vertexes are not affected in intensity and general shape.