Wavelets to reconstruct turbulence multifractals from experimental image sequences

International audienceIn the context of turbulent fluid motion measurement from image sequences, we propose in this paper to reverse the traditional point of view of wavelets perceived as an analyzing tool: wavelets and their properties are now considered as prior regularization models for the motion estimation problem, in order to exhibit some well-known turbulence regularities and multifractal behaviors on the reconstructed motion field

Effective Wavelet-Based Regularization of Divergence-free Fractional Brownian Motion

This paper presents a method for regularization of inverse problems. The vectorial bi-dimensional unknown is assumed to be the realization of an isotropic divergence-free fractional Brownian Motion (fBm). The method is based on fractional Laplacian and divergence-free wavelet bases. The main advantage of these bases is to enable an easy formalization in a Bayesian framework of fBm priors, by simply sampling wavelet coe cients according to Gaussian white noise. Fractional Laplacians and the divergence-free projector can naturally be implemented in the Fourier domain. An interesting alternative is to remain in the spatial domain. This is achieved by the analytical computation of the connection coefficients of divergence-free fractional Laplacian wavelets, which enables to easily rotate this simple prior in any sufficiently "regular" wavelet basis. Taking advantage of the tensorial structure of a separable fractional wavelet basis approximation, isotropic regularization is then computed in the spatial domain by low-dimensional matrix products. The method is successfully applied to fractal image restoration and turbulent optic-flow estimation

Wavelet-based fluid motion estimation

International audienceBased on a wavelet expansion of the velocity field, we present a novel optical flow algorithm dedicated to the estimation of continuous motion fields such as fluid flows. This scale-space representation, associated to a simple gradient-based optimization algorithm, naturally sets up a well-defined multi-resolution analysis framework for the optical flow estimation problem, thus avoiding the common drawbacks of standard multi-resolution schemes. Moreover, wavelet properties enable the design of simple yet efficient high-order regularizers or polynomial approximations associated to a low computational complexity. Accuracy of proposed methods is assessed on challenging sequences of turbulent fluids flows

Two-Component Horizontal Motion Vectors from Scanning Eye-Safe Aerosol Lidar

This poster was presented at the 19th Symposium on Boundary Layers and Turbulence, August 2010, Keystone, CO. Session P1.4.Derive the two-component vector motion field from pairs of aerosol backscatter lidar images and compare results with observations from a co-located sonic anemometer. Two methods will be tested: correlations and dense estimation

Stochastic parameterization of geophysical flows through modelling under location uncertainty

International audienceIn this talk we will describe a framework for the systematic derivation of stochastic representations of geophysical flows. This paradigm, quoted as modelling under location uncertainty, relies on a Lagrangian decomposition of the flow velocity in terms of a large-scale, smooth in time, component and a random field uncorrelated in time, which represents the small-scale velocity component. This possibly anisotropic non-homogeneous random field corresponds to the aliasing of the unresolved velocity component. Such a Lagrangian decomposition leads to a stochastic representation of the Reynolds transport theorem (RTT) and of the material derivative [1,2]. Those expressions involve a diffusive subgrid term balanced by a multiplicative noise and a modified advection drift induced by the small-scale inhomogeneity. The stochastic material derivative together with the RTT enables us to express random versions any geophysical flow dynamics within the usual physical scaling approximation.Through the presentation we will provide several stochastic representations of classical systems. Quasi-Geostrophic models (QG), and Surface Quasi Geostrophic (SQG) models will be in particular explored. We will show how different SQG approximations can be derived from different levels of noise; we will demonstrate that such systems lead to improved large-scale representations and meaningful ensemble of realizations. Compared to traditional ensemble built from a perturbation of the initial condition, the ensemble generated by the proposed stochastic representation exhibits a larger spread; this allows estimating accurately the model errors in terms of location and magnitude [2]; it leads also to efficient tracking of likely scenarios [3].The nice properties of this derivation should be particularly useful for ensemble-based data assimilation techniques or for ensemble forecasting analysis. [1] E. Mémin, Fluid flow dynamics under location uncertainty, Geophysical & Astrophysical Fluid Dynamics, 108, 2, 119–146, (2014).[2] V. Resseguier, E. Mémin, B. Chapron (2016). Geophysical flows under location uncertainty, paper submitted to Geophysical & Astrophysical Fluid Dynamics.[3] V. Resseguier, E. Mémin, B. Chapron (2016). Chaotic transitions and location uncertainty in geophysical flows, paper submitted to Chaos

Dense Motion Estimation from Eye-Safe Aerosol Lidar Data

International audienceResults of the application of optical flow methods to eye-safe aerosol lidar images leading to dense velocity field estimations are presented. A fluid motion dedicated formulation is employed, taking into account the deforming shapes and changing brightness of flow visualization. The optical flow technique has the advantage of providing a vector at every pixel in the image, hence enabling access to improved multiscale properties. In order to assess the performances of the method, we compare vectors with punctual sonic anemometer measurements. Power spectra of the velocity data are also calculated to explore the spectral behavior of the technique

Modélisation physique des erreurs de modèles pour les écoulements fluides géophysiques

