Conference Paper

Wavelet-Based Fluid Motion Estimation.

DOI: 10.1007/978-3-642-24785-9_62 Conference: Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 - June 2, 2011, Revised Selected Papers
Source: DBLP

ABSTRACT Based 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.

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    ABSTRACT: Expanding on a wavelet basis the solution of an inverse problem provides several advantages. First of all, wavelet bases yield a natural and efficient multireso-lution analysis which allows defining clear optimization strategies on nested subspaces of the solution space. Be-sides, the continuous representation of the solution with wavelets enables analytical calculation of regularization integrals over the spatial domain. By choosing differen-tiable wavelets, accurate high-order derivative regular-izers can be efficiently designed via the basis's mass and stiffness matrices. More importantly, differential constraints on vector solutions, such as the divergence-free constraint in physics, can be nicely handled with biorthogonal wavelet bases. This paper illustrates these advantages in the particular case of fluid flow motion estimation. Numerical results on synthetic and real im-ages of incompressible turbulence show that divergence-free wavelets and high-order regularizers are particu-larly relevant in this context.
    International Journal of Computer Vision 05/2013; 103(1):80--99. · 3.62 Impact Factor
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    ABSTRACT: Selecting optimal models and hyperparameters is crucial for accurate optical-flow estimation. This paper provides a solution to the problem in a generic Bayesian framework. The method is based on a conditional model linking the image intensity function, the unknown velocity field, hyperparameters, and the prior and likelihood motion models. Inference is performed on each of the three levels of this so-defined hierarchical model by maximization of marginalized a posteriori probability distribution functions. In particular, the first level is used to achieve motion estimation in a classical a posteriori scheme. By marginalizing out the motion variable, the second level enables to infer regularization coefficients and hyperparameters of non-Gaussian M-estimators commonly used in robust statistics. The last level of the hierarchy is used for selection of the likelihood and prior motion models conditioned to the image data. The method is evaluated on image sequences of fluid flows and from the "Middlebury" database. Experiments prove that applying the proposed inference strategy yields better results than manually tuning smoothing parameters or discontinuity preserving cost functions of the state-of-the-art methods.
    IEEE Transactions on Image Processing 12/2011; 21(4):1437-51. · 3.20 Impact Factor

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