On-Line Variational Estimation of Dynamical Fluid Flows with Physics-Based Spatio-temporal Regularization
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.
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- 1.Braess, D.: Finite elements. Theory, fast solver & appl. in solid mechanics. Springer, Heidelberg (1997)Google Scholar
- 3.Carlier, J., Heitz, D.: 2D turbulence sequence provided by Cemagref within the European Project Fluid Image Analysis and DescriptionGoogle Scholar
- 8.Kawamura, T., Hiwada, M., Hibino, T., Mabuchi, I., Kumada, M.: Flow around a finite circular cylinder on a flat plate. Bulletin of the JSME 27(232), 2142–2151 (1984)Google Scholar
- 11.Puckett, E.G., Colella, P.: Finite Difference Methods for Computational Fluid Dynamics (Cambridge Texts in Applied Mathematics). Cambridge University Press, Cambridge (2005)Google Scholar
- 12.Raffel, M., Willert, C., Kompenhans, J.: Particle Image Velocimetry. Springer, Heidelberg (2001)Google Scholar
- 15.Ruhnau, P., Schnörr, C.: Optical stokes flow: An imaging based control approach. Exp. Fluids (submitted, 2006)Google Scholar
- 16.Stahl, A., Ruhnau, P., Schnörr, C.: A distributed-parameter approach to dynamic image motion. In: Int. Workshop on The Repres. and Use of Prior Knowl. in Vision. LNCS. Springer, Heidelberg (2006)Google Scholar
- 17.Suter, D.: Mixed finite elements and whitney forms in visual reconstruction. In: Geometric Methods in Computer Vision II, pp. 51–62 (1993)Google Scholar
- 18.Suter, D.: Mixed-finite element based motion est. Innov. Tech. Biol. Med. 15(3) (1994)Google Scholar