International audienc

Divergence-free Wavelets and High Order Regularization

International audienceExpanding on a wavelet basis the solution of an inverse problem provides several advantages. Wavelet bases yield a natural and efficient multiresolution analysis. The continuous representation of the solution with wavelets enables analytical calculation of regularization integrals over the spatial domain. By choosing differentiable wavelets, high-order derivative regularizers can be designed, either taking advantage of the wavelet differentiation properties or via the basis's mass and stiffness matrices. Moreover, differential constraints on vector solutions, such as the divergence-free constraint in physics, can be handled with biorthogonal wavelet bases. This paper illustrates these advantages in the particular case of fluid flows motion estimation. Numerical results on synthetic and real images of incompressible turbulence show that divergence-free wavelets and high-order regularizers are particularly relevant in this context

Ondelettes et Estimation de Mouvements de Fluide

This work falls within the general problematic of designing measurement tools adapted to the specificities of fluid flows. The development of digital imaging, combined with visualization techniques commonly employed in experimental fluid dynamics, enables to extract the apparent flow motion from image sequences, thanks to computer vision methods. The objective is to propose a novel "optical flow" algorithm dedicated to the multiscale motion estimation of fluid flows, using a wavelet representation of the unknown motion field. This wavelet formulation introduces a multiscale framework, conveniently adapted both to the optical flow estimation and to the representation of turbulent motion fields. It enables as well to design divergence-free bases, thereby respecting a constraint given by fluid dynamics. Several regularization schemes are proposed; the simplest consists in truncating the basis at fine scales, while the most complex builds high-order schemes from the connection coefficients of the wavelet basis. Proposed methods are evaluated on synthetic images in the first place, then on actual experimental images of characteristic fluid flows. Results are compared to those given by the usual "cross-correlations", highlighting the advantages and limits of the wavelet-based estimator.Ces travaux se situent dans la problématique d'élaboration d'outils de mesure adaptés aux caractéristiques des écoulements fluides. Le développement de l'imagerie digitale, associée à l'utilisation de techniques de visualisation d'écoulements en mécanique des fluides, permet d'envisager l'extraction, à l'aide de méthodes de vision par ordinateur, du mouvement d'écoulements perçu dans des séquences d'images. L'objectif consiste ici à proposer une nouvelle approche de type " flux optique " pour l'estimation multiéchelle de mouvements de fluides, en s'appuyant sur une représentation en ondelettes du mouvement recherché. Cette formulation en ondelettes introduit un formalisme multiéchelle, intéressant tant du point de vue de l'estimation du flux optique que de la représentation de champs de vitesse turbulents. Elle permet en outre la construction de bases à divergence nulle, respectant ainsi une contrainte issue de la physique des fluides. Plusieurs types de régularisation sont présentés; la plus simple procède par troncature de la base aux petites échelles, la plus complexe utilise les coefficients de connexion de la base d'ondelette pour construire des schémas d'ordre élevé. Les approches proposées sont évaluées sur des images synthétiques dans un premier temps, puis sur des images expérimentales d'écoulements caractéristiques. Les résultats obtenus sont comparés à ceux fournis par la méthode usuelle des " corrélations croisées ", mettant en avant les intérêts et les limites de l'estimateur

Ondelettes et Estimation de Mouvements de Fluide

This work falls within the general problematic of designing measurement tools adapted to the specificities of fluid flows. The development of digital imaging, combined with visualization techniques commonly employed in experimental fluid dynamics, enables to extract the apparent flow motion from image sequences, thanks to computer vision methods. The objective is to propose a novel "optical flow" algorithm dedicated to the multiscale motion estimation of fluid flows, using a wavelet representation of the unknown motion field. This wavelet formulation introduces a multiscale framework, conveniently adapted both to the optical flow estimation and to the representation of turbulent motion fields. It enables as well to design divergence-free bases, thereby respecting a constraint given by fluid dynamics. Several regularization schemes are proposed; the simplest consists in truncating the basis at fine scales, while the most complex builds high-order schemes from the connection coefficients of the wavelet basis. Proposed methods are evaluated on synthetic images in the first place, then on actual experimental images of characteristic fluid flows. Results are compared to those given by the usual "cross-correlations", highlighting the advantages and limits of the wavelet-based estimator.Ces travaux se situent dans la problématique d'élaboration d'outils de mesure adaptés aux caractéristiques des écoulements fluides. Le développement de l'imagerie digitale, associée à l'utilisation de techniques de visualisation d'écoulements en mécanique des fluides, permet d'envisager l'extraction, à l'aide de méthodes de vision par ordinateur, du mouvement d'écoulements perçu dans des séquences d'images. L'objectif consiste ici à proposer une nouvelle approche de type " flux optique " pour l'estimation multiéchelle de mouvements de fluides, en s'appuyant sur une représentation en ondelettes du mouvement recherché. Cette formulation en ondelettes introduit un formalisme multiéchelle, intéressant tant du point de vue de l'estimation du flux optique que de la représentation de champs de vitesse turbulents. Elle permet en outre la construction de bases à divergence nulle, respectant ainsi une contrainte issue de la physique des fluides. Plusieurs types de régularisation sont présentés; la plus simple procède par troncature de la base aux petites échelles, la plus complexe utilise les coefficients de connexion de la base d'ondelette pour construire des schémas d'ordre élevé. Les approches proposées sont évaluées sur des images synthétiques dans un premier temps, puis sur des images expérimentales d'écoulements caractéristiques. Les résultats obtenus sont comparés à ceux fournis par la méthode usuelle des " corrélations croisées ", mettant en avant les intérêts et les limites de l'estimateur