Optical Stokes Flow Estimation: An Imaging‐Based Control Approach

We present an approach to particle image velocimetry based on optical flow estimation subject to physical constraints. Admissible flow fields are restricted to vector fields satifying the Stokes equation. The latter equation includes control variables that allow to control the optical flow so as to fit to the apparent velocities of particles in a given image pair. We show that when the real unknown flow observed through image measurements conforms to the physical assumption underlying the Stokes equation, the control variables allow for a physical interpretation in terms of pressure distribution and forces acting on the fluid. Although this physical interpretation is lost if the assumptions do not hold, our approach still allows for reliably estimating more general and highly non‐rigid flows from image pairs and is able to outperform cross‐correlation based techniques. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

[1]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[2]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[3]  Hans-Hellmut Nagel,et al.  An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Jean E. Roberts,et al.  Mixed and hybrid finite element methods , 1987 .

[5]  Max Gunzburger,et al.  Perspectives in flow control and optimization , 1987 .

[6]  L. Lourenço.  Particle Image Velocimetry , 1989 .

[7]  W. Hackbusch.  Iterative Solution of Large Sparse Systems of Equations , 1993 .

[8]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[9]  Shigeru Nishio,et al.  Image measurement of flow field using physics-based dynamic model , 2000 .

[10]  Shigeru Nishio,et al.  Standard images for particle-image velocimetry , 2000 .

[11]  P. Tabeling,et al.  Intermittency of a passive tracer in the inverse energy cascade. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Timo Kohlberger,et al.  Variational Dense Motion Estimation Using the Helmholtz Decomposition , 2003, Scale-Space.

[13]  Christoph Schnörr,et al.  Determining optical flow for irregular domains by minimizing quadratic functionals of a certain class , 1991, International Journal of Computer Vision.

[14]  H. Nobach,et al.  Full-field correlation-based image processing for PIV , 2005 .

[15]  H. Nobach,et al.  Improvements to PIV image analysis by recognizing the velocity gradients , 2005 .

[16]  Timo Kohlberger,et al.  Variational optical flow estimation for particle image velocimetry , 2005 .

[17]  Christoph Schnörr,et al.  A variational approach for particle tracking velocimetry , 2005 .

[18]  Bernhard Wieneke,et al.  Tomographic particle image velocimetry , 2006 .

[19]  Christoph Schnörr,et al.  On-Line Variational Estimation of Dynamical Fluid Flows with Physics-Based Spatio-temporal Regularization , 2006, DAGM-Symposium.

[20]  T. Corpetti,et al.  Fluid experimental flow estimation based on an optical-flow scheme , 2006 .

[21]  Jing Yuan,et al.  Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation , 2005, Journal of Mathematical Imaging and Vision.