On-Line variational estimation of dynamical fluid flows with physics-based spatio-temporal regularization

Authors:
Paul Ruhnau;Annette Stahl;Christoph Schnörr
Affiliations:
Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany;Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany;Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer Science, University of Mannheim, Mannheim, Germany
Venue:
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Year:
2006

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Abstract

We present a variational approach to motion estimation of instationary fluid flows. 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 flow variations. (ii) Regularization along the time-axis is employed as well, but formulated in a receding horizon manner contrary to previous approaches to spatio-temporal regularization. This allows for a recursive on-line (non-batch) implementation of our 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 optical flow approaches based on higher-order div-curl regularization.