Wavelets and Optical Flow Motion Estimation

Dérian, Pierre; Héas, Patrick; Herzet, Cédric; Mémin, Étienne

doi:10.4208/nmtma.2013.mssvm07

Cited by 48 publications

(24 citation statements)

References 16 publications

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“…Note that an implicit regularization by polynomial approximation has also been tested. It is a well-known approach in computer vision [4,13,31,50]. The performances were clearly below the previous approaches, so we do not display the results in this paper.…”

Section: Synthetic Image Couple Generationmentioning

confidence: 83%

“…a quasi-Newton method with a line search strategy, subject to the strong Wolf conditions [37]. Moreover, as suggested in [13] we propose to enhance optimization by solving a sequence of nested problems, in which the MAP solution is sequentially sought within higher resolution spaces. More precisely, wavelet coefficients are estimated sequentially from the coarsest scale 2 0 to the finest one 2 −sn .…”

Section: Optimizationmentioning

confidence: 99%

“…Moreover, an additional pleasant feature of wavelet representations is that it is well adapted to the non-convex optimization problem of MAP estimation, since it naturally provides a multi-resolution approach. As a matter of fact, this approach has proved to be experimentally efficient for motion estimation problems (subjected to different priors) [13,25,50]. The optimization algorithms rely on Fast Fourier Transforms (FFT) or on Fast Wavelet Transforms (FWT).…”

mentioning

confidence: 99%

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Self-Similar Prior and Wavelet Bases for Hidden Incompressible Turbulent Motion

Héas¹,

Lavancier²,

Kadri-Harouna³

2014

SIAM J. Imaging Sci.

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Abstract. This work is concerned with the ill-posed inverse problem of estimating turbulent flows from the observation of an image sequence. From a Bayesian perspective, a divergence-free isotropic fractional Brownian motion (fBm) is chosen as a prior model for instantaneous turbulent velocity fields. This self-similar prior characterizes accurately second-order statistics of velocity fields in incompressible isotropic turbulence. Nevertheless, the associated maximum a posteriori involves a fractional Laplacian operator which is delicate to implement in practice. To deal with this issue, we propose to decompose the divergent-free fBm on well-chosen wavelet bases. As a first alternative, we propose to design wavelets as whitening filters. We show that these filters are fractional Laplacian wavelets composed with the Leray projector. As a second alternative, we use a divergence-free wavelet basis, which takes implicitly into account the incompressibility constraint arising from physics. Although the latter decomposition involves correlated wavelet coefficients, we are able to handle this dependence in practice. Based on these two wavelet decompositions, we finally provide effective and efficient algorithms to approach the maximum a posteriori. An intensive numerical evaluation proves the relevance of the proposed wavelet-based self-similar priors.

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Section: Synthetic Image Couple Generationmentioning

confidence: 83%

Section: Optimizationmentioning

confidence: 99%

mentioning

confidence: 99%

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Self-Similar Prior and Wavelet Bases for Hidden Incompressible Turbulent Motion

Héas¹,

Lavancier²,

Kadri-Harouna³

2014

SIAM J. Imaging Sci.

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“…We use a standard limited-memory quasi-Newton optimization scheme [49] to solve this unconstrained minimization problem. As proposed in [9], in order to estimate accurately large displacements, the optimization procedure avoids the heuristic multiresolution optic-flow initialization, and relies instead on wavelet expansions (Coiflets with 10 vanishing moments) of the displacement variable d. An analogous expansion is used to expand the image variable x t1 accordingly. Appendix D.1 details fast evaluation procedures computing the gradient of the log posterior, similar to the one proposed in [15].…”

Section: 4mentioning

confidence: 99%

Uncertainty of Atmospheric Motion Vectors by Sampling Tempered Posterior Distributions

Héas¹,

Cérou²,

Rousset³

2022

Preprint

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Atmospheric motion vectors (AMVs) extracted from satellite imagery are the only wind observations with good global coverage. They are important features for feeding numerical weather prediction (NWP) models. Several Bayesian models have been proposed to estimate AMVs. Although critical for correct assimilation into NWP models, very few methods provide a thorough characterization of the estimation errors. The difficulty of estimating errors stems from the specificity of the posterior distribution, which is both very high dimensional, and highly ill-conditioned due to a singular likelihood, which becomes critical in particular in the case of missing data (unobserved pixels). This work studies the evaluation of the expected error of AMVs using gradient-based Markov Chain Monte Carlo (MCMC) algorithms. Our main contribution is to propose a tempering strategy, which amounts to sampling a local approximation of the joint posterior distribution of AMVs and image variables in the neighborhood of a point estimate. In addition, we provide efficient preconditioning with the covariance related to the prior family itself (fractional Brownian motion), with possibly different hyper-parameters. From a theoretical point of view, we show that under regularity assumptions, the family of tempered posterior distributions converges in distribution as temperature decreases to an optimal Gaussian approximation at a point estimate given by the Maximum A Posteriori (MAP) log-density. From an empirical perspective, we evaluate the proposed approach based on some quantitative Bayesian evaluation criteria. Our numerical simulations performed on synthetic and real meteorological data reveal that the proposed tempering and preconditioning exhibit a significant gain in terms of the accuracy of the AMV point estimates and of their associated expected error estimates, but also a substantial acceleration in the convergence speed of the MCMC algorithms.

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“…ere are several optical flow methods in the literature that have been designed and optimized for divergence-free motions [15]. However, some optical flows use periodic boundary conditions that are not well suited for experimental data [16].…”

Section: Related Workmentioning

confidence: 99%

Hybrid Adaptive Wavelet-Based Optical Flow Algorithm for Background Oriented Schlieren (BOS) Experiments

Zhang

Wei

Liu

et al. 2020

Mathematical Problems in Engineering

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Quantitative analysis of the flow field is an effective method to study hydrodynamics. As a flow field measurement technology, the Background Oriented Schlieren (BOS) is widely used. However, it is difficult to measure the complex transparent flow field (flow field with large refractive index gradient) using the BOS experiment. In order to overcome this difficulty and improve the accuracy of the BOS experiment, this paper presents a hybrid adaptive wavelet-based optical flow algorithm for the BOS. The current algorithm is a combination of the traditional optical flow algorithm and the wavelet-based optical flow algorithm. By adding the initial value constraints, the adaptive scale constraints, and the adaptive regularization constraints, the algorithm can effectively overcome the above-mentioned difficulty and also improve its accuracy. To further illustrate the feasibility of the proposed method, this paper uses the simulation data, the data of the DNS datasets, and the data of the BOS experiment to verify the performance of the algorithm. The experiment of comparing the proposed algorithm with the existing ones is carried out on the DNS datasets and the data of the BOS experiment. Finally, the proposed method is verified by a practical BOS experiment. The results show that the proposed algorithm can effectively improve the measurement accuracy of displacements.

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Wavelets and Optical Flow Motion Estimation

Cited by 48 publications

References 16 publications

Self-Similar Prior and Wavelet Bases for Hidden Incompressible Turbulent Motion

Self-Similar Prior and Wavelet Bases for Hidden Incompressible Turbulent Motion

Uncertainty of Atmospheric Motion Vectors by Sampling Tempered Posterior Distributions

Hybrid Adaptive Wavelet-Based Optical Flow Algorithm for Background Oriented Schlieren (BOS) Experiments

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