Divergence-Free Wavelets and High Order Regularization

Harouna, Souleymane Kadri; Dérian, Pierre; Héas, Patrick; Mémin, Étienne

doi:10.1007/s11263-012-0595-7

Cited by 60 publications

(58 citation statements)

References 23 publications

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“…Horizontal wind at intermediate altitude. From top to bottom, spatial subset of the two input incomplete images, estimated wind field in color representation and divergent-free component obtained by Helmoltz decomposition [20] for the proposed method, divergence-free component given by a second-order regularizer [15] (below). The inferred power-laws parameters are (γ Fig.…”

Section: Discussionmentioning

confidence: 99%

“…so that λ / ∈ D. From this observation, it follows that ∀λ ∈ D, problem (20) has an analytic solution, namely:…”

Section: A a Dual Approach For Constrained Motion Estimationmentioning

confidence: 97%

“…Finally, if a global maximizer does not exist, the dual optimization procedure (20) fails in solving problem (18) since (22) can not be satisfied. We can however find an approximation of the solution.…”

Section: A a Dual Approach For Constrained Motion Estimationmentioning

confidence: 99%

“…7 and compared to recent state of the art approaches 3 . Note that MBA and RMS errors were computed with divergence-free motion components obtained by Helmoltz decomposition [20]. Indeed, this decomposition was used here since a subset of state-of-the-art methods code implicitly an additional divergence-free constraint [20] [37], leading possibly to a bias in the regularization scheme evaluation.…”

Section: Experimental Evaluation a Simulated 2d Turbulencementioning

confidence: 99%

“…For these dense representations, regularization models are commonly used to remove the motion ambiguities and achieve inversion. However, the actual regularizers proposed in the literature are all insufficient since they impose in a small spatial neighborhood a prior smoothness which improperly describes the regularity of turbulent flows [2] [8] [9] [17] [20] [37]. Moreover, going further and assuming a set of proper models is given, choosing the most appropriate one and fixing its hyper-parameters is a tricky problem, which has only been studied for Gaussian models in the optic flow literature.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Estimation of Turbulent Motion

Herzet³

et al. 2013

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-Based on physical laws describing the multi-scale structure of turbulent flows, this article proposes a regularizer for fluid motion estimation from an image sequence. Regularization is achieved by imposing some scale invariance property between histograms of motion increments computed at different scales. By reformulating this problem from a Bayesian perspective, an algorithm is proposed to jointly estimate motion, regularization hyper-parameters, and to select the most likely physical prior among a set of models. Hyper-parameter and model inference is conducted by posterior maximization, obtained by marginalizing out non-Gaussian motion variables. The Bayesian estimator is assessed on several image sequences depicting synthetic and real turbulent fluid flows. Results obtained with the proposed approach exceed the state of the art results in fluid flow estimation.

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Section: Discussionmentioning

confidence: 99%

“…so that λ / ∈ D. From this observation, it follows that ∀λ ∈ D, problem (20) has an analytic solution, namely:…”

Section: A a Dual Approach For Constrained Motion Estimationmentioning

confidence: 97%

Section: A a Dual Approach For Constrained Motion Estimationmentioning

confidence: 99%

Section: Experimental Evaluation a Simulated 2d Turbulencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian Estimation of Turbulent Motion

Herzet³

et al. 2013

IEEE Trans. Pattern Anal. Mach. Intell.

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Physical‐based spatio‐temporal resolution enhancement of scalar data for fluid visualization

Liqun

Chen

2016

Computer Animation & Virtual

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We present a method that improves the spatio‐temporal resolution of original data with fluid scalar data. The basis of the method, velocity estimation, is constructed to be inverse and optimized problem. We reduce the calculation cost through convex optimization and make the velocity field more accurate by coupling with Navier–Stokes equations. The spatial resolution receives significant enhancement by applying advection on original data with higher‐resolution velocity field data generated by our method. The temporal resolution is improved by generating intermediate velocity fields through the solution of Navier–Stokes equations. In this paper, we demonstrate that the accuracy of our velocity estimation method is clearly better than that of optical flow methods and the enhanced data show an attractive performance in fluid visualization. Copyright © 2016 John Wiley & Sons, Ltd.

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Location Uncertainty Principle: Toward the Definition of Parameter-Free Motion Estimators

Cai

Mémin²,

Dérian³

et al. 2018

Lecture Notes in Computer Science

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In this paper, we propose a novel optical flow approach for estimating two-dimensional velocity fields from an image sequence, which depicts the evolution of a passive scalar transported by a fluid flow. The Eulerian fluid flow velocity field is decomposed into two components: a large-scale motion field and a small-scale uncertainty component. We define the small-scale component as a random field. Then the data term of the optical flow formulation is based on a stochastic transport equation, derived from a location uncertainty principle [17]. In addition, a specific regularization term built from the assumption of constant kinetic energy involves the same diffusion tensor as the one appearing in the data transport term. This enables us to devise an optical flow method dedicated to fluid flows in which the regularization parameter has a clear physical interpretation and can be easily estimated. Experimental evaluations are presented on both synthetic and real images. Results indicate very good performance of the proposed parameter-free formulation for turbulent flow motion estimation.

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Divergence-Free Wavelets and High Order Regularization

Cited by 60 publications

References 23 publications

Bayesian Estimation of Turbulent Motion

Bayesian Estimation of Turbulent Motion

Physical‐based spatio‐temporal resolution enhancement of scalar data for fluid visualization

Location Uncertainty Principle: Toward the Definition of Parameter-Free Motion Estimators

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