Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Image models for 2-D flow visualization and compression
CVGIP: Graphical Models and Image Processing
Recipes for adjoint code construction
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
A third order central WENO scheme for 2D conservation laws
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Dense Estimation of Fluid Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Extraction of Singular Points from Dense Motion Fields: An Analytic Approach
Journal of Mathematical Imaging and Vision
A Stochastic Filter for Fluid Motion Tracking
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Discrete Orthogonal Decomposition and Variational Fluid Flow Estimation
Journal of Mathematical Imaging and Vision
Variational dense motion estimation using the Helmholtz decomposition
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Discrete orthogonal decomposition and variational fluid flow estimation
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
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In this paper, we introduce a variational framework derived from data assimilation principles in order to realize a temporal Bayesian smoothing of fluid flow velocity fields. The velocity measurements are supplied by an optical flow estimator. These noisy measurement are smoothed according to the vorticity-velocity formulation of Navier-Stokes equation. Following optimal control recipes, the associated minimization is conducted through an iterative process involving a forward integration of our dynamical model followed by a backward integration of an adjoint evolution law. Both evolution laws are implemented with second order non-oscillatory scheme. The approach is here validated on a synthetic sequence of turbulent 2D flow provided by Direct Numerical Simulation (DNS) and on a real world meteorological satellite image sequence depicting the evolution of a cyclone.