Self-similar regularization of optic-flow for turbulent motion estimation

International audienceBased on self-similar models of turbulence, we propose in this paper a multi-scale regularizer in order to provide a closure to the optic-flow estimation problem. Regularization is achieved by constraining motion increments to behave as a self-similar process. The associate constrained minimization problem results in a collection of first-order optic-flow regularizers acting at the different scales. The problem is optimally solved by taking advantage of lagrangian duality. Furthermore, an advantage of using a dual formulation, is that we also infer the regularization parameters. Since, the self-similar model parameters observed in real cases can deviate from theory, we propose to add in the algorithm a bayesian learning stage. The performance of the resulting optic-flow estimator is evaluated on a particle image sequence of a simulated turbulent flow. The self-similar regularizer is also assessed on a meteorological image sequence

Power laws and inverse motion modeling: application to turbulence measurements from satellite images

International audienceIn the context of tackling the ill-posed inverse problem of motion estimation from image sequences, we propose to introduce prior knowledge on flow regularity given by turbulence statistical models. Prior regularity is formalized using turbulence power laws describing statistically self-similar structure of motion increments across scales. The motion estimation method minimizes the error of an image observation model while constraining second order structure function to behave as a power law within a prescribed range. Thanks to a Bayesian modeling framework, the motion estimation method is able to jointly infer the most likely power law directly from image data. The method is assessed on velocity fields of 2D or quasi-2D flows. Estimation accuracy is first evaluated on a synthetic image sequence of homogeneous and isotropic 2D turbulence. Results obtained with the approach based on physics of fluids outperforms state-of-the-art. Then, the method analyzes atmospheric turbulence using a real meteorological image sequence. Selecting the most likely power law model enables the recovery of physical quantities which are of major interest for turbulence atmospheric characterization. In particular, from meteorological images we are able to estimate energy and enstrophy fluxes of turbulent cascades, which are in agreement with previous in situ measurements

Bayesian selection of scaling laws for motion modeling in images

[Departement_IRSTEA]Ecotechnologies [TR1_IRSTEA]SPEEInternational audienceBased on scaling laws describing the statistical structure of turbulent motion across scales, we propose a multiscale and non-parametric regularizer for optic-flow estimation. Regularization is achieved by constraining motion increments to behave through scales as the most likely self-similar process given some image data. In a first level of inference, the hard constrained minimization problem is optimally solved by taking advantage of lagrangian duality. It results in a collection of first-order regularizers acting at different scales. This estimation is non-parametric since the optimal regularization parameters at the different scales are obtained by solving the dual problem. In a second level of inference, the most likely self-similar model given the data is optimally selected by maximization of Bayesian evidence. The motion estimator accuracy is first evaluated on a synthetic image sequence of simulated bi-dimensional turbulence and then on a real meteorological image sequence. Results obtained with the proposed physical based approach exceeds the best state of the art results. Furthermore, selecting from images the most evident multiscale motion model enables the recovery of physical quantities, which are of major interest for turbulence characterization

Turbulence power laws and inverse motion modeling in images

Based on scaling laws describing the statistical structure of turbulent motion across scales, we propose a multiscale and non-parametric regularizer for the estimation of velocity fields of bidimensional or quasi bidimensional flows from image sequences. Spatial regularization principle used in order to close the ill-posed nature of motion estimation is achieved by constraining motion increments to behave through scales as the most likely self-similar process given some image data. In a first level of inference, the estimation formulated as a hard constrained minimization problem is optimally solved by taking advantage of lagrangian duality. It results in a collection of first-order regularizers acting at different scales. This estimation is non-parametric since the optimal regularization parameters at the different scales are obtained by solving the dual problem. In a second level of inference, the most likely self-similar model given the data is optimally selected by maximization of bayesian evidence. The motion estimator accuracy is first evaluated on a synthetic image sequence of simulated bidimensional turbulence and then on a real meteorological image sequence. Results obtained with the proposed physical based approach exceeds the best state of the art results. Furthermore, selecting from images the most evident multiscale motion model enables the recovery of physical quantities which are of major interest for turbulence characterization

Pressure image assimilation for atmospheric motion estimation

The complexity of dynamical laws governing 3D atmospheric flows associated with incomplete and noisy observations makes the recovery of atmospheric dynamics from satellite images sequences very difficult. In this report, we face the challenging problem of estimating physical sound and time consistent horizontal motion fields at various atmospheric depths for a whole image sequence. Based on a vertical decomposition of the atmosphere, we propose two dynamically consistent atmospheric motion estimators relying on different multi-layer dynamical models. Both estimators use a framework derived from data assimilation and are applied on noisy and incomplete pressure difference observations derived from satellite images. In the first model, dense pressure difference maps are reconstructed according to a shallow-water model on each cloud layer. While performing this reconstruction, the variational process estimates the average horizontal wind fields of the multi-layer model. The second model relies on a simplified vorticity-divergence form of the previous multi-layer shallow-water model. In this case, average horizontal motion fields are estimated for each layer without reconstructing pressure maps. While the simplified model is not as precise as the exact shallow-water model, the latter estimator exploits finer spatio-temporal image structures and succeeds in characterizing motion at smaller spatial scales. The performance of both methods is assessed on synthetic examples and on real world meteorological satellite image sequences

Layered estimation of atmospheric mesoscale dynamics from satellite imagery

International audienceIn this paper, we address the problem of estimating I mesoscale dynamics of atmospheric layers from satellite image sequences. Due to the great deal of spatial and temporal distortions of cloud patterns and because of the sparse 3-D nature of cloud observations, standard dense-motion field-estimation techniques used in computer vision are not well adapted to satellite images. Relying on a physically sound vertical decomposition of the atmosphere into layers, we propose a dense-motion estimator dedicated to the extraction of multilayer horizontal wind fields. This estimator is expressed as the minimization of a global function including data and spatio-temporal smoothness terms. A robust data term relying on the integrated-continuity equation mass-conservation model is proposed to fit sparse-transmittance observations related to each layer. A novel spatio-temporal smoother derived from large eddy prediction of a shallow-water momentum-conservation model is used to build constraints for large-scale temporal coherence. These constraints are combined in a global smoothing framework with a robust second-order smoother, preserving divergent and vorticity structures of the flow. For optimization, a two-stage motion estimation scheme is proposed to overcome multiresolution limitations when capturing the dynamics of mesoscale structures. This alternative approach relies on the combination of correlation and optical-flow observations in a variational context. An exhaustive evaluation of the novel method is first performed on a scalar image sequence generated by direct numerical simulation of a turbulent 2-D flow. By qualitative comparisons, the method is then assessed on a METEOSAT image sequence