Abstract
We introduce a novel motion estimation approach for Echo PIV for the laminar and steady flow model. We mathematically formalize the motion estimation problem as a parametrization of a dictionary of particle trajectories by the physical flow parameter. We iteratively refine this unknown parameter by subsequent sparse approximations. We show smoothness of the adaptive flow dictionary that is a key for a provably convergent numerical scheme. We validate our approach on real data and show accurate velocity estimation when compared to the state-of-the-art cross-correlation method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
See, e.g. http://www.lavision.de/en/products/davis.php.
References
Adrian, R.J., Westerweel, J.: Particle Image Velocimetry. Cambridge University Press, Cambridge (2011)
Adrian, R.J.: Twenty years of particle image velocimetry. Exp. Fluids 39(2), 159–169 (2005)
Bodnariuc, E., Gurung, A., Petra, S., Schnörr, C.: Adaptive dictionary-based spatio-temporal flow estimation for echo PIV. In: Tai, X.-C., Bae, E., Chan, T.F., Lysaker, M. (eds.) EMMCVPR 2015. LNCS, vol. 8932, pp. 378–391. Springer, Heidelberg (2015)
Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, Heidelberg (2000)
Foucart, S., Rauhut, H.: A Mathematical Introduction to Compressive Sensing. Birkhäuser, Basel (2013)
Grant, M., Stephen Boyd, S.: CVX: Matlab Software for Disciplined Convex Programming, version 2.1, March 2014. http://cvxr.com/cvx
Heywood, J., Rannacher, R., Turek, S.: Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Meth. Fluids 22, 325–352 (1996)
Kim, H., Hertzberg, J., Shandas, R.: Development and validation of echo PIV. Exp. Fluids 36(3), 455–462 (2004)
Mifflin, R., Strodiot, J.J.: A rapidly convergent five-point algorithm for univariate minimization. Math. Program. 62, 299–319 (1993)
Minoux, M.: Mathematical Programming, Theory and Algorithms. Wiley, New York (1989)
Poelma, C., van der Mijle, R.M.E., Mari, J.M., Tang, M.X., Weinberg, P.D., Westerweel, J.: Ultrasound imaging velocimetry: toward reliable wall shear stress measurements. Eur. J. Mech. - B/Fluids 35, 70–75 (2012)
Raffel, M., Willert, C., Wereley, S., Kompenhans, J.: Particle Image Velocimery - A Practical Guide. Springer, Heidelberg (2007)
Rodriguez, S., Deschamps, M., Castaings, M., Ducasse, E.: Guided wave topological imaging of isotropic plates. Ultrasonics 54(7), 1880–1890 (2014)
Rodriguez, S., Jacob, X., Gibiat, V.: Plane wave echo particle image velocimetry. In: Proceedings of Meetings of Acoustics, POMA 19 (2013)
Schiffner, M.F., Schmitz, G.: Fast image acquisition in pulse-echo ultrasound imaging using compressed sensing. In: 2012 IEEE International Ultrasonics Symposium (IUS), pp. 1944–1947. IEEE (2012)
Womersley, J.: Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553–563 (1955)
Acknowledgements
EB, SP and CS thank the German Research Foundation (DFG) for its support via grant GRK 1653.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Bodnariuc, E., Petra, S., Poelma, C., Schnörr, C. (2016). Parametric Dictionary-Based Velocimetry for Echo PIV. In: Rosenhahn, B., Andres, B. (eds) Pattern Recognition. GCPR 2016. Lecture Notes in Computer Science(), vol 9796. Springer, Cham. https://doi.org/10.1007/978-3-319-45886-1_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-45886-1_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45885-4
Online ISBN: 978-3-319-45886-1
eBook Packages: Computer ScienceComputer Science (R0)